Analysis Of Shear Deformable Plates Research Articles

Stochastic analysis of moderately thick plates using the generalized polynomial chaos and element free Galerkin method

In this paper, the element free Galerkin method is combined with the generalized polynomial chaos to quantify the uncertainties in the bending analysis of shear deformable plates with elastically restrained edges resting on a Pasternak elastic foundation with random system properties. The plate modules of elasticity, stiffnesses of the elastically restrained edges and the foundation stiffnesses are considered as random processes and are represented by using the Karhunen–Loève expansion. It is shown that the results obtained by the presented method are in a very good agreement with the results of Monte Carlo simulations in spite of using low order polynomials in the generalized polynomial chaos expansion. Also the applicability and versatility of the presented method are demonstrated by solving numerical examples for various values of coefficient of variations, aspect ratio, thickness and several combinations of boundary conditions, different types of lateral loading and various values of stiffnesses of restrained edges and elastic foundation.

A coupled BEM-stiffness matrix approach for analysis of shear deformable plates on elastic half space

In this paper, a new direct Boundary Element Method (BEM) is presented to solve plates on elastic half space (EHS). The considered BEM is based on the formulation of Vander Weeën for the shear deformable plate bending theory of Reissner. The considered EHS is the infinite EHS of Boussinesq–Mindlin or the finite EHS (with rigid end layer) of Steinbrenner. The multi-layered EHS is also considered. In the present formulation, the soil stiffness matrix is computed. Hence, this stiffness matrix is directly incorporated inside the developed BEM. Several numerical examples are considered and results are compared against previously published analytical and numerical methods to validate the present formulation.

Dynamic analysis of shear deformable plates using the Dual Reciprocity Method

The Dual Reciprocity Method is a popular mathematical technique to treat domain integrals in the boundary element method (BEM). This technique has been used to treat inertial integrals in the dynamic thin plate bending analysis using a direct formulation of the BEM based on the elastostatic fundamental solution of the problem. In this work, this approach was applied for the dynamic analysis of shear deformable plates based on the Reissner plate bending theory, considering the rotary inertia of the plate. Three kinds of problems: modal, harmonic and transient dynamic analysis, were analyzed. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed formulation.

Buckling analysis of shear deformable plates using the quadrature element method

The recently proposed weak form quadrature element method (QEM) is applied to buckling analysis of shear deformable plates. Integrals involved in the variational description a plate are evaluated first by an efficient numerical integration scheme wherein the partial derivatives at the integration points are approximated using differential quadrature analogs. In a quadrature element, neither the node pattern nor the number of nodes is fixed, being adjustable according to convergence need. Three examples are presented and comparison with finite element results is made to demonstrate the effectiveness and computational efficiency of the QEM for buckling analysis of shear deformable plates.

Nonlinear buckling formulations and imperfection models for shear deformable plates by the boundary element method

This paper presents a nonlinear buckling analysis of shear deformable plates. Two models of imperfections are introduced: small uniform transverse loads and distributed transverse loads, according to the number of half-waves indicated by the eigenvectors from linear elastic buckling analysis. A simple numerical algorithm is presented to analyze the problems. Numerical examples with different geometries, loading and boundary conditions are presented to demonstrate the accuracy of the formulation.

Analysis of shear deformable plates with combined geometric and material nonlinearities by boundary element method

In this paper a boundary element formulation for analysis of shear deformable plates with combined geometric and material nonlinearities by boundary element method is presented. The dual reciprocity method is used in dealing with the geometric nonlinearity and domain discretization is implemented in dealing with material nonlinearity. The material is assumed to undergo large deflection with small strains. The von Mises criteria is used to evaluate the plastic zone and an elastic perfectly plastic material behaviour is assumed. An initial stress formulation is used to formulate the boundary integral equations. A total incremental method is applied to solve the nonlinear boundary integral equations. Numerical examples are presented to demonstrate the validity and the accuracy of the proposed method.

Boundary element frequency domain formulation for dynamic analysis of Mindlin plates

AbstractA new boundary element formulation for analysis of shear deformable plates subjected to dynamic loading is presented. Fundamental solutions for the Mindlin plate theory are derived in the Laplace transform domain. The characteristics of the three flextural waves are studied in the time domain. It is shown that the new fundamental solutions exhibit the same strong singularity as in the static case.Two numerical examples are presented to demonstrate the accuracy of the boundary element method and comparisons are made with the finite element method. Copyright © 2006 John Wiley & Sons, Ltd.

Buckling analysis of shear deformable plates by boundary element method

AbstractIn this paper, the derivation and numerical implementation of boundary integral equations for the buckling analysis of shear deformable plates are presented. Plate buckling equations are derived as a standard eigenvalue problem. The formulation is formed by coupling boundary element formulations of shear deformable plate and two dimensional plane stress elasticity. The eigenvalue problem of plate buckling yields the critical load factor and buckling modes. The domain integrals which appear in this formulation are treated in two different ways: initially the integrals are evaluated using constant cells, and next, they are transformed into equivalent boundary integrals using the dual reciprocity method (DRM). Several examples with different geometry, loading and boundary conditions are presented to demonstrate the accuracy of the formulation. Copyright © 2004 John Wiley & Sons, Ltd.

Boundary Element Analysis of Cracks in Shear Deformable Plates and Shells. Topics in Engineering, Vol 43

Boundary Element Analysis of Cracks in Shear Deformable Plates and Shells. Topics in Engineering, Vol 43

Moving least squares differential quadrature method and its application to the analysis of shear deformable plates

AbstractA moving least squares differential quadrature (MLSDQ) method is developed and employed for the analysis of moderately thick plates based on the first‐order shear deformation theory (FSDT). To carry out the analysis, the governing equations in terms of the generalized displacements (transverse deflection and two rotations) of the plate are formulated by employing the moving least squares approximation. The weighting coefficients used in the MLSDQ approximation are computed through a fast computation of shape functions and their derivatives. Numerical examples illustrating the accuracy, stability and convergence of the MLSDQ method are presented. Effects of support size, order of completeness and node irregularity on the numerical accuracy are investigated. Copyright © 2003 John Wiley & Sons, Ltd.

Differential cubature method for analysis of shear deformable rectangular plates on Pasternak foundations

In this paper, the differential cubature method (DCM) was applied to the bending analysis of shear deformable plates resting on Pasternak foundation. An attractive advantage of the DCM is that it can produce the acceptable accuracy of numerical results with very few grid points in the solution domain and therefore can be very useful for rapid evaluation in engineering design. The detailed procedures for discretizing the governing equations and boundary conditions of the title problems using the DCM are presented. Numerical solutions for rectangular thick plates on Pasternak foundation and subjected to different boundary conditions are obtained. The convergence studies are carried out to establish the minimal grid points needed for achieving accurate solutions. Next, the solutions for some selected cases are presented and verified by comparing them with the published values. It is observed that the DCM is able to furnish convergent solution with relatively fewer grid points than the more established differential quadrature method (DQM).

On the refined first-order shear deformation plate theory of Kármán type

A new refined first-order shear-deformation plate theory of the Karman type is presented for engineering applications and a new version of the generalized Karman large deflection equations with deflection and stress functions as two unknown variables is formulated for nonlinear analysis of shear-deformable plates of composite material and construction, based on the Mindlin/Reissner theory. In this refined plate theory two rotations that are constrained out in the formulation are imposed upon overall displacements of the plates in an implicit role. Linear and nonlinear investigations may be made by the engineering theory to a class of shear-deformation plates such as moderately thick composite plates, orthotropic sandwich plates, densely stiffened plates, and laminated shear-deformable plates. Reduced forms of the generalized Karman equations are derived consequently, which are found identical to those existe in the literature.

Vibration of mindlin plates using boundary characteristic orthogonal polynomials

Abstract The vibration analysis of shear deformable plates formulated on the basis of first order Mindlin theory is presented. The displacement and rotational functions of the plates are approximated by sets of boundary characteristic orthogonal polynomials. The ease of generation and manipulation of these polynomial functions greatly enhances the computational efficiency of the numerical method. The energy functional of the shear deformable plates derived from the Mindlin plate theory is minimized in the Ritz procedure to arrive at the governing eigenvalue equation. Corresponding natural frequencies and mode shapes can be obtained by solving the eigenvalue equation. Computed frequency results for various boundary conditions, aspect ratios a/b and thickness ratios t/b are presented to demonstrate the effects of each factor on the vibration frequencies of moderately thick plates. Vibration mode shapes in the form of contour plots are presented for a thickness ratio of t/b = 0.1. These plots are believed to be the first known in the open literature.

Geometrically nonlinear analysis of plates by assumed strain element with explicit tangent stiffness matrix

A four-node quadrilateral C 0 plate element, which can be reduced to the corresponding three-node triangular element automatically, is presented here for the geometrically nonlinear analysis of plates. The element formulation is based on the updated Lagrangian formulation, the von Karman assumption and the quasi-conforming element method (an assumed strain method). Unlike most nonlinear plate elements in which the element matrices are obtained from numerical integration, the element tangent stiffness matrix in the present work is given explicitly. Because of the explicit form of the tangent stiffness matrices, the nonlinear element developed here is extremely economical in the geometrically nonlinear analysis of shear deformable plates. Four numerical examples are given to show the efficiency and accuracy of the present nonlinear element.