An Accurate Computational Method for Buckling of Orthotropic Composite Plate with Non-Classical Boundary Restraints

Abstract

New accurate buckling analysis for rectangular orthotropic thin plates with complicated non-classical boundary restraints are conducted through adopting the finite Fourier integral transform approach. Non-classical boundaries such as rotationally restrained edges increase the mathematical difficulty in processing problems of plates, which leads to rare analytical results for benchmark use. The proposed approach is implemented in the framework of integral transform theory, in which trial function for the deflection is not necessary, and offers uniform solution procedures for problems of plates with various boundaries via adopting different integral kernels. The main merits of the approach employed is to enable one to change the complicated title problem into dealing with linear algebraic equations easily solved. Via altering the rotational spring factors introduced, buckling behaviors of plates with Levy-type boundaries and non-Levy-type boundaries can also be studied. Finally, all the given results including critical load factor and mode shape match the FEM analysis exactly, which illustrate the accuracy and validity of the method.

New Accurate Flexural Analysis for Different Types of Plates in a Rectangular Sewage Tank by Utilizing a Unified Analytic Solution Procedure

“…He et al [36] used the generalized integral transform method to analyze the bending analysis of rectangular orthotropic plates with rotationally restrained and free edges. Similarly, Zhang [37][38][39][40][41] provided a finite Fourier integral transform solution procedure for the mechanical problems of plates subjected to various non-Lévy-type boundaries, in which Fourier series was selected as the integral kernel for constructing integral pairs on the basis of the principle of integral transformation. Meng et al [42] estimated the state of nonlinear generalized systems subject to algebraic constraints by generalized inverse technique.…”

New Natural Frequency Studies of Orthotropic Plates by Adopting a Two-Dimensional Modified Fourier Series Method

“…For this reason, several representative analytical approaches for non-Lévy-type plates have been proposed. For instance, Zhang developed a finite integral transform method [36][37][38][39][40][41][42] to solve the mechanical problems of plates subjected to classical or non-classical edge conditions; the method was proven to be rigorous and effective in analyzing plate mechanical performance. Rahbar employed a semi-analytical method [43] to study the forced vibration responses of plates with clamped and simply supported edges.…”