Locking-free two-layer Timoshenko beam element with interlayer slip

Abstract

A new locking-free strain-based finite element formulation for the numerical treatment of linear static analysis of two-layer planar composite beams with interlayer slip is proposed. In this formulation, the modified principle of virtual work is introduced as a basis for the finite element discretization. The linear kinematic equations are included into the principle by the procedure, similar to that of Lagrangian multipliers. A strain field vector remains the only unknown function to be interpolated in the finite element implementation of the principle. In contrast with some of the displacement-based and mixed finite element formulations of the composite beams with interlayer slip, the present formulation is completely locking-free. Hence, there are no shear and slip locking, poor convergence and stress oscillations in these finite elements. The generalization of the composite beam theory with the consideration of the Timoshenko beam theory for the individual component of a composite beam represents a substantial contribution in the field of analysis of non-slender composite beams with an interlayer slip. An extension of the present formulation to the non-linear material problems is straightforward. As only a few finite elements are needed to describe a composite beam with great precision, the new finite element formulations is perfectly suited for practical calculations.