Effect of shear deformation on the buckling parameter of perforated and non-perforated plates studied using the boundary element method

Buckling of Perforated Plates Using the Dual Reciprocity Boundary Element Method

“…The displacement boundary integral equations (DBIEs) for the buckling problem used in Soares and Palermo [23] are given next:…”

“…According to the development in Soares and Palermo [23], the GNL effect in eqn (3) is introduced with an integral performed on the domain and a boundary integral, which is related to the natural condition in the part of the boundary when the deflection (u 3 ) is not prescribed. The result in eqn (17) Soares and Palermo [23] showed the boundary integral containing the GNL effect should only be computed along the boundary part with the prescribed deflection. The GNL effect requires the use of the BIE for the gradient of the deflection, which is written next for an internal collocation point:…”

“…The BEM formulation for buckling analyses in Soares and Palermo [23] employed two integrals containing the GNL effect, with one computed in the domain and the other on the boundary. The use of first derivatives of the deflection in kernels of integrals related to the GNL effect, instead of the second derivatives, and the fact that there was no need of relating the derivatives of in-plane forces were the main features of the alternative formulation.…”

“…The use of first derivatives of the deflection in kernels of integrals related to the GNL effect, instead of the second derivatives, and the fact that there was no need of relating the derivatives of in-plane forces were the main features of the alternative formulation. This study employs the DRM to replace the domain integral by equivalent boundary integrals in the Soares and Palermo formulation [23]. The numerical implementation employed quadratic shape functions to approximate displacements, plate rotations, distributed shears and moments in the boundary elements as implemented in the study [23], as well as the inverse iteration and Rayleigh quotient to compute the lowest eigenvalue with the corresponding eigenvector.…”

“…This study employs the DRM to replace the domain integral by equivalent boundary integrals in the Soares and Palermo formulation [23]. The numerical implementation employed quadratic shape functions to approximate displacements, plate rotations, distributed shears and moments in the boundary elements as implemented in the study [23], as well as the inverse iteration and Rayleigh quotient to compute the lowest eigenvalue with the corresponding eigenvector. The changes in the value of the buckling parameter according to the plate thickness of perforated plates are studied and compared to those in the literature.…”