Improved numerical integration for locking treatment in the Peridynamic Timoshenko beam model

Abstract

PurposeIn this paper, the standard Peridynamic Timoshenko beam model accounting for the shear deformation is chosen to describe the thick beam kinematics. Unfortunately, when applied to very thin beam structures, the standard Peridynamics (PD) encounters the shear locking phenomenon, leading to incorrect solutions.Design/methodology/approachPD 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.FindingsThe shear locking can be successfully alleviated using the developed selective integration method. In particular, this technique has been implemented in the standard PD, which allows an accurate result for a wide range of slenderness from very thin to thick (10 < L/t < 103) 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 beam structures.Originality/valueThe paper highlights the severe shear locking phenomenon in the Peridynamic Timoshenko beam available in the literature, especially for very thin structures. A new alternative for the alleviation of shear locking in the Peridynamic Timoshenko beam, using selective integration. Hence the developed Peridynamic Timoshenko beam model is effective for thin and thick structures. A new peridynamic formulation for the low-velocity impact beam models is presented and validated.HighlightsThe paper highlights the severe shear locking phenomenon in the Peridynamic Timoshenko beam proposed in the literature, especially for very thin structures.The developed Peridynamic Timoshenko beam model based on selective integration is effective for thin and thick structures.A new peridynamic formulation for the low-velocity impact beam models is presented and validated.