Numerical Simulation of Thermal Stresses and Deformations

Omar Hafez, University of California, Davis

The problem of thermal stresses calls for interesting issues from physical, mathematical and numerical standpoints for a wide range of practical applications. Examples include internal combustion engines, solar cells, computer chips, nuclear power plants and several others in fields such as aerospace, structural and biomechanical engineering.

Thermal stress theory combines elasticity and continuum mechanics with heat transfer. As with other multiphysics problems, consideration of the mechanics of a body with heat transfer is not simply a superposition of the two. Rather, the deformation of a material can absorb or release energy, and thermal gradients will produce deformations and may lead to stresses. The interaction of the two different physical phenomena can produce unexpected - and unwanted - results.

Numerical simulations of thermal stresses in beams and plates were performed. Fourier analysis was conducted to better understand the nature of the linearized equations, including the change of energy of the system over time and its behavior at high and low frequencies. Different discretizations were explored, which included both explicit and implicit schemes. The problem was treated both as second-order equations and as a system of first-order equations. Using the schemes explored, a parametric study was performed to qualitatively observe the effect of the coupling terms on the solution of the linearized equations. Currently, nonlinear coupling, which can cause interesting phenomena like finite time blow up, solitons, hysteresis, and chaos, is being considered.

Abstract Author(s): Omar Hafez