A layered shear-flexural plate/shell element using Timoshenko beam functions for nonlinear analysis of reinforced concrete plates

Abstract

Based on Mindlin–Reissner thick plate theory and Timoshenko's composite beam functions, a unified displacement-based finite element formulation of a 4-node, 24-DOF rectangular layered plate element is developed in this paper for the nonlinear finite element analysis of thin to moderately thick isotropic plates and reinforced concrete slabs. Timoshenko's composite beam functions that have been successfully used in other applications are extended for the analysis of reinforced concrete slabs, being used herein to represent the bending behaviour of the proposed layered plate element. Shear deformation effects are included in the model and the notorious problem of shear-locking is avoided naturally since the deflection and rotation functions for the element boundary obtained from Timoshenko's composite beam functions converge theoretically to the thin plate solution when the plate thickness becomes very small. The convenient in-plane displacement functions for a quadrilateral plane element with drilling degrees of freedom are used for the in-plane displacements of the element. Both geometric nonlinearity and material nonlinearity, which incorporates tension, compression, concrete cracking and tension stiffening, are included in the model. A Total Lagrangian approach is employed to formulate the element for incorporation into a nonlinear finite element solution algorithm. Numerical examples of linear and geometric nonlinear analysis of thin to moderately thick isotropic plates and of reinforced concrete slabs are shown to demonstrate the efficacy of the proposed element.