stable inversion of continuous time nonlinear systems by finite difference methods introduces finite difference methods for stable inversion of continuous time nonlinear systems a relationship between the new finite difference methods and the existing picard methods is established a damped newton finite difference method is shown to possess superior convergence properties and its effectiveness is illustrated with an inverted pendulum example

a new approach to inversion based feedforward control design for nonlinear systems the finite time transition between stationary setpoints of nonlinear siso systems is considered as a scenario for the presentation of a new design approach for inversion based feedforward control design techniques which are based on a stable system inversion result in input trajectories with pre and or post actuation intervals the presented approach treats the considered transition task as a two point boundary value problem bvp and yields causal feedforward trajectories which are constant outside the transition interval the main idea of this approach is to provide free parameters in the desired output trajectory to solve the bvp of the internal dynamics thereby a standard matlab function can be used for the numerical solution of the bvp feedforward control design techniques are illustrated by simulation results for a simple example

stable inversion of nonlinear non minimum phase systems output tracking control of non minimum phase systems is a highly challenging problem encountered in the control of flexible manipulators space structures and elsewhere classical inversion provides exact output tracking but leads to internal instability while recent nonlinear regulation provides stable asymptotic tracking but admits large transient errors as a first step to solve this problem this paper addresses the stable inversion of non minimum phase nonlinear systems using the notions of zero dynamics and stable unstable manifolds an invertibility condition is established for a class of systems a stable but non causal inverse is obtained offline that can be incorporated into a stabilizing controller for dead beat output tracking this inverse contrasts with the causal inverse proposed by hirschorn where unstable zero dynamics result in unbounded inverse solutions our results reduce to those of hirschorn for minimum phase systems however in a numerical example the stable inverse has achiev

approximated stable inversion for nonlinear systems with nonhyperbolic internal dynamics a technique to achieve output tracking for nonminimum phase nonlinear systems with nonhyperbolic internal dynamics is presented the present paper integrates stable inversion techniques that achieve exact tracking with approximation techniques that modify the internal dynamics to circumvent the nonhyperbolicity of the internal dynamics this nonhyperbolicity is an obstruction to applying presently available stable inversion techniques the theory is developed for nonlinear systems and the method is applied to a two cart with inverted pendulum example

brief paper swing up of the double pendulum on a cart by feedforward and feedback control with experimental validation the swing up maneuver of the double pendulum on a cart serves to demonstrate a new approach of inversion based feedforward control design introduced recently the concept treats the transition task as a nonlinear two point boundary value problem of the internal dynamics by providing free parameters in the desired output trajectory for the cart position a feedback control is designed with linear methods to stabilize the swing up maneuver the emphasis of the paper is on the experimental realization of the double pendulum swing up which reveals the accuracy of the feedforward feedback control scheme

brief paper on the equivalence between stable inversion for nonminimum phase systems and reciprocal transfer functions defined by the two sided laplace transform in this paper the two sided laplace transform a classical but not very common mathematical tool is revived to express the stable inversion for linear nonminimum phase systems that was recently proposed from the viewpoint of state space representations it is demonstrated that those two different expressions for the stable inversion are mathematically equivalent simple examples are presented to illustrate the two sided laplace transform as a direct and intuitive approach to stable inversion the two sided laplace transform approach is also applied to the development of an iterative learning control for nonminimum phase systems that needs neither a precise inversion model nor fourier transform computations but instead requires only measuring the system response with time reversals

reproducing kernel particle methods for large deformation analysis of non linear structures abstract large deformation analysis of non linear elastic and inelastic structures based on reproducing kernel particle methods rkpm is presented the method requires no explicit mesh in computation and therefore avoids mesh distortion difficulties in large deformation analysis the current formulation considers hyperelastic and elasto plastic materials since they represent path independent and path dependent material behaviors respectively in this paper a material kernel function and an rkpm material shape function are introduced for large deformation analysis the support of the rkpm material shape function covers the same set of particles during material deformation and hence no tension instability is encountered in the large deformation computation the essential boundary conditions are introduced by the use of a transformation method the transformation matrix is formed only once at the initial stage if the rkpm material shape functions are employed the appropriate integration procedures for the moment matrix and its derivative are studied from the standpoint of reproducing conditions in transient problems with an explicit time integration method the lumped mass matrices are constructed at nodal coordinate so that masses are lumped at the particles several hyperelasticity and elasto plasticity problems are studied to demonstrate the effectiveness of the method the numerical results indicated that rkpm handles large material distortion more effectively than finite elements due to its smoother shape functions and consequently provides a higher solution accuracy under large deformation unlike the conventional finite element approach the nodal spacing irregularity in rkpm does not lead to irregular mesh shape that significantly deteriorates solution accuracy no volumetric locking is observed when applying non linear rkpm to nearly incompressible hyperelasticity and perfect plasticity problems further model adaptivity in rkpm can be accomplished simply by adding more points in the highly deformed areas without remeshing

boundary element free method befm for two dimensional elastodynamic analysis using laplace transform in this paper we present a direct meshless method of boundary integral equation bie known as the boundary element free method befm for two dimensional 2d elastodynamic problems that combines the bie method for 2d elastodynamics in the laplace transformed domain and the improved moving least squares imls approximation the formulae for the befm for 2d elastodynamic problems are given and the numerical procedures are also shown the befm is a direct numerical method in which the basic unknown quantities are the real solutions of the nodal variables and the boundary conditions can be implemented directly and easily that leads to a greater computational precision for the purpose of demonstration some selected numerical examples are solved using the befm copyright 2005 john wiley sons ltd

postbuckling analysis of laminated composite plates using the mesh free kp ritz method abstract a ritz method based on kernel particle approximation for the field variables is proposed for the postbuckling analysis of laminated composite plates the first order shear deformation plate theory fsdt is employed to model the plate flexure the ritz method is used to obtain the discretized non linear equations a geometrically non linear analysis is used to trace the postbuckling paths of the plate typical numerical examples including isotropic plates and cross ply and angle ply laminated composite plates have been solved using the proposed method the results are in close agreement with the series solution as well as previous finite element results available in the literature

geometric non linear analysis of folded plate structures by the spline strip kernel particle method this paper investigates the geometric non linear behaviour of stiffened and un stiffened folded plate structures using the spline strip kernel particle method sskpm the first order shear deformable plate theory and large deflection theory of von karman are employed the folded plate structures are considered as assemblies of individual stiffened and un stiffened flat plates that lie on different planes we regard these stiffened and un stiffened plate structures as superelements and superpose their stiffness matrices to derive the final global stiffness matrices several numerical example problems are examined and comparison studies are carried out with other available results the effect of the size of the support the order of the polynomial basis functions and the spacing of the spline nodes on the convergence of the proposed method is examined

a general framework for approximated model stable inversion abstract in this paper we propose an approximated method for the design of feedforward actions based on model stable inversion in the proposed framework the solution of the model stable inversion is approximated in the least squares sense by a suitable combination of any arbitrary set of basis functions the paper makes use of operator theory to derive a closed form formula to compute such approximation and to provide boundedness properties for the computed solution simulations are provided to show the effectiveness of the proposed method with different families of basis functions

non linear finite strip analysis of rectangular laminates under end shortening using classical plate theory the finite strip method is developed for predicting the geometrically non linear response of rectangular composite laminates with simply supported ends when subjected to uniform end shortening in their plane at the loaded ends lateral in plane expansion may be allowed freely or may be prevented completely in different versions of the approach the permitted laminate material properties are quite general encompassing anisotropy and full coupling between in plane and out of plane behaviour the analysis is based on the use of the classical plate theory and the non linearity is introduced in the strain displacement equations in the manner of the von karman assumptions three different types of finite strip are presented with either linear quadratic or cubic interpolation of the membrane displacement components across a strip in each case the bending displacement component varies cubically across a strip results are presented for isotropic plates and for unsymmetric cross ply angle ply and arbitrary laminates

vibration of shear deformable beams using a spline function approach b spline functions are used as trial functions in a rayleigh ritz analysis of the free vibration of shear deformable timoshenko beams in a first approach it is demonstrated in numerical applications that when the lateral deflection and the cross sectional rotation are represented by functions of equal order the calculated natural frequencies are of good accuracy for stocky beams but can overestimate the true frequencies very considerably for slender beams this is identified as a shear locking difficulty and consideration of its causes points clearly to the adoption of a new displacement field in which the deflection is represented by a b spline function which is one order higher than that used to represent the rotation numerical results using this new displacement field demonstrate good accuracy for both stocky and slender beams the shear locking difficulty is completely eliminated this has clear significance for the analysis of shear deformable plates and shells when using b spline functions

stable inversion for nonlinear nonminimum phase time varying systems we extend stable inversion to nonlinear time varying systems and study computational issues the technique is applicable to minimum phase as well as nonminimum phase systems the inversion technique is new even in the linear time varying case and relies on partitioning the dichotomic split of the linearized system dynamics into time varying stable and unstable submanifolds this dichotomic split is used to build time varying filters which are in turn the basis of a contraction used to find a bounded inverse input state trajectory finding the inverse input state trajectory allows the development of exact output tracking controllers the method is local to the time varying trajectory and requires that the internal dynamics vary slowly however the method represents a significant advance relative to presently available tracking controllers present techniques are restricted to time invariant nonlinear systems and in the general case track only asymptotically

stable inversion for nonlinear systems abstract there have been two recent major developments in output tracking for nonlinear systems and our first main contribution is to relate these under appropriate assumptions we show that the bounded solution of the partial differential equation of isidori and byrnes for each trajectory of an exosystem must be given by an integral representation formula of devasia chen and paden under restrictive hypotheses devasia chen and paden develop a picard process that converges to the solution of the integral equation this solution to the integral equation is also a bounded solution to a dynamical equation driven by the desired outputs in aircraft applications our nonlinear systems are perturbations of pure feedback systems with outputs and we find a solution to the stable inversion problem i e finding bounded controls and bounded state trajectories in response to bounded output signals in two steps the first step ignores the perturbation error and computes the major part of the desired control and corresponding state trajectory the second step computes the remaining control and states by finding a noncausal and stable solution to an error driven dynamical equation in other words the method of devasia chen and paden is applied to an error system and not to the full system this two step procedure is the second main contribution of this paper throughout this paper it is assumed that our nonlinear systems have vector relative degree

comparison of some single step methods for the numerical solution of the structural dynamic equation this paper compares the performance of the ss22 and ss23 references 1 and 2 single step algorithms for the numerical solution of the second order structural dynamic equation and a related new algorithm ss32b applied to the equivalent first order system with sine and step forcing functions various aspects of stability relevant to these equations are discussed

a multi term semi energy finite strip method for post buckling analysis of composite plates in this paper a finite strip approach based on the concept of a rigorous post buckling solution for composite plates namely the semi energy approach is presented moreover in semi energy finite strip approach the out of plane displacement field of the finite strip is the only displacement which is postulated by a deflected form the postulated deflected form is substituted into von karman s compatibility equation which is solved exactly to obtain the corresponding forms of the mid plane stresses and displacements the solution of von karman s compatibility equation and the postulated out of plane deflected form are then used to evaluate the potential energy of the related finite strip finally by invoking the principle of minimum potential energy the equilibrium equations of the finite strip are derived the developed finite strip method fsm is applied to analyse the post buckling behaviour of laminated composite plates as far as the validity and numerical efficiency of the developed semi energy fsm is concerned the results obtained from semi energy fsm approach are compared with those obtained from a fairly conventional and well exploited finite strip technique namely the full energy finite strip method the study of the results revealed that the developed semi energy fsm provides a very higher convergence and stress distribution properties in comparison with the full energy solution by incorporating considerably less number of degrees of freedom this means that from the computational economy point of view the developed semi energy fsm is superior to the full energy fsm copyright 2006 john wiley sons ltd

conditions for the existence of a flat input we introduce the concept of an affine flat input to a non linear system with a given output function this approach can be seen as dual to the search for a flat output of a control system with given input our results provide a necessary and sufficient condition for the existence of a flat input in the siso case which also allows to construct of the vector field associated to the flat input in addition a relation between the flat input vector field and non linear observer design is discussed a population model is used to illustrate the construction of a flat input

weighting parameters for unconditionally stable higher order accurate time step integration algorithms part 2 second order equations in this paper unconditionally stable higher order accurate time step integration algorithms suitable for linear second order differential equations based on the weighted residual method are presented the second order equations are manipulated directly as in part 1 of this paper instead of specifying the weighting functions the weighting parameters are used to control the algorithm characteristics the algorithms are at least nth order accurate if the numerical solution for displacement is approximated by a polynomial of degree n 1 with n undetermined coefficients by choosing the weighting parameters carefully the order of accuracy can be improved the generalized pade approximations for the second order equations are considered the ultimate spectral radius is an algorithmic parameter by relating the approximate solutions to the equivalent formulations presented in part 1 of this paper the required weighting parameters are found explicitly any set of linearly independent functions can be used to construct the corresponding weighting functions from the weighting parameters the stabilizing weighting functions for the weighted residual method are found explicitly to ensure higher order accuracy in the general solution the accuracy of the particular solution due to excitation is also examined copyright 1999 john wiley sons ltd

a time integration algorithm for linear transient analysis based on the reproducing kernel method in this paper a new algorithm based on the reproducing kernel method is presented for linear transient analysis using very large time steps in the conventional time integration methods the required accuracy is always achieved by either decreasing the size of time steps or increasing the order of approximations the proposed method however does not require a restriction on the size of the time step the required approximating functions for integration of governing equations are determined using the concept of reproduction of the solution within each time step a recurrence relationship is obtained through solving the governing equation by the point collocation based reproducing kernel method within the time step in collocation points the values of external excitation can be obtained either through the approximation between the values at the beginning and the end of each time step or assigning the exact values of the external force hence one advantage of this new method is the independency of the sampling rates of external excitation from the size of the time step the proposed method is applied for solving first and second order differential equations and advantages of the method are illustrated through a number of numerical examples

nonlinear inversion based output tracking an inversion procedure is introduced for nonlinear systems which constructs a bounded input trajectory in the preimage of a desired output trajectory in the case of minimum phase systems the trajectory produced agrees with that generated by hirschorn s inverse dynamic system however the preimage trajectory is noncausal rather than unstable in the nonminimum phase case in addition the analysis leads to a simple geometric connection between the unstable manifold of the system zero dynamics and noncausality in the nonminimum phase case with the addition of stabilizing feedback to the preimage trajectory asymptotically exact output tracking is achieved tracking is demonstrated with a numerical example and compared to the well known byrnes isidori regulator rather than solving a partial differential equation to construct a regulator the inverse is calculated using a picard like interaction when preactuation is not possible noncausal inverse trajectories can be truncated resulting in the tracking error transients found in other control schemes

complex variable moving least squares method a meshless approximation technique based on the moving least squares mls approximation we propose a new approximation method the complex variable moving least squares cvmls approximation with the cvmls approximation the trial function of a two dimensional problem is formed with a one dimensional basis function the number of unknown coefficients in the trial function of the cvmls approximation is less than in the trial function of the mls approximation and we can thus select fewer nodes in the meshless method that is formed from the cvmls approximation than are required in the meshless method of the mls approximation with no loss of precision the meshless method that is derived from the cvmls approximation also has a greater computational efficiency from the cvmls approximation we propose a new meshless method for two dimensional elasticity problems the complex variable meshless method cvmm and the formulae of the cvmm for two dimensional elasticity problems are obtained compared with the conventional meshless method the cvmm has a greater precision and computational efficiency for the purposes of demonstration some selected numerical examples are solved using the cvmm

continuous time linear predictive control and flatness a module theoretic setting with examples a general flatness based framework for linear continuous time predictive control is presented the mathematical setting which is valid for multivariable systems is provided by the algebraic theory of modules where a controllable system corresponds to a finitely generated free module over a principal ideal ring any basis of this free module is a flat output which yields an easy calculation of the predicted trajectory this formalism permits one to handle non minimum phase systems system constraints and to deal with additive perturbations three concrete case studies namely a dc motor a flexible system and a cement mill are analysed and simulations are given these examples are written in such a way that any reader who is not familiar with module theory may nevertheless grasp the proposed control strategy

buckling and free vibration analyses of stiffened plates using the fsdt mesh free method this paper presents a mesh free galerkin method for the free vibration and stability analyses of stiffened plates via the first order shear deformable theory fsdt the model of a stiffened plate is formed by 1 regarding the plate and the stiffener separately 2 imposing displacement compatible conditions between the plate and the stiffener so that displacement fields of the stiffener can be expressed in terms of the mid surface displacement of the plate and 3 superimposing the strain energy of plate and stiffener because there are no meshes used in this method the stiffeners can be placed anywhere on the plate and need not be placed along the mesh lines several numerical examples are computed by this method to show its accuracy and convergence the present results demonstrate good agreement with the existing solutions given by other researchers and the ansys influences of support size and order of the complete basis functions on the numerical accuracy are also investigated

the norsett time integration methodology for finite element transient analysis this paper presents a set of methods for time integration of problems arising from finite element semidiscretizations the purpose is to obtain computationally efficient methods which possess higher order accuracy and controllable dissipation in the spurious high modes the methods are developed and analysed by a general collocation methodology which leads to the class of norsett approximants an algorithmic parameter is used to achieve an effective control over numerical dissipation moreover a simple and efficient implementation scheme is presented at each time step algorithms based on p order collocation polynomials require the solution of p sets of linear algebraic equations with the same coefficient matrix in this way a single factorization is needed and no transformations are required to recover the approximate solution at the end or within the time interval to demonstrate the performance of the proposed algorithms a wide experimental evaluation is carried out on typical test problems in finite element transient analysis

constrained reachability and trajectory generation for flat systems we consider the problem of trajectory generation for constrained differentially flat systems based on the topological properties of the set of admissible steady state values of a flat output we derive conditions which allow for an a priori verification of the feasibility of constrained set point changes we propose to utilize this relation to generate feasible reference trajectories to this end we suggest to split the trajectory generation problem into two stages a the planning of geometric reference paths in the flat output space combined with b an assignment of a dynamic reference motion to these paths this assignment is based on a reduced optimal control problem the unique feature of the approach is that due to the specific construction of the reference paths the optimal control problem to be solved is guaranteed to be feasible to illustrate our results we consider a van de vusse reactor as an example

optimal inversion based control for the set point regulation of nonminimum phase uncertain scalar systems we propose an optimal inversion based control for the set point constrained regulation of nonminimum phase uncertain scalar systems this approach is based on a new control architecture where the main purpose of the feedback is to reduce the sensitivity to parametric plant uncertainties permitting in such a way the effective use of a feedforward action determined via a stable dynamic inversion essential constituents of the architecture are a parameterized family of transition polynomials to shape ideal output transfers and a parameterized controller ensuring the internal model principle the methodology is then centered on the optimal combined design of the feedback controller and of the inversion based command signal in order to minimize the worst case settling time subject to an amplitude constraint on the control variable and to arbitrarily assigned overshoot and undershoot bounds finally an approximate or suboptimal solution to the resulting nonlinear optimization problem can be obtained by genetic algorithms a worked example highlights the effectiveness of the overall methodology

collocation time finite element procedures for integration of strongly nonlinear initial value problems by use of a collocation time finite element formulation a modification of the well known generalized midpoint method is derived the new family possesses an additional free parameter this allows for significant improvement of the numerical solution in strongly nonlinear situations numerical results show the accuracy of the proposed algorithm in comparison to the midpoint method

brief optimal noncausal set point regulation of scalar systems this paper presents a novel system inversion approach to the set point regulation of linear scalar minimum phase systems this approach uses closed form expressions of cause effect pairs that make possible an arbitrarily smooth transition between two given output set points the cause effect pairs are based on the introduced concept of transition polynomials simple optimization procedures are then proposed to solve the relevant optimal output synthesis and optimal input synthesis the potentiality of the method is highlighted by the examples presented namely a synthesis of elevator velocity profiles and the performance improving of a pid controller

elasto plasticity revisited numerical analysis via reproducing kernel particle method and parametric quadratic programming aiming to simplify the solution process of elasto plastic problems this paper proposes a reproducing kernel particle algorithm based on principles of parametric quadratic programming for elasto plasticity the parametric quadratic programming theory is useful and effective for the assessment of certain features of structural elasto plastic behaviour and can also be exploited for numerical iteration examples are presented to illustrate the essential aspects of the behaviour of the model proposed and the flexibility of the coupled parametric quadratic programming formulations with the reproducing kernel particle method copyright 2002 john wiley sons ltd

flatness and defect of non linear systems introductory theory and examples we introduce flat systems which are equivalent to linear ones via a special type of feedback called endogenous their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of kalman s controllability the distance to flatness is measured by a non negative integer the defect we utilize differential algebra where flatness and defect are best defined without distinguishing between input state output and other variables many realistic classes of examples are flat we treat two popular ones the crane and the car with n trailers the motion planning of which is obtained via elementary properties of plane curves the three non flat examples the simple double and variable length pendulums are borrowed from non linear physics a high frequency control strategy is proposed such that the averaged systems become flat

a time stepping procedure for structural dynamics using gauss point collocation when a cubic function is interpolated between the prescribed initial displacement and velocity and the exact displacement and velocity at the end of a time step for a single degree of freedom system the error or residual in the governing equation is zero at a number of times it is shown that for a general undamped system in the limit as the time step approaches zero these times correspond to gauss points this observation is verified by considering a general collocation procedure in which the displacement in any time step is approximated as a cubic function of time with two coefficients chosen to satisfy the displacement and velocity at the beginning of the time step with the other two coefficients being chosen to satisfy the governing differential equation at any two times it is shown that optimum accuracy is obtained if these points are the gauss points detailed expressions are then presented for this particular case and stability of the algorithm is investigated showing that the procedure is conditionally stable for time steps which are a small proportion of the least period of vibration of the structure the algorithm is considered to be the most accurate possible procedure based on cubic approximation of the displacement

unconditionally stable collocation algorithms for second order initial value problems abstract in this paper unconditionally stable higher order accurate time step integration algorithms suitable for second order initial value problems in collocation form are presented the second order equations are manipulated directly if the approximate solution is expressed as a polynomial of degree n 1 there are n unknowns to be determined after taking into account the two given initial conditions it is well known that by suppressing the residuals of the governing equations at n distinct collocation points only the resultant algorithms are only conditionally stable in this paper linear combinations of the residuals at n 1 distinct collocation points are used to solve for the n unknowns the collocation points and the relative weights between the residuals are derived from the weighted residual method the weighting functions are arbitrary polynomials of degree not exceeding n 1 to control the accuracy and stability properties of the resultant algorithms the reduced integration technique is used to evaluate the integrals in the formulation once the reduced integration rules are decided the equivalent collocation form can be derived it is found that the resultant algorithms cast in the collocation form are easy to implement and can be used to tackle non linear problems directly numerical examples are given to illustrate the validity of the present formulation

postbuckling analysis of composite laminated panels a description is given of the development of a spline e nite strip method for predicting the response of composite laminated prismatic panels to a progressive uniform end shortening the response is assumed to be geometrically nonlinear with the nonlinearity introduced in enhanced strain displacement equations in a total langrangian approach the set of nonlinear equilibrium equations obtained by appropriate energy minimization is solved using the newton raphson method the development of the properties of a e at e nite strip is made in the contexts of both e rst order shear deformation plate theory and classical plate theory and a number of strip models is available corresponding to different displacement e elds presented applications concern a box section and several longitudinally stiffened panels that include curved panels modeled as faceted shells comparison of the e nite strip predictions is made where possible with results from other sources and such comparison is shown to be close

asymptotic post buckling analysis of rectangular plates by hc finite elements the present paper extends the finite element perturbation approach already presented for pin jointed and framed structures15 to rectangular thin plates koiter s asymptotic strategy2 is coupled with a high continuity finite element discretization of the plate 22 the consistency of the discrete model is discussed from the kinematical and numerical points of view and several numerical tests are reported it appears that use of the hc elements makes the perturbation algorithm insensitive to the locking phenomenon occurring in the evaluation of the postbuckling behaviour it also allows the use of very fine discretization meshes at low computational cost

a spline strip kernel particle method and its application to two dimensional elasticity problems in this paper we present a novel spline strip kernel particle method sskpm that has been developed for solving a class of two dimensional 2d elasticity problems this new approach combines the concepts of the mesh free methods and the spline strip method for the interpolation of the assumed displacement field we employed the kernel particle shape functions in the transverse direction and the b3 spline function in the longitudinal direction the formulation is validated on several beam and semi infinite plate problems the numerical results of these test problems are then compared with the existing solutions obtained by the exact or numerical methods from this study we conclude that the sskpm is a potential alternative to the classical finite strip method fsm copyright 2003 john wiley sons ltd

unconditionally stable higher order accurate collocation time step integration algorithms for first order equations abstract in this paper unconditionally stable higher order accurate time step integration algorithms for linear first order differential equations based on the collocation method are presented the amplification factor at the end of the spectrum is a controllable algorithmic parameter the collocation parameters for unconditionally stable higher order accurate algorithms are found to be given by the roots of a polynomial in terms of the ultimate amplification factor in general when the numerical solution is approximated by a polynomial of degree n this approximation is at least n th order accurate however by using the above collocation parameters the order of accuracy can be improved to 2 n 1 or 2 n the approximate solutions are found to be equivalent to the generalized pade approximations furthermore it is shown that the accuracy of the particular solution due to excitation given by the present method is compatible with the homogeneous solutions no modification of the collocation parameters is required

buckling of folded plate structures subjected to partial in plane edge loads by the fsdt meshfree galerkin method this paper presents a meshfree galerkin method that is based on the first order shear deformation theory fsdt to study the elastic buckling behaviour of stiffened and un stiffened folded plates under partial in plane edge loads the un stiffened folded plates are modelled as assemblies of flat plates the stiffness and initial stress matrices of the flat plates are derived by the meshfree galerkin method a treatment is implemented to modify the stiffness and initial stress matrices and the matrices are then superposed to obtain the stiffness and initial stress matrix of the entire folded plate the analytical process for stiffened folded plates is similar except that the effects of the stiffeners must be taken into account because no mesh is required the proposed method is superior for studying problems that would involve remeshing in the finite element method several examples are employed to show the convergence and accuracy of the proposed method the results obtained show good agreement with the results computed from the finite element analysis software ansys copyright 2005 john wiley sons ltd

complex time step newmark methods with controllable numerical dissipation in this paper unconditionally stable higher order accurate time step integration algorithms with controllable numerical dissipation are presented the algorithms are based on the newmark method with complex time steps the ultimate spectral radius the sub step locations j and the weighting factors j are the algorithmic parameters for an algorithm that is 2n 1 th order accurate the sub step locations which may be complex are shown to be the roots of an nth degree polynomial the polynomial is given explicitly in terms of n and the weighting factors are then obtained by solving a system of n simultaneous equations it is further shown that the order of accuracy is increased by one for the non dissipative algorithms with 1 the stability properties of the present algorithms are studied it is shown that if the ultimate spectral radius is set between 1 and 1 the eigenvalues of the numerical amplification matrix are complex with magnitude less than or equal to unity the algorithms are therefore unconditionally c stable when the ultimate spectral radius is set to 0 or 1 the algorithms are found to be equivalent to the first sub diagonal and diagonal pade approximations respectively the present algorithms are more general as the numerical dissipation is controllable and are very suitable for parallel computers the accuracy of the excitation responses is found to be enhanced by the present complex time step procedure to maintain high order accuracy the excitation may need some modifications 1998 john wiley sons ltd

non linear analysis of rectangular laminates under end shortening using shear deformation plate theory consideration is given to the prediction of the geometrically non linear elastic response of rectangular composite laminates with simply supported ends when subjected to uniform end shortening in their plane at the loaded ends lateral in plane expansion is either allowed freely or is prevented completely material properties of the laminates are quite general encompassing anisotropy and full coupling between in plane and out of plane behaviour first order shear deformation plate theory is used as the mathematical model of laminate behaviour and the non linearity is introduced in the strain displacement equations in the manner of the von karman assumptions the finite strip method is used as the main numerical analysis procedure and subsidiary use is made of the finite element method close comparison of results generated using the two methods is demonstrated in applications ranging from isotropic plates to unsymmetric anisotropic laminates further comparison with the results of an earlier developed finite strip method wherein properties are based on the use of classical plate theory shows the effect of through thickness shearing action in different situations

feedforward control design for finite time transition problems of non linear mimo systems under input constraints a new approach is presented for the feedforward control design of non linear systems with the application to finite time setpoint transitions under input constraints this contribution extends recently presented results for the siso case to non linear quadratic mimo systems the inversion based design treats the transition task as a two point boundary value problem bvp defined in the input output coordinates of the considered system for its solvability free parameters are provided in ansatz functions for the highest output derivatives this concept allows the direct incorporation of input constraints within the formulation of the bvp the resulting bvp with free parameters can be solved e g with a standard matlab function the load transport of an overhead crane serves as an example to illustrate the concept

a transient response analysis in the state space applying the average velocity concept an implicit direct time integration method for obtaining transient responses of general dynamic systems is described the conventional newmark method cannot be directly applied to state space first order differential equations which contain no explicit acceleration terms the method proposed here is the state space newmark method that incorporates the average velocity concept and can be applied to an analysis of general dynamic systems that are expressed by state space first order differential equations it is also readily coded into a program stability and accuracy analyses indicate that the method is numerically unconditionally stable like the conventional newmark method and has a period error of second order accuracy for small damping and fourth order for large damping and an amplitude error of second order regardless of damping in addition its utility and validity are confirmed by two application examples the results suggest that the proposed state space newmark method based on average velocity be generally applied to the analysis of transient responses of general dynamic systems with a high degree of reliability with respect to stability and accuracy

nonlinear analysis of corrugated plates using a fsdt and a meshfree method this paper presents a geometrically nonlinear analysis of stiffened and un stiffened corrugated plates using a meshfree galerkin method that is based on the first order shear deformation theory fsdt the strains are assumed to be small and the corrugated plates are modeled approximately as equivalent orthotropic plates the large deflection theory of von karman is adopted in the nonlinear analysis of the orthotropic plate and the equivalent flexure properties of the orthotropic plate are derived both the equivalent flexure and extensional properties are employed in the nonlinear analysis the stiffened corrugated plates are analyzed as stiffened orthotropic plates in which the stiffeners are modeled as beams and fitted to the equivalent orthotropic plate by implementing displacement compatibility conditions between the plate and the stiffeners because no mesh is required in the proposed method the stiffeners can be placed anywhere on the plate and changes to the positions of the stiffeners do not entail the remeshing of the plate to demonstrate the convergence and accuracy of the proposed method several numerical examples are employed the solutions that are computed by the proposed method are compared with precise solutions that are given by ansys using shell elements and with the results of other research work