A general laminated plate theory accounting for continuity of displacements and transverse shear stresses at material interfaces

Abstract

A general two-dimensional theory, suitable for the static and/or the dynamic analysis of transverse shear deformable laminated plates, is presented. This displacement-based theory is capable of satisfying continuity of both displacements and transverse shear stresses at the plate material interfaces. The derivation of its governing differential equations is based on the application of Hamilton's principle in conjunction with the method of Lagrange multipliers. Moreover, this new theory is capable of accounting for unlimited multiple choices of continuous displacement distributions, through the plate thickness, while, starting with the smallest possible number of independent displacement components (five, for a shear deformation theory), it is capable of further operating with as many degrees of freedom as desired. With such a double-infinite freedom, it is concluded that for the analysis of the particular laminated plate considered one may start with the solution of the governing equations of the 5-degrees-of-freedom theory derived for relatively simple choices of through-the-thickness displacement distributions. Then, either increasing the number of the degrees of freedom or reforming, suitably, the aforementioned displacement distributions, one may iteratively improve the efficiency of the theory until a sufficient degree of accuracy is achieved for the results obtained.