Finite Element Method-Based Dynamic Response of Micropolar Polymers with Voids

Abstract

Composite-based polymer materials are manufactured in a wide variety of types with different compositions, structures, geometries, and topological descriptions. Among these, micropolar materials with voids have become increasingly studied in the literature. This paper establishes the equations of motion for such a material for the purpose of dynamic analysis via the finite element method (FEM). The Euler–Lagrangian formalism, based on the expressions of kinetic energy, potential energy, and mechanical work, is used. Hence, it is possible to study the dynamic response of such a system in the most general configuration case. The choice of the shape functions will determine the matrix coefficients for each particular case. An application illustrates the presented results.

Keywords

• micropolar
• voids
• finite element
• minimum principle
• Lagrange