Extended framework of Hamilton's principle for thermoelastic continua

Based upon the extended framework of Hamilton's principle, a variational formulation for fully coupled thermoelasticity is presented. The resulting formulation can properly account for all the governing differential equations as well as initial/boundary conditions. Thus, it provides the basis for a class of unified space-time finite element methods. By employing bar elements in one-dimensional space along with linear shape functions temporally, the simplest space-time finite element method is presented herein with representative examples for its validity.