Geometric thermomechanical coupling in the large-displacement analysis of articulated dynamical systems

Abstract

A new approach is proposed to account for the geometric thermomechanical coupling in the large-displacement analysis of continua and articulated mechanical systems (AMS) subject to motion constraints. The approach accounts for the geometric coupling between temperature and deformation coordinates in both mechanical and heat equations and for the effect of motion constraints introduced using Lagrange-D’Alembert principle on the heat equation. The nonlinear dependence of the heat equations on the deformation coordinates is formulated using the current-configuration coordinates, arbitrarily complex reference-configuration geometry can be described, and multiplicative decomposition of the matrix of position-gradient vectors is used to systematically account for the stress-free thermal expansion in the absence of any motion restrictions. To this end, the finite element (FE) absolute nodal coordinate formulation (ANCF) is used for the position interpolation, while temperature interpolation can be chosen to ensure continuity of the temperature and its spatial derivatives at the nodal points. The first-order-ordinary temperature differential equations can be solved simultaneously with the constrained AMS dynamic equations. New Cholesky-heat-coordinate transformation is used to define an identity coefficient matrix to solve efficiently for the heat-coordinate time derivatives. Because motion effect on temperature is considered, the proposed approach captures conversion of kinetic energy to heat energy and vice versa.