One-dimensional Solution of Hygrothermoelastic Rod Problem by Laplace Transformation

A thermal shock problem in a hygrothermoelastic rod of length $$l$$ is solved by the Laplace transformation technique. One end of the rod is subjected to a sudden heat source. The governing equations of the medium are transformed using Laplace transformation and the analytical expressions of displacement, moisture concentration, temperature distribution, and stresses are obtained. These transformed components are then inverted by the numerical inversion method and are presented graphically for different periods. The effect of moisture concentration is also shown through the graphical representations.