Locking alleviation technique for the peridynamic Reissner–Mindlin plate model: the developed reduced integration method

Abstract

Peridynamics (PD) differs from classical continuum mechanics and other nonlocal theories that do not involve spatial derivatives of the displacement field. PD is based on the integral equation instead of differential equations to handle discontinuities and other singularities. In this paper, the standard peridynamic Reissner–Mindlin plate model (standard PD) accounting for the shear deformation is chosen to describe the thick plate kinematics. Unfortunately, when applied to very thin plate structures, the standard PD encounters shear locking phenomenon, leading to incorrect solutions. This shear locking can be successfully alleviated using the developed reduced or selective integration method. In particular, this technique has been implemented in the standard PD, which allows an accurate result for a wide range from very thin (L/ t> 10 3) to thick (L/ t∼ 10) plate structures. It can also accelerate the computational time for particular dynamic problems using fewer neighboring integration particles. Several numerical examples are solved to demonstrate the effectiveness of the proposed method for modeling plate structures.