A high-order theory for laminated composite plates using lagrange multiplier technique

Abstract

In this paper, a high-order theory for laminated composite plates with shear deformations using the Lagrange multiplier technique is presented. The formulation of the theory is based on the minimization of the total potential energy obtained by using the displacement field proposed by Lo, Christensen and Wu [ J. appl. Mech. 663–676, (1977)]. Some examples using the finite rectangular plates subjected to uniformly distributed and sinusoidal loads and a concentrated load are solved by the finite element method. In this study, the Lagrange multipliers are also employed to constrain the displacement functions to satisfy the stress boundary conditions. The solutions agree well with those presented in earlier investigations for thin plates. Under realistic boundary conditions, this study predicts about 10% higher values of nondimensional stresses in thick plates leading to the conclusion that the in-plane displacement modes should be included in the expressions of the displacement fields.