Buckling and vibration of finite-length composite prismatic plate structures with diaphragm ends, part I: finite strip formulation

Abstract

A finite strip approach is presented for the determination of buckling stresses and natural frequencies of vibration of prismatic plate structures of finite length which have diaphragm ends. The structures are assembled from plate flats which generally are laminates of fibre-reinforced composite material and a very broad specification of material properties is allowed which includes anisotropy and bending/stretching coupling. Modes of buckling or vibration may be of an overall or a local type. To accommodate the presence of applied in-plane shear stress (as well as biaxial direct stress) and material anisotropy the finite strip method is of the multi-term type, i.e., in the strip formulation each displacement-type component is represented by a finite series of products of longitudinal trigonometric functions and crosswise polynomial functions. The out-of-plane properties of plate flats are based in turn on the use of first-order shear deformation plate theory (accounting for the through-thickness shear effects which are often significant) and classical plate theory. Strip properties, as represented by the elastic stiffness matrix, the geometric stiffness matrix and the consistent mass matrix, are derived through potential energy principles and are approximate. However, through the use of a repetitive substructuring scheme, so-called superstrips are created economically with properties which are effectively exact within the confines of the particular background theory. Following a transformation to a global coordinate system, incorporating the effects of eccentric connections as well as accounting for the arbitrary inclination of plate flats, multi-level substructuring procedures are invoked to reduce the number of effective freedoms of the structure. The eigenvalues are determined using the extended Sturm sequence-bisection approach. This paper contains no numerical applications: consideration of such applications is deferred to a companion paper.