Buckling of folded plate structures subjected to partial in‐plane edge loads by the FSDT meshfree Galerkin method

Abstract

SUMMARYThis 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.

A meshless method for the nonlinear von Kármán plate with multiple folds of complex shape

“…The moment matrix can be inverted quickly using an iterative algorithm based on the Sherman-Morrison formula [28] which provides explicit equations for M −1 and proved to reduce sensibly the computational costs associated with Eqs. (24) and (21). The same formula (21) stands for ψ I (X).…”

“…Notable examples in the meshfree literature include [21,22], where the fold geometry is introduced a priori, by joining different plates through boundary conditions. A meshfree method discretises each plate, and the folded plate is an assembly of individual plates.…”

Static and frequency optimization of folded laminated composite plates using an adjusted Differential Evolution algorithm and a smoothed triangular plate element

“…This is because folded plate structures possess many advantages such as lightweight, easy manufacture, suitable cost, and high load carrying capacity compared to flat plates. Due to such superior characteristics and wide range of application, the analyses of folded plate structures have attracted a certain attention from researchers around the world [1][2][3][4][5][6][7][8][9][10][11][12]. Goldberg and Leve [1] are regarded as the first persons to give the exact static solution of folded plates.…”

FEM and EFG Quasi-Static Explicit Buckling Analysis for Thin-Walled Members

“…Chinnaboon [10] developed a BEM-based meshless method for buckling analysis of elastic plates with various boundary conditions that include elastic supports and restraints. Liew [11] used an EFG method to study the elastic buckling behavior of stiffened and un-stiffened folded plates under partial in-plane edge loads. Tamijani [12] employed the EFG method for buckling and static analysis of plates with arbitrary curvilinear stiffeners.…”