Computational algorithm for the solution of coupled thermomechanical large-displacement problems

Abstract In case of extreme thermal loads, using coupled thermomechanical analysis (CTMA) that accounts for the effect of deformation and geometry on the heat equation is necessary to ensure the solution accuracy. This paper describes the computer implementation of a new CTMA formulation applicable to articulated mechanical systems that consist of interconnected components. The CTMA formulation employs finite elements (FE) based on the absolute nodal coordinate formulation (ANCF), a Lagrangian form of the heat equation, and a kinetic energy thermal expansion approach. The ANCF finite elements ensure gradient continuity and capture accurately large displacements and geometric nonlinearities. The Lagrangian temperature field used to solve the heat equation ensures the continuity of the temperature gradients and captures effects of geometry changes due to mechanical deformation on the temperature distribution. The kinetic energy approach of the thermal expansion eliminates artificial stresses induced by the conventional strain energy approach commonly used in the FE literature. The paper describes the CTMA implementation and uses its matrix structure to develop a robust solution algorithm applicable to a wide range of problems. The procedure for computing the new matrices, which do not appear in the Eulerian formulation of the heat equation, is explained. Numerical and analytical examples are used to verify the results and demonstrate the implementation of the proposed approach.