Elastic buckling analysis of folded plates using the moving-least square meshfree method

A moving-least square meshfree method is introduced to investigate the elastic buckling behaviors of folded plates subjected to partial in-plane edge loads. The folded plates are regarded as assemblies of flat plates that lie in different planes. Based on the first-order shear deformation theory (FSDT) and the moving-least square approximation, the stiffness equations of the flat plates subjected to partial in-plane edge loads are derived. A treatment is implemented to modify the equations, and the equations are then superposed to obtain the stiffness equation of the entire folded plate. The equation is solved for the nodal parameters and the initial stress matrices of the flat plates. After the same modification, the matrices are supposed to give the initial stress matrix of the entire structure. The governing equation that gives critical buckling load of the folded plate subjected to partial in-plane edge loads is thus established. Unlike the finite element methods, no mesh is required in determining the stiffness equations for the flat plates in this paper, which means time-consuming remeshing is entirely avoided for large deformation problems of the structures. To demonstrate the accuracy and convergence of the method, several numerical examples are calculated. Good agreement is observed between the results given by the proposed method and the commercial finite element software ANSYS.