A highly accurate analytical spectral flexibility formulation for buckling and wrinkling of orthotropic rectangular plates

Abstract

This paper proposes analytical solutions for highly accurate and efficient buckling or wrinkling analysis of rectangular orthotropic plates that are fully clamped, completely guided and completely simply supported. Firstly, the exact general solution of the buckling differential equation of a fully clamped orthotropic rectangular plate is derived by using a one-dimensional modified Fourier series. After symbolic manipulations, a spectral flexibility matrix relating the coefficients of boundary shear forces and boundary transverse displacements is formulated. Then, a generalized version of Wittrick-Williams algorithm is applied directly to the spectral flexibility matrix to compute the critical buckling load parameters, which is demonstrated to be extremely accurate and efficient. In addition, the dependence of critical buckling load parameters on plate aspect ratio, orthotropy ratio, inplane load combination and boundary conditions is investigated comprehensively. Another novelty of this paper lies in that our investigation on the plate reveals two completely different types of buckling modes: a long-wavelength buckling mode and a short-wavelength wrinkling mode. In particular, the short-wavelength modes of a fully clamped plate appear an interference pattern similar to the ’beat’ phenomenon in acoustics, for which insights on their occurrence and influence factors are gained from both physical and mathematical aspects.