Journal
POLYMERS
Volume 13, Issue 21, Pages -Publisher
MDPI
DOI: 10.3390/polym13213727
Keywords
micropolar; voids; finite element; minimum principle; Lagrange
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This paper investigates the dynamic analysis of micropolar materials with voids, establishing equations of motion and using the finite element method. The Euler-Lagrangian formalism, along with expressions of kinetic energy, potential energy, and mechanical work, allows for studying the dynamic response of the system in the most general configuration case.
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.
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