On the peridynamic formulation for an orthotropic Mindlin plate under bending

Abstract

Composite materials are becoming increasingly widespread across applications such as aerospace, automotive, wind and solar energy systems, on account of their superior specific strength and stiffness. There are still unresolved challenges in the structural analysis of composite materials in practical engineering applications, owing to their complex structures. Peridynamic theory is a robust technique for the analysis of composite structures; however, it is computationally costly. Structural idealizations are commonly applied in engineering applications to represent structures with a reasonable simplicity, thus reducing the computational cost. Idealization of a planar structure, such as a plate, reduces the number of peridynamic interactions to be solved. In this study, a peridynamic plate formulation of an orthotropic plate with transverse shear deformation is proposed. Peridynamic bond parameters are derived by localizing the peridynamic equations of motion and comparing them with equations of motion obtained using classical continuum mechanics. A failure theory is implemented in the formulation in order to perform crack propagation simulations. A MATLAB script is written using the proposed formulation for the solution of orthotropic plates under bending. The peridynamic solutions are obtained for both elastic deformations and failure prediction of pre-cracked plates, and are validated using finite-element analysis solutions.