Application of a Refined Multi-Field Beam Model for the Analysis of Complex Configurations

Abstract

This article proposes a complex application of a refined electro-mechanical beam formulation. Lagrange-type polynomials are used to interpolate the unknowns over the beam cross section. Three- (L3), four- (L4), and nine-point (L9) polynomials, which lead to linear, bi-linear, and quadratic displacement field approximations over the beam cross-section, are considered. Finite elements are obtained by employing the principle of virtual displacement in conjunction with the Carrera unified formulation (CUF). With the CUF application, the finite element matrices and vectors are expressed in terms of fundamental nuclei whose forms do not depend on the assumption made (L3, L4, or L9). Additional refined beam models are implemented by introducing further discretizations over the beam cross-section. Some assessments from the bibliography have been considered in order to validate the electro-mechanical formulation. Complex three-dimensional geometries have been studied in order to demonstrate the capabilities of the present formulation.