exact characteristic equations for some of classical boundary conditions of vibrating moderately thick rectangular plates the dimensionless equations of motion are derived based on the mindlin plate theory to study the transverse vibration of thick rectangular plates without further usage of any approximate method the exact closed form characteristic equations are given within the validity of the mindlin plate theory for plates having two opposite sides simply supported the six distinct cases considered involve all possible combinations of classical boundary conditions at the other two sides of rectangular plates accurate eigenfrequency parameters are presented for a wide range of aspect ratio and thickness ratio for each case the three dimensional deformed mode shapes together with their associated contour plots obtained from the exact closed form eigenfunctions are also presented finally the effect of boundary conditions aspect ratios and thickness ratios on the eigenfrequency parameters and vibratory behavior of each distinct cases are studied in detail it is believed that in the present work the exact closed form characteristic equations and their associated eigenfunctions except for the plates with four edges simply supported for the rest of considered six cases are obtained for the first time

elastoplastic truss design using a displacement based optimization abstract a displacement based optimization dbo method is applied to truss design problems with material nonlinearities to explore feasibility and verify efficiency of the method as compared to traditional structural optimization minimum weight truss sizing problems with various path independent elastoplastic laws including elastic perfectly plastic linear strain hardening and ramberg osgood models are investigated this type of material nonlinearity allows us to naturally extend the linear elastic truss sizing in the dbo setting to nonlinear problems to implement the methodology a computer program that uses the commercially available optimizer dot by vr d and imsl linear programming solver by visual numerics is developed several test problems are successfully solved using the dbo approach and solutions are compared to those available in the literature demonstrating significant reduction of computational time in comparison to the traditional structural optimization method in particular the dbo approach is found to be suitable for truss topology design since the method allows member areas to have cross sectional areas equal to zero exactly

direct adaptive controller for nonaffine nonlinear systems using self structuring neural networks a direct adaptive state feedback controller is proposed for highly nonlinear systems we consider uncertain or ill defined nonaffine nonlinear systems and employ a neural network nn with flexible structure i e an online variation of the number of neurons the nn approximates and adaptively cancels an unknown plant nonlinearity a control law and adaptive laws for the weights in the hidden layer and output layer of the nn are established so that the whole closed loop system is stable in the sense of lyapunov moreover the tracking error is guaranteed to be uniformly asymptotically stable uas rather than uniformly ultimately bounded uub with the aid of an additional robustifying control term the proposed control algorithm is relatively simple and requires no restrictive conditions on the design constants for the stability the efficiency of the proposed scheme is shown through the simulation of a simple nonaffine nonlinear system

solution of the poisson equation by differential quadrature the method of differential quadrature is demonstrated by solving the two dimensional poisson equation the results for three test problems are compared with the exact analytical solutions and the numerical solutions obtained by others for the galerkin the control volume and the five point finite difference methods the method of differential quadrature leads to more accurate results for comparable levels of computational effort

vibrations of axially moving viscoelastic plate with parabolically varying thickness based on the two dimensional viscoelastic differential constitutive relation the differential equation of motion of the axially moving viscoelastic rectangular plate constituted by the kelvin voigt model with parabolically varying thickness in the y direction is derived the dimensionless complex frequencies of axially moving viscoelastic plate with different boundary conditions versus the dimensionless moving speed for various aspect ratio thickness parameter and the dimensionless delay time are analyzed by the differential quadrature method the effects of various parameters such as aspect ratio thickness parameter the dimensionless moving speed and the dimensionless delay time on the vibration characteristics of the axially moving viscoelastic rectangular plate with parabolically varying thickness are discussed

a differential quadrature procedure for three dimensional buckling analysis of rectangular plates abstract this paper presents an application of the differential quadrature dq method for three dimensional buckling analysis of rectangular plates the governing equations of the plate model are first presented in terms of displacement stress displacement relationship and boundary conditions with three dimensional flexibility these equations are then normalised and discretised using the dq procedure example problems pertaining to the buckling of rectangular plates with generic boundary conditions are selected to illustrate the efficiency and simplicity of implementing the dq procedure the convergence characteristics of the method are first conducted based on numerical studies the dq solutions are then compared where possible with exact or approximate solutions it is found that the differential quadrature method yields accurate results for the plate problems under the current investigation in addition to the above some parametric studies are carried out by varying the plates aspect ratio boundary conditions and thickness to width ratio under axial and biaxial loading

ergodic primal convergence in dual subgradient schemes for convex programming lagrangean dualization and subgradient optimization techniques are frequently used within the field of computational optimization for finding approximate solutions to large structured optimization prob lems the dual subgradient scheme does not automatically produce primal feasible solutions there is an abundance of techniques for computing such solutions via penalty functions tangential approximation schemes or the solution of auxiliary primal programs all of which require a fair amount of computational effort we consider a subgradient optimization scheme applied to a lagrangean dual formulation of a convex program and construct at minor cost an ergodic sequence of subproblem solutions which converges to the primal solution set numerical experiments performed on a traffic equilibrium assignment problem under road pricing show that the computation of the ergodic sequence results in a considerable improvement in the quality of the primal solutions obtained compared to those generated in the basic subgradient scheme

modeling via differential quadrature method three dimensional solutions for rectangular plates this paper presents the formulation and numerical analysis of the three dimensional plate model using the differential quadrature dq method the equilibrium equations stress displacement relations and boundary conditions for the three dimensional plate model are first presented these equations are then normalised and discretised using the dq procedure example problems for rectangular plates with generic boundary conditions are selected to illustrate the computational efficiency and applicability of the dq procedure the convergence characteristics of the method are first conducted based on numerical studies the solutions are then compared where possible with the analytical or exact solutions it is found that the differential quadrature method yields accurate results for the plate problems under the current investigation

three dimensional free vibrations of thick skewed cantilevered plates abstract the natural frequencies of skewed cantilevered thick plates are determined by using the ritz method the present work is the first known three dimensional study of the problem assumed displacement functions are in the form of algebraic polynomials which satisfy the fixed face conditions exactly and which are mathematically complete accurate natural frequencies are calculated for skewed thick plates having arbitrary degrees of skewness detailed numerical studies reveal interesting trends concerning the variation of frequencies with increasing skew angle results obtained by using the present method are compared with those obtained by using three dimensional finite elements

a variable kinematic ritz formulation for vibration study of quadrilateral plates with arbitrary thickness a new variable kinematic ritz method applied to free vibration analysis of arbitrary quadrilateral thin and thick isotropic plates is presented carrera s unified formulation and the versatile pb 2 ritz method are properly combined to build a powerful yet simple modeling and solution framework the proposed technique allows to generate arbitrarily accurate ritz solutions from a large variety of refined two dimensional plate theories by expanding so called ritz fundamental nuclei of the plate mass and stiffness matrices theoretical development of the present methodology is described in detail convergence and accuracy of the method are examined through several examples on thin moderately thick and very thick plates of rectangular skew trapezoidal and general quadrilateral shapes with an arbitrary combination of clamped free and simply supported edges present results are compared with existing three dimensional solutions from open literature maximum and average differences of various higher order plate theories and three dimensional results are also presented with the aim of providing useful guidelines on the choice of appropriate plate theory to get a desired accuracy on frequency parameters

an eight node curvilinear differential quadrature formulation for reissner mindlin plates a first endeavour to exploit the differential quadrature dq method as a simple accurate and efficient numerical technique for the bending of quadrilateral reissner mindlin plates with curvilinear boundaries is made the curvilinear quadrilateral is mapped onto a square domain by using the geometric coordinate transformation this geometric mapping technique is employed to transform the governing differential equations and boundary conditions of the problem from the physical domain onto the computational domain the dq procedures are then applied to discretise the transformed set of differential equations and boundary conditions into a set of linear algebraic equations the numerical solutions to the problem are obtained by solving this set of linear algebraic equations examples illustrating the accuracy and convergence of the dq method for reissner mindlin plates with curvilinear boundaries are presented the great development potential of the dq method as an alternative to other approximate techniques for solving problems related to engineering sciences and structural mechanics is exploited in the present study

topology optimization of sheets in contact by a subgradient method we consider the solution of finite element discretized optimum sheet problems by an iterative algorithm the problem is that of maximizing the stiffness of a sheet subject to constraints on the admissible designs and unilateral contact conditions on the displacements the model allows for zero design volumes and thus constitutes a true topology optimization problem we propose and evaluate a subgradient optimization algorithm for a reformulation into a non differentiable convex minimization problem in the displacement variables the convergence of the method and its low computational complexity are established an optimal design is derived through a simple averaging scheme which combines the solutions to the linear design problems solved within the subgradient method to illustrate the efficiency of the algorithm and investigate the properties of the optimal designs thealgorithm is numerically tested on some medium and large scale problems 1997 by john wiley sons ltd

first and second order methods for semidefinite programming in this paper we survey the most recent methods that have been developed for the solution of semidefinite programs we first concentrate on the methods that have been primarily motivated by the interior point ip algorithms for linear programming putting special emphasis in the class of primal dual path following algorithms we also survey methods that have been developed for solving large scale sdp problems these include first order nonlinear programming nlp methods and more specialized path following ip methods which use the preconditioned conjugate gradient or residual scheme to compute the newton direction and the notion of matrix completion to exploit data sparsity

online adaptive fuzzy neural identification and control of a class of mimo nonlinear systems this paper presents a robust adaptive fuzzy neural controller afnc suitable for identification and control of a class of uncertain multiple input multiple output mimo nonlinear systems the proposed controller has the following salient features 1 self organizing fuzzy neural structure i e fuzzy control rules can be generated or deleted automatically 2 online learning ability of uncertain mimo nonlinear systems 3 fast learning speed 4 fast convergence of tracking errors 5 adaptive control where structure and parameters of the afnc can be self adaptive in the presence of disturbances to maintain high control performance 6 robust control where global stability of the system is established using the lyapunov approach simulation studies on an inverted pendulum and a two link robot manipulator show that the performance of the proposed controller is superior

analytical three dimensional elasticity solutions to some plate problems and some observations on mindlin s plate theory abstract solutions are obtained using the exact three dimensional theory of elasticity to i the eigenvalue problem or buckling under biaxial compression or the free lateral vibration of a simply supported rectangular plate with orthotropic stress strain properties and ii the static response of the same plate to a lateral load that varies sinusoidally in two directions the eigenvalue in problem i and the lateral deflections of both the surface and middle plane of the plate as well as the bending strains in problem ii are obtained in the form of series expansions in even powers of the plate thickness exact algebraic expressions are presented for the first two coefficients in the case of orthotropic plates additional coefficients can be obtained if required and are given for the much simpler case of isotropic plates in all cases the first term agrees with classical plate theory the solutions are compared with those obtained from mindlin s plate theory in neither problem is it found to be possible in general to choose values for mindlin s effective shear moduli to make the mindlin solution agree with the first two terms of the exact solution there are however two exceptions to this namely a restricted class of orthotropic materials embracing all isotropic ones in which the elastic constants satisfy a certain condition and the case of cylindrical bending when the mindlin plate reduces to a timoshenko beam of wide rectangular cross section in both these exceptional cases appropriate values for the effective shear moduli are obtained

three dimensional vibration analysis of a cantilevered parallelepiped exact and approximate solutions the paper investigates the hypothetical assumption of neglecting transverse normal stress in vibration analysis for cantilevered thick plates and rectangular parallelepiped the analysis solves the three dimensional elasticity energy functional including as well as excluding transverse normal stress and obtains free vibration solutions for a cantilevered parallelepiped although it is widely accepted the omission of transverse normal stress is well justified in kirchhoff love thin plate theory and higher order thick plate models the transverse normal stress effects and thickness extent to which the thick plate models apply as the thickness increases are practically unknown the inconsistency of assuming constant transverse normal displacement through thickness for thick plate models is also addressed the paper concludes that for a rectangular parallelepiped with thickness exceeding a certain limit there is considerable discrepancy if transverse normal stress is neglected

a study on the linear elastic stability of mindlin plates the debate on the performance of lagrangian and serendipity elements in mindlin s plate theory has been going on for quite some time limited published results for static and vibration analysis based on exact integration demonstrated a drastic deterioration in accuracy as the thickness of the plate decreases and reduced selective integration schemes have been suggested to improve their performance appreciable improvement for lagrangian elements has been recorded but it is only marginal for the serendipity elements on the strength of such observations one would then be tempted to rule out the exact integration schemes and serendipity elements in this paper the above problem is reviewed for stability analysis of plates two elements are chosen from each family one representing the higher order and the other the lower order element contrary to published results all elements can attain very accurate solutions independent of the integration schemes for a sufficiently restrained plate although in general the serendipity elements will require a more refined mesh than the lagrangian ones however for loosely restrained plates the solution failed when integration is performed by reduced selective schemes the failure marks the limitation of the reduced selective schemes which have somehow introduced spurious modes into the system but on the other hand it is ironical that these spurious modes in fact contribute to the improvement of performance of the restrained cases therefore one can equally improve the serendipity elements by a selective scheme which can introduce additional zero modes a scheme based on 5 5 integration points for flexural stiffness and 3 3 integration points for shear stiffness improved the 17se serendipity elements remarkably however because of the lack of bounds in most cases the use of reduced selected schemes is still not recommended finally this paper also proposed an approximate formulation of the geometric stiffness matrices to replace the full formulation such an approximate formulation reduces the number of variables considerably in the eigenvalue search and can still give reasonably accurate results for thin plates with a t 15

comparative accuracy of dq and hdq methods for three dimensional vibration analysis of rectangular plates an accuracy study between the differential quadrature dq and harmonic differential quadrature hdq methods for three dimensional elasticity solutions of free vibration of rectangular plates is carried out the solution capability of the dq and hdq methods is first studied then the numerical performance of both the methods is compared it is found that the dq method displays more superior convergence characteristics over the hdq method for the lower modes of vibration however the hdq method is advantageous over the dq method for computing higher modes of vibration it is also discovered that the dq and hdq methods produce better convergent solutions than the finite element method fem when a similar number of discrete points nodes are used copyright 1999 john wiley sons ltd

robust truss topology design via semidefinite programming we present and motivate a new model of the truss topology design problem where the rigidity of the resulting truss with respect both to given loading scenarios and small occasional loads is optimized it is shown that the resulting optimization problem is a semidefinite program we derive and analyze several equivalent reformulations of the problem and present illustrative numerical examples

three dimensional vibration analysis of thick rectangular plates using chebyshev polynomial and ritz method this paper describes a method for free vibration analysis of rectangular plates with any thicknesses which range from thin moderately thick to very thick plates it utilises admissible functions comprising the chebyshev polynomials multiplied by a boundary function the analysis is based on a linear small strain three dimensional elasticity theory the proposed technique yields very accurate natural frequencies and mode shapes of rectangular plates with arbitrary boundary conditions a very simple and general programme has been compiled for the purpose for a plate with geometric symmetry the vibration modes can be classified into symmetric and antisymmetric ones in that direction in such a case the computational cost can be greatly reduced while maintaining the same level of accuracy convergence studies and comparison have been carried out taking square plates with four simply supported edges as examples it is shown that the present method enables rapid convergence stable numerical operation and very high computational accuracy parametric investigations on the vibration behaviour of rectangular plates with four clamped edges have also been performed in detail with respect to different thickness side ratios aspect ratios and poissons ratios these results may serve as benchmark solutions for validating approximate two dimensional theories and new computational techniques in future 2002 elsevier science ltd all rights reserved

three dimensional elasticity solutions to some orthotropic plate problems abstract this paper presents a three dimensional analysis of rectangular orthotropic plates by employing the differential quadrature dq method the derivation of the governing equations from the governing equations and the stress strain relationship of the three dimensional elasticity model is detailed the constrained conditions of the orthotropic plate edges are given the governing equations and boundary conditions are first normalized and discretized according to the dq procedure example problems pertaining to the bending buckling and free vibration of orthotropic plates with generic boundary conditions are selected to illustrate the simplicity and applicability of the dq method the convergence characteristics of the dq method are first obtained based on numerical studies after which the dq solutions are compared where possible with exact solutions it is found that the dq method yields accurate results for the plate problems under investigation

three dimensional vibration analysis of rectangular thick plates on pasternak foundation the free vibration characteristics of rectangular thick plates resting on elastic foundations have been studied based on the three dimensional linear and small strain elasticity theory the foundation is described by the pasternak two parameter model the ritz method is used to derive the eigenvalue equation of the rectangular plate by augmenting the strain energy of the plate with the potential energy of the elastic foundation the chebyshev polynomials multiplied by a boundary function are selected as the admissible functions of the displacement functions in each direction the approach is suitable for rectangular plates with arbitrary boundary conditions convergence and comparison studies have been performed on square plates on elastic foundations with different boundary conditions it is shown that the present method has a rapid convergent rate stable numerical operation and very high accuracy parametric investigations on the dynamic behaviour of clamped square thick plates on elastic foundations have been carried out in detail with respect to different thickness span ratios and foundation parameters some results found for the first time have been given and some important conclusions have been drawn

differential quadrature method based on the highest derivative and its applications the numerical differentiation is often used when dealing with the differential equations using the numerical differentiation the differential equations can be transformed into algebraic equations then we can get the numerical solution from the algebraic equations but the numerical differentiation process is very sensitive to even a small level of errors in contrast it is expected that on average the numerical integration process is much less sensitive to errors in this paper we provide a new method using the dq method based on the interpolation of the highest derivative dqihd for the differential equations the original function is then obtained by integration in this paper the dqihd method was applied to the buckling analysis of thin isotropic plates and winkler plates the numerical results agree well with the analytic solutions and the results show that our method is of high accuracy of good convergence with little computational efforts and it is easy to deal with the boundary conditions

numerical aspects for free vibration of thick plates part i formulation and verification abstract this paper investigates the numerical aspects for free vibration analysis of a class of thick relative thickness ratio t b 0 2 shear deformable rectangular plates with all possible combinations of edge conditions these thick plate vibration frequencies most probably cannot be accurately determined using the classical thin plate theory or the mindlin plate theory the effect of transverse shear strain has been considered by using a higher order plate theory without the need for a shear correction factor unlike some domain discretization methods this analysis assumes a single global element for the entire plate the strain and kinetic energy integrals of the global plate element are formulated and the energy functional is minimized to yield the natural frequencies a set of boundary compliant admissible shape functions is developed to obtain solutions which are unattainable using the classical trigonometric admissible functions the numerical efficiency of symmetry classification is investigated and on certain computational platforms more than 80 of the execution time can be saved while maintaining the same level of accuracy

a new method for optimal truss topology design truss topology optimization formulated in terms of displacements and bar volumes results in a large nonconvex optimization problem for the case of maximization of stiffness for a prescribed volume this paper presents a new equivalent an unconstrained and convex minimization problem in displacements only where the function to be minimized is the sum of terms each of which is the maximum of two convex quadratic functions existence of solutions is proved as is the convergence of a nonsmooth steepest descent type algorithm for solving the topology optimization problem the algorithm is computationally attractive and has been tested on a large number of examples some of which are presented

free vibration of thick layered rectangular plates with point supports by finite layer method in this paper the free vibration of thick isotropic and laminated composite rectangular plates with point supports is analyzed by the finite layer method a new set of two dimensional basic functions which satisfies the kinematic boundary conditions at the edges of the plate and the zero displacement conditions at point supports is developed to describe the variation of three dimensional displacements in the plane of a thin finite layer one dimensional linear or quadratic shape functions are adopted to describe the variation of the displacements through the thickness layer the governing eigenvalue equation of the plate is derived via the conventional displacement method numerical results for the three dimensional vibration of rectangular plates with point supports are presented herein for the first time the eigenfrequencies of simply supported rectangular plates with a central point support are studied in detail by considering the variations of aspect ratio side to thickness ratio properties of materials number of laminates and stacking sequences comparison with known thin plate and mindlin plate solutions is carried out to verify the applicability and accuracy of the proposed method

an optimization problem for predicting the maximal effect of degradation of mechanical structures this paper deals with a nonlinear nonconvex optimization problem that models prediction of degradation in discrete or discretized mechanical structures the mathematical difficulty lies in equality constraints of the form sum m i 1 frac 1 y i a i x b where ai are symmetric and positive semidefinite matrices b is a vector and x y are the vectors of unknowns the linear objective function to be maximized is x y mapsto b tx in a first step we investigate the problem properties such as existence of solutions and the differentiability of related marginal functions as a by product this gives insight in terms of a mechanical interpretation of the optimization problem we derive an equivalent convex problem formulation and a convex dual problem and for dyadic matrices ai a quadratic programming problem formulation is developed a nontrivial numerical example is included based on the latter formulation

free vibration analysis of three dimensional solids by bem in practical applications it is often necessary to determine the natural frequencies and mode shapes of a solid in addition to the static response under a variety of loading conditions this paper discusses the calculation of natural frequencies and mode shapes of three dimensional solids using the boundary element method the method developed is based on the use of particular integrals of the elastic equilibrium equations and employs only real arithmetic it represents an extension to three dimensions of work previously carried out for two dimensional problems in references 1 and 15 the method has been incorporated for multiregion analysis in the best3d boundary element solution technology three dimensional computer program 11 results of the boundary element calculations are compared with analytical finite element and experimental results

a nonlinear control method based on anfis and multiple models for a class of siso nonlinear systems and its application this paper presents a novel nonlinear control strategy for a class of uncertain single input and single output discrete time nonlinear systems with unstable zero dynamics the proposed method combines adaptive network based fuzzy inference system anfis with multiple models where a linear robust controller an anfis based nonlinear controller and a switching mechanism are integrated using multiple models technique it has been shown that the linear controller can ensure the boundedness of the input and output signals and the nonlinear controller can improve the dynamic performance of the closed loop system moreover it has also been shown that the use of the switching mechanism can simultaneously guarantee the closed loop stability and improve its performance as a result the controller has the following three outstanding features compared with existing control strategies first this method relaxes the assumption of commonly used uniform boundedness on the unmodeled dynamics and thus enhances its applicability second since anfis is used to estimate and compensate the effect caused by the unmodeled dynamics the convergence rate of neural network learning has been increased third a one to one mapping technique is adapted to guarantee the universal approximation property of anfis the proposed controller is applied to a numerical example and a pulverizing process of an alumina sintering system respectively where its effectiveness has been justified

observer based direct adaptive fuzzy neural control for nonaffine nonlinear systems in this paper an observer based direct adaptive fuzzy neural control scheme is presented for nonaffine nonlinear systems in the presence of unknown structure of nonlinearities a direct adaptive fuzzy neural controller and a class of generalized nonlinear systems which are called nonaffine nonlinear systems are instead of the indirect one and affine nonlinear systems given by leu et al by using implicit function theorem and taylor series expansion the observer based control law and the weight update law of the fuzzy neural controller are derived for the nonaffine nonlinear systems based on strictly positive real spr lyapunov theory the stability of the closed loop system can be verified moreover the overall adaptive scheme guarantees that all signals involved are bounded and the output of the closed loop system will asymptotically track the desired output trajectory to demonstrate the effectiveness of the proposed method simulation results are illustrated in this paper

the problem of plate modeling theoretical and computational results abstract the paper analyzes in detail the problem of various plate models properties of their solution and the question how well these models approximate the three dimensional formulation the boundary layer and corner singularities of the solution are analyzed a hierarchy of the models converging to the three dimensional solution is constructed the detailed numerical computations show various basic aspects of plate modeling in a concrete setting

analytical 3 d p element for quadrilateral plates part 1 thick isotropic plate structures an analytical three dimensional 3 d p version element for the vibration analysis of arbitrary quadrilateral thick plates is presented with the additional hierarchical shape functions and analytically integrated element matrices the computed accuracy is considerably improved the computed natural frequencies of cantilever and simply supported square plates show that the convergence rate of the present element is very fast with respect to the number of hierarchical terms and it can predict very accurate modes the element is applicable to the free vibration analysis of quadrilateral polygonal plates as well as 3 d space structures the continuous wavelet transform cwt is applied for the identification of damping ratios based on the rayleigh damping model the damped vibration response is obtained a simple experiment is performed to verify the predicted vibration responses the results show that the proposed element is also efficient for the vibration response analysis of plates

3 d vibration analysis of generalized super elliptical plates using chebyshev ritz method the three dimensional free vibration of generalized super elliptical plates is analysed based on the exact small strain and linear elasticity theory the ritz method is applied to derive the frequency equation the triplicate chebyshev polynomial series form the backbones of the admissible functions as modified by a characteristic boundary function to ensure the satisfaction of geometric boundary conditions of the plate utilizing the symmetry of the plate under consideration eight distinct vibration modes can be classified and individually solved while maintaining the same level of accuracy the accuracy of the present method has been examined by the convergence and comparison studies the effect of geometric parameters on vibration behaviour of the generalized super elliptical plates with free and fixed perimeters have been studied for different powers thickness ratios and aspect ratios

self organizing adaptive fuzzy neural control for a class of nonlinear systems this paper proposes a self organizing adaptive fuzzy neural control safnc via sliding mode approach for a class of nonlinear systems the proposed safnc system is comprised of a computation controller and a supervisory controller the computation controller including a self organizing fuzzy neural network sofnn identifier is the principal controller the sofnn identifier is used to online estimate the controlled system dynamics with the structure and parameter learning phases of fuzzy neural network fnn simultaneously the structure learning phase possesses the ability of online generation and elimination of fuzzy rules to achieve optimal neural structure and the parameter learning phase adjusts the interconnection weights of neural network to achieve favorable approximation performance the supervisory controller is used to achieve the l2 norm bound tracking performance with a desired attenuation level moreover all the parameter learning algorithms are derived based on lyapunov function candidate thus the system stability can be guaranteed finally simulation results show that the safnc can achieve favorable tracking performances

applications of second order cone programming in a second order cone program socp a linear function is minimized over the intersection of an affine set and the product of second order quadratic cones socps are nonlinear convex problems that include linear and convex quadratic programs as special cases but are less general than semidefinite programs sdps several efficient primaldual interior point methods for socp have been developed in the last few years after reviewing the basic theory of socps we describe general families of problems that tan be recast as socps these include robust linear programming and robust leastsquares problems problems involving sums or maxima of norms or with convex hyperbolic constraints we discuss a variety of engineering applications such as filter design antenna array weight design truss design and grasping forte optimization in robotics we describe an efficient primaldual interior point method for solving socps which shares many of the features of primaldual interior point methods for linear program

on the three dimensional vibrations of the cantilevered rectangular parallelepiped a solution is presented for the three dimensional problem of determining the free vibration frequencies and mode shapes for a rectangular parallelepiped which is completely fixed on one face and free on the other five faces this problem apparently is previously unsolved in the published literature the ritz method is used with displacements assumed in the form of algebraic polynomials convergence is studied numerical results are given for the first five frequencies of each of the four symmetry classes of vibration for five thick parallelepiped configurations including the cube contour plots are exhibited for the modal displacements of the cube the effects of varying poisson s ratio are also observed

three dimensional vibration of rectangular plates variance of simple support conditions and influence of in plane inertia plate models developed on the basis of the three dimensional elasticity theory are crucial to the correct solutions in dynamics problems in a three dimensional setting there exist numerous possible definitions of boundary conditions this paper attempts to identify the variance of three dimensional simple support conditions existing in practice the hard simple support condition assumes vanishing normal stresses at the edges and zero transverse and tangential displacement at the peripheries the soft simple support on the other hand imposes zero transverse displacement with vanishing normal and shear stresses at the boundaries to quantify the relative effects of each boundary condition on the vibratory responses of thick plates a global three dimensional ritz formulation is employed for analysis this technique uses sets of finite polynomial series in cartesian co ordinates to approximate the global normal mode variations of the plate these separable one dimensional polynomials are orthogonally generated within the plate domain such that all the essential edge conditions are identically satisfied the accuracy of the proposed three dimensional ritz method is assured from the convergence and comparison studies numerical experiments have been conducted to study firstly the effects of geometric parameters on the overall normal mode characteristics of simply supported plates and secondly the effects of in plane inertia on the vibration frequencies of plates with different thicknesses the three dimensional deformed mode shapes for selected cases have also been computed these have served to describe more vividly the normal mode characteristics of different types of simply supported rectangular plates

application of differential quadrature to transport processes the methodology and numerical solution of problems concerning transport processes via the method of differential quadrature are presented application of the method is demonstrated by solving a simple one dimensional time dependent transient diffusion process involving an irreversible reaction without any flux across the end boundary in addition the same technique is used for the first time to the authors knowledge to solve a steady state problem for this purpose a convection diffusion problem involving an irreversible reaction is considered the demonstration is carried out in two ways 1 using the bellman et al technique which employs approximation formulas for higher order partial derivatives derived by iterating the linear quadrature approximation for the first order partial derivative and 2 using individual quadratures to approximate the partial derivatives of first as well as higher orders as suggested by mingle both approaches give the same results however the latter saves an appreciable amount of iterative computing effort despite the fact that it requires separate weighting coefficients for each individual quadrature since the technique of differential quadrature can produce solutions with sufficient accuracy even when using as few as three discrete points both the programming task and computational effort are alleviated considerably for these reasons the differential quadrature approach appears to be very practical in solving a variety of problems related to transport phenomena

vibration and stability of an initially stressed thick plate according to a high order deformation theory in this paper the average stress method is used to derive the governing equation for a thick rectangular plate according to a high order deformation theory the applied load is taken to be a combination of a pure bending stress plus an extensional stress in the plane of the plate the buckling loads and natural frequencies of simply supported plates are also investigated present results based on high order theory are compared with the results of brunelle s theory and reddy s theory in addition the effects of various parameters on the natural frequencies are studied more accurate results can be obtained by using the present theory than those of the other theories

adaptive asymmetric fuzzy neural network controller design via network structuring adaptation this paper proposes a self structuring fuzzy neural network sfnn using asymmetric gaussian membership functions in the structure and parameter learning phases an adaptive self structuring asymmetric fuzzy neural network control asafnc system which consists of an sfnn controller and a robust controller is proposed the sfnn controller uses an sfnn with structure and parameter learning phases to online mimic an ideal controller simultaneously the structure learning phase consists of the growing and pruning algorithms of fuzzy rules to achieve an optimal network structure and the parameter learning phase adjusts the interconnection weights of neural network to achieve favorable approximation performance the robust controller is designed to compensate for the modeling error between the sfnn controller and the ideal controller an online training methodology is developed in the lyapunov sense and thus the stability of the closed loop control system can be guaranteed finally the proposed asafnc system is applied to a second order chaotic dynamics system the simulation results show that the proposed asafnc can achieve favorable tracking performance

static analysis of thick rectangular laminated plates three dimensional elasticity solutions via differential quadrature element method this article presents the first endeavor to develop the differential quadrature element method for static solution of three dimensional elasticity equations of thick rectangular laminated composite plates the domain decomposition technique is employed to decompose a laminated plate into elements according to material layers the differential quadrature dq method is then applied to each element where the material properties are continuous to form the element weighting coefficient matrix and element force vector the discretized element weighting coefficient matrices and element force vectors are assembled together to form the global weighting coefficient matrix and global force vector for the whole plate using connection conditions the solution for the entire plate is obtained by solving the final algebraic equation system detailed formulations and numerical procedures are presented and the convergence characteristics of the method are investigated the numerical results are then compared where possible with the analytical solutions to verify the present solutions consequently some new numerical results are computed and analyzed using the present numerical method for laminated rectangular plates with different boundary conditions which are not solvable directly by the global dq method

three dimensional vibration of rectangular plates effects of thickness and edge constraints abstract a continuum three dimensional ritz formulation is presented for the free vibration analysis of homogeneous isotropic thick rectangular plates the method is applied specifically to investigate the effects of boundary constraints and thickness ratios on the vibration responses of these plates a general switching of transverse vibratory motions to surface parallel modes at the higher thickness ratio is manifested vividly through three dimensional deformed mode shape plots the present formulation is based on the linear three dimensional small strain elasticity energy principle in the solution process sets of self generating polynomial shape functions are used to derive the governing eigenvalue equation in essence these functions comprise a class of orthogonal polynomial functions and a basic function which is chosen to satisfy the essential geometric boundary conditions at the outset they are found very suitable for the computationally intensive task of 3 d modelling due to the ease of generation and numerical implementation several numerical examples have been computed to demonstrate the accuracy and efficiency of the method the influences of plate thickness and boundary constraints on the overall vibratory characteristics of thick plates are also discussed in detail

design of planar articulated mechanisms using branch and bound this paper considers an optimization model and a solution method for the design of two dimensional mechanical mechanisms the mechanism design problem is modeled as a nonconvex mixed integer program which allows the optimal topology and geometry of the mechanism to be determined simultaneously the underlying mechanical analysis model is based on a truss representation allowing for large displacements for mechanisms undergoing large displacements elastic stability is of major concern we derive conditions modeled by nonlinear matrix inequalities which guarantee that a stable equilibrium is found and that buckling is prevented the feasible set of the design problem is described by nonlinear differentiable and non differentiable constraints as well as nonlinear matrix inequalities to solve the mechanism design problem a branch and bound method based on convex relaxations is developed to guarantee convergence of the method two different types of convex relaxations are derived the relaxations are strengthened by adding valid inequalities to the feasible set and by solving bound contraction sub problems encouraging computational results indicate that the branch and bound method can reliably solve mechanism design problems of realistic size to global optimality

3 d theory versus 2 d approximate theory of free orthotropic isotropic plate and shell vibrations part 1 derivation of governing equations in part 1 of the paper the basic assumptions of the shells with added masses considered are introduced they serve for a derivation of the governing equations which are analyzed in part 2 of the paper

a neuro fuzzy system modeling with self constructing rule generationand hybrid svd based learning we propose an approach for neuro fuzzy system modeling a neuro fuzzy system for a given set of input output data is obtained in two steps first the data set is partitioned automatically into a set of clusters based on input similarity and output similarity tests membership functions associated with each cluster are defined according to statistical means and variances of the data points included in the cluster then a fuzzy if then rule is extracted from each cluster to form a fuzzy rule base second a fuzzy neural network is constructed accordingly and parameters are refined to increase the precision of the fuzzy rule base to decrease the size of the search space and to speed up the convergence we develop a hybrid learning algorithm which combines a recursive singular value decomposition based least squares estimator and the gradient descent method the proposed approach has advantages of determining the number of rules automatically and matching membership functions closely with the real distribution of the training data points besides it learns faster consumes less memory and produces lower approximation errors than other methods

three dimensional elasticity solutions for free vibrations of rectangular plates by the differential quadrature method this paper presents accurate three dimensional elasticity solutions for free vibrations of six types of plates having free lateral surfaces two opposite sides simply supported and two other sides having combinations of simply supported clamped and free boundary conditions the solution methodology adopted in the present work first reduces the spatial variables in the governing elasticity equations to two by using displacement functions in the forms which satisfy the boundary conditions of the assumed simply supported sides the eigenvalue equations are then formulated from the reduced governing equations and the boundary conditions via the differential quadrature method the numerical results include the first nine natural frequencies of the six plate configurations for combinations of three aspect ratios and two thickness ratios these results are supported by appropriate convergence studies and comparisons with the results of other authors

two new approximate methods for analyzing free vibration of structural components two approximate methods which have not previously been used for structural dynamics problems are applied to the free vibration analysis of various structural components the first method is a new version of the complementary energy method it is shown to be considerably more accurate than the conventional rayleigh and rayleigh schmidt methods when applied to spatially one dimensional free vibration problems prismatic and tapered bars prismatic beams and axisymmetric motion of circular membranes the second method is the differential quadrature method introduced by bellman and his associates it is applied successfully here to all of the problems mentioned plus square membranes and circular and square plates

a fast approach for automatic generation of fuzzy rules by generalized dynamic fuzzy neural networks a fast approach for automatically generating fuzzy rules from sample patterns using generalized dynamic fuzzy neural networks gd fnns is presented the gd fnn is built based on ellipsoidal basis functions and functionally is equivalent to a takagi sugeno kang fuzzy system the salient characteristics of the gd fnn are 1 structure identification and parameters estimation are performed automatically and simultaneously without partitioning input space and selecting initial parameters a priori 2 fuzzy rules can be recruited or deleted dynamically 3 fuzzy rules can be generated quickly without resorting to the backpropagation bp iteration learning a common approach adopted by many existing methods the gd fnn is employed in a wide range of applications ranging from static function approximation and nonlinear system identification to time varying drug delivery system and multilink robot control simulation results demonstrate that a compact and high performance fuzzy rule base can be constructed comprehensive comparisons with other latest approaches show that the proposed approach is superior in terms of learning efficiency and performance

a continuum three dimensional vibration analysis of thick rectangular plates abstract this paper presents a continuum three dimensional ritz formulation for the vibration analysis of homogeneous thick rectangular plates with arbitrary combinations of boundary constraints this model is formulated on the basis of the linear three dimensional small deformation elasticity theory to predict the vibratory responses of these thick rectangular plates the displacement fields in the transverse and in plane directions are expressed by sets of orthogonally generated polynomial functions these shape functions are intrinsically a product of a class of orthogonal polynomial functions and a basic function which are chosen to satisfy the essential geometric boundary conditions at the outset sets of frequency data for plates with various aspect ratios and thickness ratios have been presented these data are used to examine the merits and limitations of the classical plate theory and mindlin plate theory by direct comparisons finally using the three dimensional continuum approach sets of first known deformed mode shapes have been generated thus helping to understand the vibratory motion furthermore these results may also serve as the benchmark to further research into the refined plate theories

modal analysis of cantilever plates undergoing accelerated in plane motion a modeling method for the modal analysis of cantilever plates undergoing accelerated in plane motion is presented in this paper von karman strain measures are employed to derive the in plane and the lateral equations of motion in plane strain measures of the accelerated plates are obtained from the in plane equations and substituted into the lateral equations to obtain the linear equations for modal analysis the resulting equations are transformed into dimensionless forms in which dimensionless parameters are identified the effects of dimensionless parameter variations on the modal characteristics of the accelerated plates are investigated through numerical studies

observer based decentralized fuzzy neural sliding mode control for interconnected unknown chaotic systems via network structure adaptation in this paper an observer based fuzzy neural sliding mode control ofnsmc scheme for interconnected unknown chaotic systems is developed the ofnsmc system is composed of a computation controller and a robust controller the computation controller containing a self structuring fuzzy neural network sfnn identifier is the principle controller and the robust controller is designed to achieve l 2 tracking performance the sfnn identifier uses the structure and parameter learning phases to perform the estimation of the interconnected unknown chaotic system dynamics the structure learning phase consists of the growing of membership functions the splitting of fuzzy rules and the pruning of fuzzy rules and thus the sfnn identifier can avoid the time consuming trial and error tuning procedure for determining the network structure of fuzzy neural network the total states of the interconnected chaotic systems are not assumed to be available for measurement also the unknown nonlinearities of the interconnected chaotic systems are not restricted to the systems output only to demonstrate the effectiveness of the proposed method simulation results are illustrated in this paper

evolutionary algorithm based learning of fuzzy neural networks part 2 recurrent fuzzy neural networks fuzzy neural networks fnn as opposed to neuro fuzzy systems whose main task is to process numerical relationships can process both numerical measurement based information and perception based information in spite of great importance of fuzzy feed forward and recurrent neural networks for solving wide range of real world problems today there are no effective training algorithm for them currently there are two approaches for training of fnn first approach is based on application of the level sets of fuzzy numbers and the back propagation bp algorithm the second approach involves using evolutionary algorithms to minimize error function and determine the fuzzy connection weights and biases the method based on the second approach was proposed by the authors and published in part 1 of this paper r a aliev b fazlollahi r vahidov genetic algorithm based learning of fuzzy neural networks part 1 feed forward fuzzy neural networks fuzzy sets and systems 118 2001 351 358 in contrast to the bp and other supervised learning algorithms evolutionary algorithms do not require nor use information about differentials and hence they are most effective in case where the derivative is very difficult to obtain or even unavailable however the main deficiency of the existing fnn based on the feed forward architecture is its adherence to static problems in case of dynamic or temporal problems there is a need for recurrent fuzzy neural networks rfnn designing efficient training algorithms for rfnn has recently become an active research direction in this paper we propose an effective differential evolution optimization deo based learning algorithm for rfnn with fuzzy inputs fuzzy weights and biases and fuzzy outputs the effectiveness of the proposed method is illustrated through simulation of benchmark forecasting and identification problems and comparisons with the existing methods the suggested approach has also been used for real applications in an oil refinery plant for petrol production forecasting

buckling and free vibration analysis of thick rectangular plates resting on elastic foundation using mixed finite element and differential quadrature method abstract in this article a combination of the finite element fe and differential quadrature dq methods is used to solve the eigenvalue buckling and free vibration equations of rectangular thick plates resting on elastic foundations the elastic foundation is described by the pasternak two parameter model the three dimensional linear and small strain theory of elasticity and energy principle are employed to derive the governing equations the in plane domain is discretized using two dimensional finite elements the spatial derivatives of equations in the thickness direction are discretized in strong form using dqm buckling and free vibration of rectangular thick plates of various thicknesses to width and aspect ratios with pasternak elastic foundation are investigated using the proposed fe dq method the results obtained by the mixed method have been verified by the few analytical solutions in the literature it is concluded that the mixed fe dq method has good convergancy behavior and acceptable accuracy can be obtained by the method with a reasonable degrees of freedom

three dimensional elasticity solutions to vibration of cantilevered skewed trapezoids an accurate three dimensional elasticity model for determining the free vibration response of skewed trapezoidal plates is presented the method is formulated on the basis of a linear small strain three dimensional elasticity theory with the ritz minimization procedure the solution method uses sets of uniquely defined one and twodimensional polynomial functions to approximate the trial displacements in the thickness and surface directions respectively these functions are orthogonally generated and have been proven to be highly efficient and numerically stable the proposed technique yields natural frequencies and mode shapes for a wide range of cantilevered skewed trapezoidal plates of arbitrary planform the accuracy of these results whenever possible is validated through comparison with the analytical and experimental data parametric investigations on the vibration behavior of cantilevered trapezoidal plates with respect to different thickness ratios skew angles and chord ratios have been carried out for the first time the presence of surface parallel symmetric thickness modes for these plates is demonstrated in vivid three dimensional mode shape plots

alternative formulations for structural optimization an evaluation by using trusses the concept of simultaneous analysis and design sand is revisited with two objectives in mind 1 to study and evaluate three alternative formulations for structural optimization using trusses as examples and 2 to implement the formulations with a structural analysis program and study their implementation aspects the idea is to gain insights for use of the alternative formulations for structural optimization three alternative formulations are defined using displacements and forces or stresses as optimization variables all of the problem functions in the formulations become explicit in terms of the variables gradients of the functions can be evaluated more easily compared to the conventional approach where special design sensitivity analysis methods are needed existing analysis software is integrated with an optimizer based on a sparse sequential quadratic programming method to solve examples with known solutions with the sand type formulations only the pre and postprocessing capabilities of the analysis software are used to evaluate the problem functions however the conventional formulation also needs the equation solving capabilities for analysis as well as design sensitivity analysis performance of the formulations is evaluated with extensive numerical experiments and their advantages and disadvantages are discussed based on the present research it is concluded that the alternative sand formulations are more efficient compared to the conventional approach and have potential for further development for practical applications particularly the formulations that do not require calculation of the global stiffness matrix

buckling of rectangular mindlin plates with internal line supports this paper considers the elastic buckling of rectangular mindlin plates under normal inplane forces the plates may have any number of internal line straight or curved supports that span between any two edges based on the energy functional derived from the incremental total potential energy approach the newly developed pb 2 rayleigh ritz method is applied for solution the special feature of this method is the pb 2 ritz function which consists of the product of 1 a two dimensional polynomial function and 2 a basic function formed from taking the product of the equations of the boundaries and internal line supports with each equation raised to appropriate powers as shown herein the method is convenient for analysts since no discretization is required and very accurate results can be obtained buckling load intensity factors for rectangular plates with various boundary conditions and various thickness and aspect ratios are tabulated for designers these may also serve as benchmark values for the testing of other numerical methods

free material optimization via mathematical programming this paper deals with a central question of structural optimization which is formulated as the problem of finding the stiffest structure which can be made when both the distribution of material as well as the material itself can be freely varied we consider a general multi load formulation and include the possibility of unilateral contact the emphasis of the presentation is on numerical procedures for this type of problem and we show that the problems after discretization can be rewritten as mathematical programming problems of special form we propose iterative optimization algorithms based on penalty barrier methods and interior point methods and show a broad range of numerical examples that demonstrates the efficiency of our approach

three dimensional vibration analysis of cantilevered skew plates three dimensional 3 d free vibration of cantilevered thick skew plates is analyzed based on the exact linear and small strain elasticity theory the skew domain of the plate is mapped onto a cubic domain a set of triplicate chebyshev polynomials multiplied by a boundary function is developed as the trial functions of each displacement components using the ritz method the eigenvalue equation is derived from the strain energy and kinetic energy of the plate the vibration modes are divided into the antisymmetric and symmetric ones in the thickness direction therefore can be studied individually the convergence study shows that the first eight frequency parameters for each mode categories can be obtained with an accuracy of at least four significant figures the effect of geometric parameters such as skew angle aspect ratio and span thickness ratio on frequency parameters is studied the results are compared with those obtained by using the algebraic polynomials as trial functions and the 3 d finite element solutions respectively it is shown that the chebyshev polynomials can provide better numerical stability than the algebraic polynomials especially for the plates with large skew angle the present results can serve as the benchmark data for the accuracy evaluation of other computational techniques

numerical study of grid distribution effect on accuracy of dq analysis of beams and plates by error estimation of derivative approximation the accuracy of global methods such as the differential quadrature dq approach is usually sensitive to the grid point distribution this paper is to numerically study the effect of grid point distribution on the accuracy of dq solution for beams and plates it was found that the stretching of grid towards the boundary can improve the accuracy of dq solution especially for coarse meshes the optimal grid point distribution corresponding to optimal stretching parameter depends on the order of derivatives in the boundary condition and the number of grid points used the optimal grid distribution may not be from the roots of orthogonal polynomials this differs somewhat from the conventional analysis this paper also proposes a simple and effective formulation for stretching the grid towards the boundary the error distribution of derivative approximation is also studied and used to analyze the effect of grid point distribution on accuracy of numerical solutions copyright 2001 john wiley sons ltd

vibrations of cantilevered skewed plates with corner stress singularities in conjunction with classical thin plate theory the ritz trial space of assumed transverse displacement functions consists of algebraic polynomials which are mathematically complete and corner functions which account for the singular behaviour of bending stresses at the reentrant corner

differential quadrature for multi dimensional problems the technique of differential quadrature for the solution of partial differential equations introduced by bellman et al is extended and generalized to encompass partial differential equations involving multiple space variables approximation formulae for a variety of first and second order partial derivatives and typical weighting coefficients are presented application of these formulae is demonstrated on the solution of the convection diffusion equation for the two and three dimensional space dependent cases and for both the transient and steady state dispersion of inert neutrally buoyant pollutants from continuous sources into an unbounded atmosphere

robust topology optimization under loading uncertainty based on linear elastic theory and orthogonal diagonalization of symmetric matrices abstract this paper proposes an efficient approach to solving robust topology optimization problem of structures under loading uncertainty the objective is to minimize a weighted sum of the mean and standard deviation of structural compliance loading uncertainties can be in either concentrated loads or uniformly distributed loads by exploiting of the linear elastic nature of structure monte carlo sampling is completely separated from the topology optimization process thus accurate calculation of objective function becomes possible efficient sensitivity analysis method is developed and its computational cost is only linearly proportional to the number of uncertain loads the sensitivity analysis is also integrated into the density based topology optimization approach to solve the robust topology optimization problems the numerical examples demonstrate the effectiveness of the proposed approach the effect of uncertainty level probability distribution of uncertainty and different influence of loading magnitude and directional uncertainty on the robust designs are also shown by the numerical examples

dynamic structure adaptive neural fuzzy control for mimo uncertain nonlinear systems this paper proposes a novel dynamic structure neural fuzzy network dsnfn to address the adaptive tracking problems of multiple input multiple output mimo uncertain nonlinear systems the proposed control scheme uses a four layer neural fuzzy network nfn to estimate system uncertainties online the main feature of this dsnfn is that it can either increase or decrease the number of fuzzy rules over time based on tracking errors projection type adaptation laws for the network parameters are derived from the lyapunov synthesis approach to ensure network convergence and stable control a hybrid control scheme that combines the sliding mode control and the adaptive bound estimation control with different weights improves system performance by suppressing the influence of external disturbances and approximation errors as the employment of the dsnfn high quality tracking performance could be achieved in the system furthermore the trained network avoids the problems of overfitting and underfitting simulations performed on a two link robot manipulator demonstrate the effectiveness of the proposed control scheme

new models for optimal truss topology in limit design based on unified elastic plastic analysis abstract this paper presents several equivalent formulations for a structural design problem where the load carrying capacity is maximized for a prescribed volume subject to bounds on complementary energy and stresses this limit design model covers the full range of strictly elastic elastic plastic and strictly plastic designs and is based on the unified analysis model of ben tal and taylor 1 while this design model is convex it is nonlinearly constrained and is of a very high dimension for topology design problems application of duality principles leads to several simpler but nonsmooth equivalent models in particular for the case when the design variables do not have explicit bounds the dual models reduce to a minimization subject to a single linear constraint of a pointwise maximum of a finite number of convex functions more importantly these simpler design models are of greatly reduced size since they contain only nodal variables further the two cases of strictly plastic as well as strictly elastic limit design models can be reduced to linear programs both of which unexpectedly are shown to be equivalent to the more widely studied model for minimum compliance topology design of elastic trusses several numerical examples illustrate the usefulness of these new dual formulations

on mathcalvu theory for functions with primal dual gradient structure we consider a general class of convex functions having what we call primal dual gradient structure it includes finitely determined max functions and maximum eigenvalue functions as well as other infinitely defined max functions for a function in this class we discuss a space decomposition that allows us to identify a subspace on which the function appears to be smooth moreover using the special structure of such a function we compute smooth trajectories along which certain second order expansions can be obtained we also give an explicit expression for the hessian of a related lagrangian

three dimensional free vibration analysis of isotropic rectangular plates using the b spline ritz method abstract this paper presents three dimensional free vibration analysis of isotropic rectangular plates with any thicknesses and arbitrary boundary conditions using the b spline ritz method based on the theory of elasticity the proposed method is formulated by the ritz procedure with a triplicate series of b spline functions as amplitude displacement components the geometric boundary conditions are numerically satisfied by the method of artificial spring to demonstrate the convergence and accuracy of the present method several examples with various boundary conditions are solved and the results are compared with other published solutions by exact and other numerical methods based on the theory of elasticity and various plate theories rapid stable convergences as well as high accuracy are obtained by the present method the effects of geometric parameters on the vibrational behavior of cantilevered rectangular plates are also investigated the results reported here may serve as benchmark data for finite element solutions and future developments in numerical methods

free vibrations of a simply supported rectangular plate an exact elasticity solution abstract an exact three dimensional solution for the free vibrations of simply supported rectangular plates of arbitrary thickness within the linear theory of elastodynamics is given in this paper the solution obtained in a semi inverse fashion as was the solution of the elastostatic problem for such plates satisfies all of the boundary conditions of the problem in a pointwise manner it is found that there are two types of modes of oscillation possible which are consistent with the kinematic assumptions made to find the semi inverse solution other modes of oscillation may exist in the three dimensional theory of elastodynamics for such plates but our kinematic assumptions would not be consistent with such modes the two types of modes found are analogous to the flexural modes of classical plate theory and the thickness twist modes here called breathing modes of mindlin plate theory some numerical results are given which indicate that the predictions of mindlin plates are uncannily good approximations to the flexural frequencies given by the present three dimensional analysis even for very thick plates however the predictions of mindlin plate theory for the thickness twist or breathing frequencies are not nearly so good these discrepancies are discussed briefly in an appendix

simplified interval type 2 fuzzy neural networks this paper describes a self evolving interval type 2 fuzzy neural network fnn for various applications as type 1 fuzzy systems cannot effectively handle uncertainties in information within the knowledge base we propose a simple interval type 2 fnn which uses interval type 2 fuzzy sets in the premise and the takagi sugeno kang tsk type in the consequent of the fuzzy rule the tsk type consequent of fuzzy rule is a linear combination of exogenous input variables given an initially empty the rule base all rules are generated with on line type 2 fuzzy clustering instead of the time consuming k m iterative procedure the design factors ql and qr are learned to adaptively adjust the upper and lower positions on the left and right limit outputs using the parameter update rule based on a gradient descent algorithm simulation results demonstrate that our approach yields fewer test errors and less computational complexity than other type 2 fnns

normal modes in a continuum model of vocal fold tissues the ritz method is used to calculate eigenmodes and eigenfrequencies in a continuum model of the vocal folds the investigation represents a rectification and extension of previous studies emphasizing the indispensability of utilizing natural boundary conditions when computing the characteristic modes of a system concurring with previous assertions two of the lower order eigenmodes are theorized to play a major role in facilitating self oscillation of the folds during phonation one mode related to vertical phasing is shown to have a more direct control over glottal convergence divergence than indicated in previous calculations unlike lumped element models the continuum model predicts that the eigenfrequencies of the two modes are closely spaced over an extensive range of tissue sizes and stiffnesses this finding may help explain why the two modes entrain so naturally over a wide range of phonatory adjustments in human phonation

bem analysis of free vibration problems using polynomial particular integrals abstract the development of a boundary element method for free vibration analysis using particular solutions is discussed the formulation presented is based on treating the forcing function in the governing differential equation as an initially unknown distributed body force within the domain the volume integral due to this body force is then eliminated by approximating the inertia force by global interpolation and polynomial function representations and finding particular solutions for the governing inhomogeneous equations the resulting non symmetric system matrix is solved by using a modified arnoldi s algorithm that takes advantage of the special structure of the substructured boundary element method the techniques described here are embedded in a computer program gpbest and the numerical examples arc solved by using this computer code

on the three dimensional vibration analysis of simultaneously skewed and twisted cantilevered parallelepipeds the natural frequencies of simultaneously skewed and twisted cantilevered parallelepipeds are determined using the ritz method the present work is the first known three dimensional study of the problem assumed displacement functions are in the form of algebraic polynomials which satisfy the fixed face conditions exactly and which are mathematically complete reasonably accurate natural frequencies are calculated for low aspect ratio thick parallelepipeds having arbitrary degrees of twist and skewness detailed numerical studies show that a three dimensional analysis is essential in monitoring complicated coupled mode sensitivities in the variation of non dimensional natural frequencies with increasing skew and twist angles and thickness ratio results obtained using the present method are compared with those obtained in a detailed three dimensional finite element analysis where the suitability and limitations of s version solid element discretizations are clearly brought out

up to lowest 100 frequencies of rectangular plates using jacobi polynomials and tsndt abstract this paper finds up to lowest 100 free vibration frequencies of isotropic and linearly elastic plates with thickness to side length ratio varying from 0 001 to 0 5 by using the ritz method a third order shear and normal deformable plate theory tsndt and weighted jacobi polynomials as admissible functions that are mutually orthogonal and exactly satisfy essential boundary conditions the numerical method is stable even for 18th degree polynomials as basis functions it is shown that this approach requires fewer degrees of freedom than those in the traditional finite element method fem to find converged lowest 100 frequencies and the corresponding mode shapes no shear correction factor is employed in the tsndt the presently computed results agree well with those from either analytical or numerical solutions of the corresponding 3 dimensional linearly elastic problems obtained with the commercial fe software abaqus furthermore results for plates made of an incompressible material can be computed by setting poisson s ratio 0 49

solving ax b a method with reduced storage requirements it is shown that a recently developed method for solving ax b can be arranged so that it requires approximately one quarter of the in core storage capacity of other comparable solution procedures for the solution of large systems

dynamic stability of a non conservative viscoelastic rectangular plate abstract based on the thin plate theory and the two dimensional 2d viscoelastic differential constitutive relation the differential equation of motion of the viscoelastic rectangular plate subjected to uniformly distributed tangential follower force in laplace domain is deduced the equation is suitable for various viscoelastic models of differential type the differential equation of motion of the viscoelastic plate constituted by the kelvin voigt model under the action of uniformly distributed tangential follower force in time domain is also derived the generalized eigenequations of non conservative viscoelastic rectangular plate with four edges simply supported two opposite edges simply supported and other two edges clamped are established by the differential quadrature method and the curves of real parts and imaginary parts of the first three order dimensionless complex frequencies vs uniformly distributed tangential follower force are obtained the factors influencing the dynamic stability of the visoelastic rectangular plate are discussed

discontinuous piecewise linear optimization a theoretical framework and a practical algorithm are presented to solve discontinuous piecewise linear optimization problems dealing with functions for which theridges are known a penalty approach allows one to consider such problems subject to a wide range of constraints involving piecewise linear functions although the theory is expounded in detail in the special case of discontinuous piecewiselinear functions it is straightforwardly extendable using standard nonlinear programming techniques tononlinear discontinuous piecewise differentiable functions the descent algorithm which is elaborated uses active set and projected gradient approaches it is a generalization of the ideas used by conn to deal with nonsmoothness in thel1 exact penalty function and it is based on the notion ofdecomposition of a function into a smooth and a nonsmooth part the constrained case is reduced to the unconstrained minimization of a piecewise linear l1 exact penalty function we also discuss how the algorithm is modified when it encounters degenerate points preliminary numerical results are presented the algorithm is applied to discontinuous optimization problems from models in industrial engineering 1998 the mathematical programming society inc published by elsevier science b v

on coupled longitudinal and lateral vibrations of elastic rods abstract in this paper the coupled longitudinal and lateral vibrations of a rectangular parallelepiped composed of a uniform isotropic elastic body are examined the one dimensional model for the body was developed by green naghdi and several of their co workers it is based on a cosserat or directed rod theory the frequency spectrum is found to divide naturally into three regions which are separated by degenerate cases when the cross section of the body is square a natural splitting of the modes occurs one half of this split involves motions coupling the axial extension and symmetric lateral deformation of the body the other half involves asymmetric lateral deformations the cases of a free free rod and a cantilevered rod are discussed and the results compared to existing works in the literature which use the three dimensional theory of elasticity to model the vibrations