Formulation of Explicit Nonlinear Thermoelastic Terms Using Additive Thermal Strains

A new method of including geometrically nonlinear thermoelastic effects in a total Lagrangian finite element formulation is developed and demonstrated. This method provides explicit formulas for the thermoelastic terms, allows greater insight into the relationship between linear and nonlinear thermoelasticity and provides alternative nonlinear solution methods. The explicit formulation is accomplished through defining a new thermal strain term, called the additive thermal strain. The relative difference between the exact thermoelastic load and commonly used approximations is investigated. It is shown that the geometrically nonlinear thermoelastic formulation reduces to the standard linear thermoelastic formulation with appropriate assumptions.