buckling of arbitrary quadrilateral anisotropic plates the problem of buckling of arbitrary quadrilateral anisotropic plates with different boundary conditions under combined in plane loading is considered a rayleigh ritz method combined with a variational formulation and a first order transverse shear deformation theory is used the ritz functions consist of polynomials which include circulation functions that impose various boundary conditions numerical results are obtained for isotropic orthotropic and anisotropic plates with skewed geometries and are compared with existing results that use series solutions and with results generated from finite element simulations

separation of variables for quantum integrable systems on elliptic curves we extend sklyanin s method of separation of variables to quantum integrable models associated to elliptic curves after reviewing the differential case the elliptic gaudin model studied by enriquez feigin and rubtsov we consider the difference case and find a class of transfer matrices whose eigenvalue problem can be solved by separation of variables these transfer matrices are associated to representations of the elliptic quantum group e sl2 by difference operators one model of statistical mechanics to which this method applies is the interaction round a face model with antiperiodic boundary conditions the eigenvalues of the transfer matrix are given as solutions of a system of quadratic equations in a space of higher order theta functions

eigenvalue analysis of doubly connected plates with different configurations this paper deals with the vibration and buckling analyses of the first order shear deformable rhombic and square plates using a p type variational method the formulation includes rotary inertia and transverse shear terms the full plate is modeled with a single domain defined by a set of geometric points in the plane of the plate square and rectangular plates with a circular hole at the center are treated as the numerical example for the doubly connected plate and are modeled using one quarter of the geometry and only two elements the symmetry about x and y axes with regards to load and boundary conditions are exploited buckling coefficients and natural frequencies are calculated and compared with results from the published sources and the finite element method

vibrations of cylindrical shells with intermediate supports this paper is concerned with the free vibrations of circular cylindrical shells with rigid intermediate supports the simplest form of thin shell theory according to donnell and the reputed best first order approximation theory of sanders are considered an automated rayleigh ritz method is adopted to evaluate the natural frequencies and the mode shapes of the structures a proposed unified set of ritz functions is used to span the displacement fields of various types and combinations of end boundary conditions comparison and convergence studies are carried out to verify and establish the appropriate number of ritz functions to produce results with an acceptable order of accuracy shells with any number of intermediate supports and any combination of end boundary conditions can be analyzed by the proposed method effects of intermediate supports and their locations on natural frequencies of the shells are studied and the results presented for easy access by design engineers

prebuckling and buckling of unsymmetrically laminated composite panels with stringer run outs a meshless approach is developed and used to predict buckling loads of discretely assembled composite panels made from skin and stiffeners particular emphasis is given to stringer run outs within a stiffened panel where abrupt eccentricity can trigger very large transverse displacements of the skin in front of the run out tip and perturb the internal in plane loads distribution the effect of load eccentricity is included in the formulation the final set of nonlinear equations is obtained by combining von karman s formulation for moderately large deflections in plates with an extended timoshenko approach for small initial perturbations solutions are calculated by means of a rayleigh ritzmethod in conjunctionwith agalerkin technique orthogonal eigenfunctions are employed to expand the variables of interest in generalized fourier series an iterative algorithm is proposed to calculate buckling loads limits of applicability convergence of results and further potential exploitations are discussed numerical results are compared with those from finite element analysis and other numerical approaches

static and stability analyses of arbitrary straight sided quadrilateral thin plates by dqm abstract a differential quadrature dq methodology is employed for the static and stability analysis of irregular quadrilateral straight sided thin plates a four noded super element is used to map the irregular physical domain into a square computational domain second order transformation schemes with relative ease and low computational effort are employed to transform the fourth order governing equations of thin plates between the domains within the domain the displacements are the only degrees of freedom whereas along the boundaries the displacements as well as the second order derivatives of the displacements with respect to the associated normal coordinate variables in the computational domain are the two sets of degrees of freedom the implementation procedures for different boundary conditions including free edge boundaries are formulated to demonstrate the accuracy convergency and stability of the methodology detailed studies of skewed and trapezoidal plates for different geometries under different boundary and loading conditions are made good agreement is achieved between the results of the present methodology and those of other dq methodologies or other comparable numerical algorithms

existence of solutions for first order ordinary differential equations with nonlinear boundary conditions we present an existence theorem for nonlinear ordinary differential equations of first order with nonlinear boundary conditions the result includes for instance the initial value problem the final value problem and the antiperiodic boundary value problem the main novelty of the method lies in that it unifies different techniques for initial or boundary conditions

a generalized approach for implementing general boundary conditions in the gdq free vibration analysis of plates abstract a new approach for implementing general boundary conditions in the gdq free vibration analysis of rectangular plates is presented in this paper the proposed approach directly couples the boundary conditions with the governing equations and is referred to as the cbcge approach it can be applied to any combination of simply supported clamped and free boundary conditions the generality and accuracy of the cbcge approach are demonstrated through its application to the vibration analysis of a rectangular plate with various combinations of free edges and corners in particular the effect of grid point distribution on the numerical results for plates with free boundary conditions is discussed and a new grid point distribution is suggested

dsc ritz method for the free vibration analysis of mindlin plates this paper introduces a novel method for the free vibration analysis of mindlin plates the proposed method takes the advantage of both the local bases of the discrete singular convolution dsc algorithm and the pb 2 ritz boundary functions to arrive at a new approach called dsc ritz method two basis functions are constructed by using dsc delta sequence kernels of the positive type the energy functional of the mindlin plate is represented by the newly constructed basis functions and is minimized under the ritz variational principle extensive numerical experiments are considered by different combinations of boundary conditions of mindlin plates of rectangular and triangular shapes the performance of the proposed method is carefully validated by convergence analysis the frequency parameters agree very well with those in the literature numerical experiments indicate that the proposed dsc ritz method is a very promising new method for vibration analysis of mindlin plates copyright 2004 john wiley sons ltd

coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces abstract we introduce the concept of a mixed g monotone mapping and prove coupled coincidence and coupled common fixed point theorems for such nonlinear contractive mappings in partially ordered complete metric spaces presented theorems are generalizations of the recent fixed point theorems due to bhaskar and lakshmikantham t g bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal tma 65 2006 1379 1393 and include several recent developments

existence results for extremal solutions of interval fractional functional integro differential equations abstract in this study we introduce interval fractional functional integro differential equations iffides under the caputo generalized hukuhara fractional differentiability we establish some necessary comparison results and use the monotone iterative technique combined with the method of upper and lower solutions to investigate the existence of extremal solutions for iffides an example is presented to illustrate the results

formulation of mindlin engesser model for stiffened plate vibration in this paper a mindlin engesser model is developed for the vibration analysis of moderately thick plates with arbitrarily oriented stiffeners the theoretical derivation incorporates the mindlin theory to account for the effects of transverse shear deformation and rotary inertia of plates and the engesser theory to account for the shear deformation of stiffeners with the inclusion of torsion effect in the method of solution the resulting energy functionals are minimized using the ritz procedure with a set of admissible two dimensional functions expressed in the form of simple polynomials the key kinematic feature of these shape functions is that they are boundary oriented and no boundary losses are introduced as in discretization methods with the aim of demonstrating the applicability and versatility of the method numerical examples including plates of various shapes with arbitrarily oriented stiffeners are presented several findings and conclusions regarding the method have been highlighted and discussed

modeling of biological population problems using the element free kp ritz method a degenerate parabolic equation arising in the spatial diffusion of biological population is analyzed using the mesh free kp ritz method the mesh free kernel particle estimate is employed to approximate the 2d displacement field a system of discrete equations is obtained through application of the ritz minimization procedure to the energy expressions to validate the accuracy of the results and stability of the present method convergence studies were carried out based on influences of support size and number of nodes effectiveness of the mesh free kp ritz method for biological population model is investigated by numerical examples in this paper the present results were compared with results reported in extant literature and were found to be in good agreement with the literature

a mortar segment to segment contact method for large deformation solid mechanics abstract contact modeling is still one of the most difficult aspects of non linear implicit structural analysis most 3d contact algorithms employed today use node on segment approaches for contacting dissimilar meshes two pass node on segment contact approaches have the well known deficiency of locking due to over constraint in this work we develop and demonstrate a segment to segment contact approach based on the mortar method by eliminating the over constraint this method appears to be much more robust than the node on segment approach furthermore node on segment approaches suffer when individual nodes slide out of contact at contact surface boundaries or when contacting nodes slide from facet to facet this causes jumps in the contact forces due to the discrete nature of the constraint enforcement and difficulties in convergence for implicit solution techniques these jumps in forces are avoided in the segment to segment approach since penetration is measured by the occluded weighted volume which varies smoothly with perturbations until now all mortar schemes have been developed for small deformation sliding and have mainly been applied on flat surfaces here we will present the integration scheme and the linearization approach used for handling the contact surface integrals in the event of large sliding the schemes are designed to conserve linear momentum and can be applied to arbitrarily curved 3d surfaces although expensive our numerical examples demonstrate that the approach is far more robust than even smoothed node on segment contact techniques that is problems previously not solvable with node on segment can now be solved with our segment to segment contact

first order impulsive ordinary differential equations with anti periodic and nonlinear boundary conditions the monotone iterative technique is a powerful method that have been used to approximate the extremal solutions of several problems 1 2 on the other hand impulsive differential equations are a basic tool to study some problems of biology medicine engineering and physics 3 in this paper we deal with the following nonlinear boundary value problem for first order differential equation with impulses at fixed points

bending and buckling analysis of antisymmetric laminates using the moving least square differential quadrature method in this paper the moving least square differential quadrature mlsdq method is employed to bending and buckling analysis of antisymmetric thick laminates based on the first order shear deformation theory the displacement and rotation components of the plate are independently assumed with the centered moving least square mls approximation within each domain of influence the weighting coefficients are associated with the nodal partial derivatives which are calculated through a fast computation procedure together with the mls nodal shape functions numerical examples are illustrated to study the accuracy stability and convergence of the mlsdq method effects of support size order of the complete basis functions and node irregularity on the numerical accuracy are investigated typical computational results of displacements stresses and critical buckling loads of various laminated plates are presented and compared with the available exact and finite element solutions

buckling of arbitrary quadrilateral plates with intermediate supports using the galerkin method abstract a numerical method is developed for the stability analysis of arbitrary quadrilateral shaped elastic plates with internal supports the procedure uses the galerkin method in conjunction with the natural coordinates of the plate as a basis for the analysis of general plates the method is programmed and several numerical exaples are presented to illustrate the scope and efficacy of the procedure local plate buckling loads of skew rhombic trapezoidal and rectangular plates with intermediate line supports are obtained and where possible the results are compared with known solutions in the literature

approximate nonlinear analysis method for debonding of skin stringer composite assemblies doi 10 2514 1 31914 a nonlinear approach is developed and used to predict crack initiation in discretely assembled composite panels made from skin and stringers particular emphasis is given to stringer run outs within a stiffened panel for the optimization of novel composite wing configurations the nonlinear structural behavior is obtained by means of the von karman formulation for moderately large deflections in plates three dimensional assemblies are schematized and the effect of eccentricity is included in the simulation solutions are calculated by means of a rayleigh ritz approach based on galerkin s orthogonal eigenfunctions and a linear elastic fracture mechanics based model is used to simulate the crack initiation in the critical regions numerical results obtained by means of the present method are validated against tests reported in the literature and compared with advanced nonlinear finite element analysis limits of applicability and further potential exploitations are discussed a validation study showed fairly good correlation with reported experimental data

a new approach to the differential quadrature method for fourth order equations a generalized and more complete methodology for treating boundary conditions in the differential quadrature method dqm is presented this improved approach eliminates the deficiencies of the type grid arrangement which represents an approximation by applying the boundary conditions exactly two kinds of basis functions chebyshev and lagrange are used for concept demonstration it is found that the new approach cures most deficiencies of the current dqm 1997 by john wiley sons ltd

free vibration analysis of laminated orthotropic spherical shells abstract analytical solutions are presented for the free vibration of laminated orthotropic spherical shells the analysis is based on the application of the chebyshev galerkin spectral method for the evaluation of free vibration frequencies and mode shapes the eigenvalue problem is defined in terms of five equations of motion in terms of the meridional coordinate the circumference variation of the displacements being represented in a fourier series numerical results are presented to show the validity and accuracy of the proposed method results of parametric studies for laminated annular spherical shells with different orthotropic ratios opening angles lamination sequences and shear deformation are also presented

static and dynamic analysis of arbitrary quadrilateral flexural plates by b3 spline functions abstract this paper presents static and free vibration analysis of arbitrary quadrilateral flexural plates by b3 spline functions an actual arbitrary quadrilateral thin flat plate is mapped onto a square basic plate and a superelement is constructed for the whole plate the present numerical analysis is based on a spline net with finite spline points on the square basic plate combination of b3 spline functions gives an easy way to satisfy various boundary conditions the displacement function constructed by b3 spline functions in two directions has been formed to possess more flexibility to model the deflection shape efficiently the main features of the present method are minimal input preparation easier programming and higher accuracy achieved by a system with fewer degrees of freedom compared with analytical solutions and other numerical methods the method proposed yields excellent results for the test cases considered

monotone method for first order functional differential equations with retardation and anticipation abstract this paper discusses first order functional differential equations with retardation and anticipation by using the method of upper and lower solutions coupled with monotone iterative technique new existence results are obtained which improve known results in the literature

nonlinear boundary value problems of fractional differential systems in this paper we consider the existence of generalized solutions for fractional differential systems with nonlinear boundary value conditions we first establish a new comparison theorem by applying the monotone iterative technique and the method of lower and upper generalized solutions we obtain sufficient conditions for existence of extremal generalized solutions

a mixed higher order fem for fully coupled compressible transversely isotropic finite hyperelasticity a higher order mixed finite element method is presented for compressible transversely isotropic finite hyperelasticity the independent variables of the three field formulation are displacement fibre tension and fibre stretch the formulation admits the description of a fully coupled stress response which evolves from an almost isotropic one into a hyper anisotropic simply nearly inextensible response with increasing fibre tension as for example observed in soft tissue biomechanics standard displacement approximation of order p in h1 is used while the auxiliary variables are approximated element wise by square integrable functions of order p 1 in l2 for finite extensibility the auxiliary variables are statically condensed out yielding a pure displacement based method it is implemented in an hp adaptive finite element code a matching residual based error estimation capability is added and exercised numerical evidence indicating stability of approximation is supplied resolving a boundary layer caused by almost inextensible fibres coupled and uncoupled stress responses are compared a generalised compressible transversely isotropic holzapfel gasser ogden model is developed for the formulation that intentionally avoids the volumetric isochoric split solutions obtained with the mixed method compare favourably to the corresponding ones obtained with pure displacement formulation the latter fails in certain strongly anisotropic cases

a semi smooth newton method for orthotropic plasticity and frictional contact at finite strains abstract a new approach for the unified treatment of frictional contact and orthotropic plasticity at finite strains using semi smooth newton methods is presented the contact discretization is based on the well known mortar finite element method using dual lagrange multipliers to facilitate the handling of the additional lagrange multiplier degrees of freedom exploiting the similarity of the typical inequality constraints of plasticity and friction all involved discrete inequalities are reformulated as nonlinear non smooth equations using complementarity functions the resulting set of discrete semi smooth equations can be solved efficiently by a variant of newton s method where all additionally introduced variables are condensed from the global system so that a linear system only consisting of the displacement degrees of freedom has to be solved in each iteration step in contrast to classical radial return mapping methods for computational plasticity the plastic constraints are not required to hold at every iterate in the nonlinear solution procedure but only at convergence this relaxation in the pre asymptotic behavior results in an increased flexibility regarding algorithm design and a potentially higher robustness compared to radial return mapping algorithms the presented elasto plasticity algorithm includes arbitrary isotropic hyperelasticity an anisotropic hill type yield function with isotropic and kinematic hardening plastic spin and appropriate finite element technology for nearly incompressible materials therefore it is well suited for the modeling of sheet metal forming and similar processes several numerical examples underline the robustness of the proposed plasticity algorithm and the efficient treatment of elasto plastic contact problems

an edge based smoothed finite element method es fem with stabilized discrete shear gap technique for analysis of reissner mindlin plates abstract an edge based smoothed finite element method es fem for static free vibration and buckling analyses of reissner mindlin plates using 3 node triangular elements is studied in this paper the calculation of the system stiffness matrix is performed by using the strain smoothing technique over the smoothing domains associated with edges of elements in order to avoid the transverse shear locking and to improve the accuracy of the present formulation the es fem is incorporated with the discrete shear gap dsg method together with a stabilization technique to give a so called edge based smoothed stabilized discrete shear gap method es dsg the numerical examples demonstrated that the present es dsg method is free of shear locking and achieves the high accuracy compared to the exact solutions and others existing elements in the literature

stability and vibration of shear deformable plates first order and higher order analyses abstract this work presents the highly accurate numerical calculation of the natural frequencies and buckling loads for thick elastic rectangular plates with various combinations of boundary conditions the reissener mindlin first order shear deformation plate theory and the higher order shear deformation plate theory of reddy have been applied to the plate s analysis the governing equations and the boundary conditions are derived using the dynamic version of the principle of minimum of the total energy the solution is obtained by the extended kantorovich method this approach is combined with the exact element method for the vibration and stability analysis of compressed members which provides for the derivation of the exact dynamic stiffness matrix including the effect of in plane and inertia forces the large number of numerical examples demonstrates the applicability and versatility of the present method the results obtained by both shear deformation theories are compared with those obtained by the classical thin plate s theory and with published results many new results are given too

fixed point theorems in partially ordered metric spaces for operators with ppf dependence abstract in this paper fixed point theorems of a nonlinear operator are developed where the domain space c a b e is different from the range e which is a metric space with partial order an application of the fixed point theorem to a periodic boundary value problem with delay is also given

toward a universal h p adaptive finite element strategy part 1 constrained approximation and data structure abstract this is the first of a series of papers devoted to the development of an adaptive finite element method to solve various boundary value problems arising in solid and fluid mechanics the paper deals with the general concepts of h p finite element methods constrained approximation and data structure and related issues several numerical examples illustrate the main ideas of the method

free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first order shear deformation theory in this study free vibration of laminated skew plates was investigated discrete singular convolution dsc method is used for numerical solution of vibration problems the straight sided quadrilateral domain is mapped into a square domain in the computational space using a four node element by using the geometric transformation typical results are presented for different geometric parameters and boundary conditions it is concluded from the results that the skew angle have considerable influence on the variations of the frequencies with fibre orientation angle and number of layers in the laminate the results obtained by dsc method are compared with those obtained by analytical and numerical approaches it is shown that reasonable accurate results are obtained present work also indicates that the method of dsc is a promising and potential approach for computational mechanics copyright 2009 john wiley sons ltd

dynamic stability analysis of composite laminated cylindrical shells via the mesh free kp ritz method abstract in this paper a novel numerical technique is developed for the dynamic stability analysis of composite laminated cylindrical shells under static and periodic axial forces the mesh free kernel particle kp estimate is employed in hybridized form with harmonic functions to approximate the 2 d transverse displacement field a system of mathieu hill equations is obtained through the application of the ritz minimization procedure to the energy expressions the principal instability regions are then analyzed via bolotin s first approximation the mesh free kp ritz method is validated through comparison with existing available numerical data taken from open literature effects of boundary conditions and lamination schemes on the instability regions are also examined in detail

existence results and monotone iterative technique for impulsive hybrid functional differential systems with anticipation and retardation we study some existence results for impulsive hybrid functional differential equations with anticipation and retardation by using the existence theory of impulsive hybrid delay differential equations the monotone iterative technique relative to the coupled lower and upper solutions has also been developed for impulsive hybrid functional differential equations with both anticipation and retardation

rapid analysis of variable stiffness beams and plates legendre polynomial triple product formulation copyright 2017 john wiley sons ltd numerical integration techniques are commonly employed to formulate the system matrices encountered in the analysis of variable stiffness beams and plates using a ritz based approach computing these integrals accurately is often computationally costly herein a novel alternative is presented the recursive analytical polynomial integral definition rapid formulation the rapid formulation offers a significant improvement in the speed of analysis achieved by reducing the number of numerical integrations that are performed by an order of magnitude a common legendre polynomial basis is employed for both trial functions and stiffness load variations leading to a common form for the integrals encountered the legendre polynomial basis possesses algebraic recursion relations that allow these integrals to be reformulated as triple products with known analytical solutions defined compactly using the wigner 3j coefficient the satisfaction of boundary conditions calculation of derivatives and transformation to other bases is achieved through combinations of matrix multiplication with each matrix representing a unique boundary condition or physical effect therefore permitting application of the rapid approach to a variety of problems indicative performance studies demonstrate the advantage of the rapid formulation when compared to direct analysis using matlab s integral and integral2 copyright 2017 john wiley sons ltd

static analysis of frame structures by the differential quadrature element method in this paper a new version of differential quadrature method dqm is proposed and then extended to analyse frame structures the new method called the differential quadrature element method dqem retains all advantages of the earlier version of the differential quadrature method and overcomes some critical shortcomings existing in the original dqm the proposed method is however different from the quadrature element method qem proposed earlier by striz et al the methodology is explained in details herein via a differential quadrature beam element and some numerical examples are given to show the efficiency of the present method 1997 by john wiley sons ltd

buckling analysis of general triangular anisotropic plates using polynomials the problem of buckling of general triangular anisotropic plates with different boundary conditions subjected to combined in plane loads is considered solutions for plate buckling are obtained by using a rayleigh ritz method combined with a variational formulation the ritz functions consist of polynomials that include circulation functions that are used to impose various boundary conditions both classical laminated plate theory and first order shear deformation theory are used numerical buckling results obtained for isotropic and anisotropic triangular plates are compared with results from existing series solutions

functional determinants from wronski green functions a general technique is developed for calculating functional determinants of second order differential operators with dirichlet periodic and antiperiodic boundary conditions without the knowledge of spectral properties as an example we give explicit formulas for a harmonic oscillator with an arbitrary time dependent frequency where our result is a generalization of the gel fand yaglom famous formula for dirichlet boundary conditions our technique is based on the wronski s construction of green functions which does not require spectral knowledge our final formula expresses the ratios of functional determinants in terms of an ordinary 2 2 determinant of a constant matrix constructed from two linearly independent solutions of the homogeneous differential equations associated with second order differential operators for ratios of determinants encountered in semiclassical fluctuations around a classical solution the result can further be expressed in terms of the classical solution special properties of operators with a zero mode are exhibited

dual quadratic mortar finite element methods for 3d finite deformation contact mortar finite element methods allow for a flexible and efficient coupling of arbitrary nonconforming interface meshes and are by now quite well established in nonlinear contact analysis in this pa

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

analysis finite element computation and error estimation in transversely isotropic nearly incompressible finite elasticity abstract in this paper we present constitutive models for nearly incompressible transversely isotropic materials in finite hyperelasticity particularly for reinforced rubber like materials which are of essential engineering interest the theory is developed using a convected curvilinear coordinate system based on a mixed two field displacement pressure energy functional furthermore an a posteriori error estimator without multiplicative constants is derived for non linear anisotropic problems which measures the discretization error in the first piola kirchhoff stresses in the l 2 norm by solving local neumann problems with equilibrated tractions illustrative numerical examples demonstrate the anisotropic material behaviour of reinforced materials and the efficiency of using adaptive finite element methods

buckling of rectangular mindlin plates subjected to partial in plane edge loads using the radial point interpolation method this paper considers the elastic buckling of rectangular mindlin plates that are subjected to partially distributed in plane edge loadings a numerical algorithm based on the radial point interpolation method rpim is proposed for the solution of such plates the pre buckling stresses are first determined using the rpim based on a two dimensional 2 d elastic plane stress problem the buckling load intensity factors for rectangular plates that incorporate these predetermined pre buckling stresses are then computed via the rpim based on the mindlin plate theory numerical examples of the plates with various boundaries and subjected to different partially distributed in plane edge loadings are presented shear locking of the buckling load is studied the results demonstrate the high accuracy of the proposed rpim

the free flexural vibration of right triangular isotropic and orthotropic plates abstract a simple straighforward rayleigh ritz analysis is given for the determination of an eigenproblem for the free flexural vibration of thin right triangular plates having any combination of the classical free simply supported or clamped boundary conditions simple polynomials are used as the admissible functions and a recurrence relationship facilitates the evaluation of the necessary integrals the analysis is developed for specially orthotropic plates but numerical results are given primarily for the isotropic case

a new differential quadrature methodology for beam analysis and the associated differential quadrature element method this paper presents a computationally efficient and an accurate new methodology in differential quadrature analysis of beam elements the methodology would overcome the difficulties in boundary conditions implementations of fourth order differential equations encountered in such problems the methodology benefited from defining the second order derivatives along the boundaries as independent degrees of freedom would enable the differential quadrature method to exactly satisfy some types of boundary conditions where by most other conventional algorithms have to be satisfied approximately the weighting coefficients employed are not exclusive and any accurate and efficient method such as the generalized differential quadrature method may be used to produce the methods weighting coefficients by solving some typical stability deflection and frequency analysis beam problems and by comparing the results with those of exact solutions and or those of other methodologies accuracy convergency and efficiency of the methodology is asserted in order to generalize its application to large scale beam structures and to the cases with the discontinuity in loading conditions and geometry a new one dimensional differential quadrature element method formulation is presented and implemented

a semi analytical dqem for free vibration analysis of thick plates with two opposite edges simply supported this paper is introducing a semi analytical differential quadrature element method dqem based on first order shear deformation theory for free vibration analysis of thick plates by decomposing the plate into a series of sub domains or elements any discontinuity in geometry material properties and elastic foundations in one direction can be handled conveniently classical as well as non classical boundary conditions can be imposed one benefits of this semi analytical dqem is reducing the storage requirements and the computational efforts needed to assemble the global equations the method would also increase the computational efficiency in comparison with the finite element method fem or differential quadrature method dqm analysis of such problems the accuracy versatility stability and convergence of the algorithm are certified

free vibration and buckling analyses of shear deformable plates based on fsdt meshfree method abstract a meshfree method based on the reproducing kernel particle approximate is employed for the free vibration and buckling analyses of shear deformable plates in this approach the first order mindlin reissner plate theory fsdt is used and the displacement shape functions are constructed using the reproducing kernel approximation satisfying the consistency condition the essential boundary conditions are enforced by a transformation method numerical examples considering various aspect ratios skew angles and boundary conditions are demonstrated to show the validity of the proposed method and satisfactory results were obtained when comparisons are made with the exact and other available numerical results existing in the literature

buckling of thick skew plates the paper considers the elastic buckling of thick skew plates up to now very little work has been done on this subject and the paper aspires to fill this gap based on the principle of stationary total potential energy and the recently developed pb 2 rayleigh ritz method as a solution procedure buckling solutions for skew plates of various aspect ratios skew angles and boundary conditions are determined the tabulation of these results not available thus far should be useful to designers and researchers who may use them as benchmark values to test the validity and convergence of their numerical techniques and softwares for thick plate analysis

an h adaptive mortar finite element method for finite deformation contact with higher order p extension in this work we present a generalization of the mortar segment to segment method for finite deformations contact to an h adaptive version with possible p extension i e using higher order approximation we recall the main ideas of the mortar algorithm and present the key aspects of adaptivity error estimation and an h adaptive strategy the p extension exploits the feature of the hp adaptive code in which the contact solver is implemented to handle meshes with nodes of nonuniform orders we use it to set interior nodes to higher order while leaving linear boundary contact nodes which can be processed by the standard mortar algorithm accuracy of elements with low order nodes is restored by adequate subdividing of these elements adaptivity and p extension are illustrated with a few numerical tests

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

analysis of axisymmetric free vibration of isotropic shallow spherical sheels with a circular hole abstract a general solution for the third order differential equations of a thin isotropic shallow spherical shell with a circular hole subject to axisymmetric free vibration is presented in this paper the frequency equation in terms of bessel functions and modified bessel functions is solved for the fundamental vibrational frequency and mode shape a finite element model is presented for comparison with the analytical solution the relationship between the vibrational frequency and mode shape and the size of the cutout is discussed

some a posteriori error estimators for elliptic partial differential equations we present three new a posteriori error estimators in the energy norm for finite element solutions to elliptic partial differential equations the estimators are based on solving local neumann problems in each element the estimators differ in how they enforce consistency of the neumann problems we prove that as the mesh size decreases under suitable assumptions two of the error estimators approach upper bounds on the norm of the true error and all three error estimators are within multiplicative constants of the norm of the true error we present numerical results in which one of the error estimators appears to converge to the norm of the true error

out of plane static analysis of circular arches by dqm the differential quadrature dq methodology introduced by the authors see comput methods appl mech engng 191 2002a 3509 int j solids struct 39 19 2002b 4927 int j numer methods engng 54 3 2003a 847 j sound vibrat 263 2 2003b 415 is employed for out of plane static analysis of circular arches under a wide spectrum of boundary conditions in addition to the classical boundary conditions elastic restraints against translation and rotation are also considered different loading conditions are examined several examples of arches with uniform continuous or stepped varying cross sections are presented to demonstrate the accuracy of the methodology the domain decomposition technique in conjunction with the present dq methodology is examined for certain cases the results are compared with those of exact solutions for several uniform or stepped sections arches and also for arches on elastic foundations accurate converged numerical solutions are obtained with only few grid points

an efficient differential quadrature methodology for free vibration analysis of arbitrary straight sided quadrilateral thin plates in this paper a new differential quadrature dq methodology is employed to study free vibration of irregular quadrilateral straight sided thin plates a four nodded super element is used to map the irregular physical domain into a square domain in the computational domain second order transformation schemes with relative ease and less computation are employed to transform the fourth order governing equation of thin plates between the two domains the only degree of freedom within the domain is the displacement whereas along the boundaries the displacement as well as the second order derivative of the displacement with respect to associated normal co ordinate variable in computational domain are the two degrees of freedom implementing the method the formulation for the dq method for the free vibration analysis of plates of straight sided shapes was presented together with the implementation procedure for the different boundary conditions to demonstrate the accuracy convergency and stability of the new methodology detail studies are made on isotropic plates at acute angles with different geometries boundary and loading conditions including dq free edge boundary condition implementations accurate results even with fewer degrees of freedom than for those of comparable numerical algorithms were achieved

a segment to segment mortar contact method for quadratic elements and large deformations abstract this paper describes a new extension of mortar based segment to segment algorithms for large deformation contact analysis permitting their use when quadratic interpolations are used in the underlying finite element method the work builds upon results previously described by puso and laursen m a puso t a laursen a mortar segment to segment contact method for large deformation solid mechanics comput methods appl mech engrg 193 2004 601 629 m a puso t a laursen a mortar segment to segment frictional contact method for large deformations comput methods appl mech engrg 193 2004 601 629 where methods were developed for quasistatic and implicit dynamic analysis in the context of linear element interpolations here we see that many algorithmic ideas from the linear case can be adopted for use with quadratic elements along with different alternative interpolations of the mortar contact multipliers the result is a class of methods appropriate for use for either mesh tying true large sliding simulation frictionless or frictional and readily admits mixing of element types several numerical examples are given to demonstrate the effectiveness of the approach

approximation of the buckling problem for reissner mindlin plates this paper deals with the approximation of the buckling coefficients and modes of a clamped plate modeled by the reissner mindlin equations these coefficients are the reciprocals of the eigenvalues of a noncompact operator we give a spectral characterization of this operator and show that the relevant buckling coefficients correspond to isolated nondefective eigenvalues then we consider the numerical computation of these coefficients and their corresponding modes for the finite element approximation of reissner mindlin equations it is well known that some kind of reduced integration or mixed interpolation has to be used to avoid locking in particular we consider duran liberman elements which have been already proved to be locking free for load and vibration problems we adapt the classical approximation theory for noncompact operators to obtain optimal order error estimates for the eigenfunctions and a double order for the eigenvalues these estimates are valid with constants independent of the plate thickness we report some numerical experiments confirming the theoretical results finally we refine the analysis in the case of a uniformly compressed plate

nonlinear boundary value problems of fractional functional integro differential equations in this paper we consider the existence of generalized solutions for fractional functional integro differential equations of mixed type with nonlinear boundary value conditions by establishing a new comparison theorem and applying the monotone iterative technique we show the existence of extremal generalized solutions

quasilinearization for functional differential equations with retardation and anticipation abstract the technique of generalised quasilinearization is developed using the method of lower and upper solutions and the monotone iterative technique mit to prove the existence of unique solutions for functional differential equations fde with retardation and anticipation

monotone iterative technique for functional differential equations with retardation and anticipation abstract the method of the monotone iterative technique together with coupled lower and upper solutions is employed to prove existence and uniqueness results for functional differential equations involving retardation and anticipation

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

a mixed finite element formulation for slightly compressible finite elasticity with stiff fibre reinforcement two fibre families uniaxial tension formulation abstract we propose a novel finite element based formulation for the solution of the static mechanical mixed boundary value problem of a finite elastic solid reinforced by two distinct stiff fibre families the fibre tensions are assumed decoupled and uniaxial at out set the associated energy conjugate fibre stretch rates are shown to be uniaxial by duality the natively displacement dependent fibre tension fibre stretch pairs are replaced by auxiliary independent variables the complementary displacement based stresses and energy conjugate strain rates become tensionless and stretch rate less in the two fibre directions respectively by construction an additively decoupled hyperelastic strain energy ansatz in terms of the fibre stretches and a novel apparently doubly stretchless cauchy green tensor is used the displacement based part of the formulation is set in an apparently inextensible fibre metric space the proposed uniaxial fibre tension description is statically exact for the fully constrained problem and the novel doubly stretchless cauchy green tensor is conditionally kinematically admissible in its vicinity the formulation is realised as a five field mixed finite element method admitting separate higher order approximations in h 1 for the displacement and in l 2 for the energy conjugate fibre tensions and stretches respectively the convergence and correctness of the implementation is verified by numerical and analytical examples

implementation of clamped and simply supported boundary conditions in the gdq free vibration analysis of beams and plates abstract in this paper a new methodology for implementing the clamped and simply supported boundary conditions is presented for the free vibration analysis of beams and plates using the generalized differential quadrature gdq method the proposed approach directly substitutes the boundary conditions into the governing equations and is referred to as sbcge approach the sbcge approach is presented to overcome the drawbacks of previous approaches in treating the boundary conditions a comparison of the sbcge approach with the method of modifying weighting coefficient matrices mwcm is made by their application to the vibration analysis of beams and plates with combinations of simply supported and clamped boundary conditions some details of the gdq method are also described in the paper

application of two dimensional orthogonal plate function to flexural vibration of skew plates abstract a set of two dimensional orthogonal plate functions is used as an admissible deflection function for the study of the flexural vibration of skew plates by the rayleigh ritz method from a prescribed starting function satisfying the boundary conditions the higher terms in the two dimensional orthogonal plate functions are generated by using the gram schmidt orthogonalization process the method is applied to obtain results for a few particular rhombic plates with different support conditions at various skew angles where possible the numerical results presented are compared with the values obtained by other numerical methods in the literature the results should be of considerable value and practical significance in design applications

the element free kp ritz method for free vibration analysis of conical shell panels in this paper the free vibration of conical panels is analyzed by the mesh free kp ritz method both 1 d and 2 d versions of the kp ritz approach are formulated for conical panels for conical panels with two simply supported straight edges the 1 d kp ritz version is used where the kernel particle estimation is employed in hybridized form with harmonic functions to approximate the 2 d displacement field for conical panels having arbitrary boundary conditions the displacement field is approximated by the 2 d kp ritz version with 2 d form of kernel particle functions employed the classical thin shell theory based on love s hypothesis is employed in the present analyses and based on the kernel particle concept and ritz technique the eigenequations of the frequencies of the conical panels are obtained to validate the accuracy of stability of the present method convergence studies were carried out based on the influences of the support size and the number of nodes comparisons were also made with existing results available in the open literature this study also examines in detail the effects of variation in the semi vertex angle and boundary conditions on the frequency characteristics of conical panels

existence of a solution for the fractional differential equation with nonlinear boundary conditions using the method of upper and lower solutions and its associated monotone iterative we present an existence theorem for a nonlinear fractional differential equation with nonlinear boundary conditions

existence results for discontinuous functional differential systems in this paper we study solvability of first order discontinuous functional differential systems equipped with discontinuous functional initial conditions a concrete example is presented and solved to illustrate the obtained results

a posteriori error estimates for nonlinear problems finite element discretizations of elliptic equations we give a general framework for deriving a posteriori error estimates for approximate solutions of nonlinear problems in a first step it is proven that the error of the approximate solution can be bounded from above and from below by an appropriate norm of its residual in a second step this norm of the residual is bounded from above and from below by a similar norm of a suitable finite dimensional approximation of the residual this quantity can easily be evaluated and for many practical applications sharp explicit upper and lower bounds are readily obtained the general results are then applied to finite element discretizations of scalar quasi linear elliptic partial differential equations of 2nd order the eigenvalue problem for scalar linear elliptic operators of 2nd order and the stationary incompressible navier stokes equations they immediately yield a posteriori error estimates which can easily be computed from the given data of the problem and the computed numerical solution and which give global upper and local lower bounds on the error of the numerical solution

analyzing two dimensional sine gordon equation with the mesh free reproducing kernel particle ritz method abstract we consider an analysis of the non linear two dimensional sine gordon sg equation the analysis is performed using the mesh free reproducing kernel particle ritz method kp ritz method the mesh free kernel particle estimate is employed to approximate the 2d displacement field a system of discrete equations is obtained through application of the ritz minimization procedure to the energy expressions to validate the accuracy of the results and stability of the present method convergence studies were carried out based on influences of support size and number of nodes the present results were compared with results reported in extant literature and were found to be in good agreement with the literature

the generalized differential quadrature rule for fourth order differential equations the generalized differential quadrature rule gdqr proposed here is aimed at solving high order differential equations the improved approach is completely exempted from the use of the existing point technique by applying multiple conditions in a rigorous manner the gdqr is used here to static and dynamic analyses of bernoulli euler beams and classical rectangular plates numerical error analysis caused by the method itself is carried out in the beam analysis independent variables for the plate are first defined the explicit weighting coefficients are derived for a fourth order differential equation with two conditions at two different points it is quite evident that the gdqr expressions and weighting coefficients for two dimensional problems are not a direct application of those for one dimensional problems the gdqr are implemented through a number of examples good results are obtained in this work copyright 2001 john wiley sons ltd

iterative solutions for a coupled system of fractional differential integral equations with two point boundary conditions abstract in this paper we deal with a coupled system of fractional differential integral equations with two point boundary conditions the maximal and minimal solutions are obtained by using the monotone iterative technique combined with the method of upper and lower solutions meantime the error estimate of the solutions are given in the end some examples are given to illustrate the results

a dual mortar approach for 3d finite deformation contact with consistent linearization in this paper an approach for three dimensional frictionless contact based on a dual mortar formulation and using a primal dual active set strategy for direct constraint enforcement is presented we focus on linear shape functions but briefly address higher order interpolation as well the study builds on previous work by the authors for two dimensional problems first and foremost the ideas of a consistently linearized dual mortar scheme and of an interpretation of the active set search as a semi smooth newton method are extended to the 3d case this allows for solving all types of nonlinearities i e geometrical material and contact within one single newton scheme owing to the dual lagrange multiplier approach employed this advantage is not accompanied by an undesirable increase in system size as the lagrange multipliers can be condensed from the global system of equations moreover it is pointed out that the presented method does not make use of any regularization of contact constraints numerical examples illustrate the efficiency of our method and the high quality of results in 3d finite deformation contact analysis

a posteriori error estimates of higher order finite elements for frictional contact problems abstract in this paper a posteriori estimates are derived for higher order finite element methods and frictional contact problems the discretization is based on a mixed approach where the geometrical and frictional constraints are captured by lagrange multipliers the use of higher order polynomials leads to a certain non conformity in the discretization which requires special attention in the error analysis as a main result an error estimation is proposed which consists of the dual norm of a residual plus some computable remainder terms the residual is estimated by well known a posteriori error estimates for variational equations the remainder terms represent typical sources resulting from the non conforming mixed discretization numerical experiments confirm the applicability of the a posteriori estimates to adaptive mesh refinements

buckling of moderately thick arbitrarily shaped plates with intermediate point supports using a simple hp cloud method abstract this paper presents the simple hp cloud meshless method for the stability analysis of moderately thick plates with various shapes subjected to uniaxial and biaxial in plane compressive and pure shear loads to allow the effect of transverse shear deformation on the critical buckling load of the plate the mindlin s plate theory is employed simple hp cloud method is applied for constructing the cloud shape functions and for discretization of the domain shepard functions are also used for the partition of unity and complete polynomials are utilized for the enrichment functions part the simple hp cloud method has kronecker delta property so contrary to most of meshless methods the essential boundary conditions can be imposed directly constructing the stiffness and geometry matrices leads to an eigenvalue problem that should be solved to determine the critical buckling load of the plate numerical results are verified against the results reported elsewhere to illustrate the accuracy and effectiveness of the present method to show the applications of simple hp cloud method in the buckling analysis of moderately thick plates local buckling coefficients of various shapes of plates rectangular skew trapezoidal triangular circular semi circular hexagonal and general shape with different boundary conditions are determined also local buckling coefficients of plates with point supports and intermediate support are calculated

quasilinear iterative scheme for a fourth order differential equation with retardation and anticipation abstract in this paper the estimations of error between the approximate solution and the solution for a fourth order differential equation with retardation and anticipation are given by employing the quasilinear iterative scheme and the approximate quasilinear iterative scheme

a unified approach to a posteriori error estimation using element residual methods this paper deals with the problem of obtaining numerical estimates of the accuracy of approximations to solutions of elliptic partial differential equations it is shown that by solving appropriate local residual type problems one can obtain upper bounds on the error in the energy norm moreover in the special case of adaptiveh p finite element analysis the estimator will also give a realistic estimate of the error a key feature of this is the development of a systematic approach to the determination of boundary conditions for the local problems the work extends and combines several existing methods to the case of fullh p finite element approximation on possibly irregular meshes with elements of non uniform degree as a special case the analysis proves a conjecture made by bank and weiser some a posteriori error estimators for elliptic partial differential equations math comput 44 283 301 1985