A Timoshenko's beam function-based layered element for nonlinear analysis of isotropic plates and reinforced concrete slabs

摘要

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 nonlinear finite element analysis of thin to moderately thick isotropic plates and reinforced concrete slabs. The in-plane displacement functions for a quadrilateral plane element with drilling degrees of freedom are taken as the in-plane displacements of the element. Timoshenko's composite beam functions are employed to represent the bending behaviour of the proposed layered plate element. Shear deformation effects are included in the proposed element model to provide more accurate analysis of moderate thick reinforced concrete slabs, whereas the notorious problem of shear-locking is avoided naturally. 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 computed to demonstrate the efficacy of the element.