Abstract
The paper presents a numerical analysis of a nonlinear, coupled, thermoelastic rapidly heated rod. The geometric relations, mechanical equilibrium equations, and Fourier law are linear, whereas the energy equation and the constitutive relations accounting for the third-order elastic moduli and the temperature dependent second-order elastic moduli and a coefficient of thermal expansion are nonlinear. Coupling between thermal and displacement fields is considered. Computations are based on spectral methods generalized to include nonlinear cases. An iterative variational case of the Tau method is introduced in which a discretization of the space and time variables of a function is treated in the same way. The iterative weak solutions are defined. Domain of a function is divided along a wave front to account for a boundary condition for temperature given by the Heaviside function and to include a jump of stresses on the wave front. Moduli ofD54S aluminum alloy are used in the computations. The results indicat...
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