Reciprocal and variational theorems on the two-temperature Green-Lindsay thermoelasticity theory

The motive of the present work is to establish the reciprocal and variational theorems for the two-temperature Green-Lindsay thermoelasticity in an isotropic thermoelastic medium. The alternate formulation of the mixed boundary-initial value problem in which initial conditions are incorporated in field equations is derived using the Laplace transform. This alternative formulation is the foundation for the convolution-type variational principle and reciprocity relation. The convolutional-type variational principle can be replaced by an approximate formulation in which a space finite element method is combined with a time approximation and suitable for numerical solutions based on a Ritz method. The reciprocity theorem is helpful in the theoretical development of boundary and finite element methods. The current effort can be valuable for the problem of coupling effects of thermal and mechanical fields, especially in geophysics and mining.