Kinetic- and Strain-Energy Approaches in the Thermal Analysis of Constrained Mechanical Systems: A Comparative Study

Abstract Despite the unconstrained thermal expansion is assumed stress-free, the conventional FE approach requires formulating elastic forces, and this in turn leads to elastic stresses. A displacement-based formulation, on the other hand, can be used to address this limitation by converting the thermal energy to kinetic energy instead of strain energy. The fundamental differences between the strain- and kinetic-energy approaches are discussed. It is shown that the unconstrained thermal expansion predicted using the kinetic-energy approach is independent of the continuum constitutive model, and consequently, such a formulation can be used for both solids and fluids. The displacement (kinetic) and strain (stress) formulations are discussed to shed light on the mechanism of thermal expansion at the macroscopic level. The thermal-expansion displacement formulation (TEDF) and position-gradient multiplicative decomposition into thermal and mechanical parts are used to compute the thermal stresses due to boundary and motion constraints (BMC). TEDF implementation issues are discussed and constant matrices evaluated at a preprocessing stage after applying sweeping matrix technique to eliminate rigid-body thermal-displacement translational modes are identified. Furthermore, the softening effect due to the constitutive-model dependence on the temperature is investigated at high temperatures. Numerical results are presented to show fundamental differences between the TEDF approach that converts heat energy to kinetic energy and conventional FE approach that converts heat energy to strain energy that produces elastic stresses.