Boundary Element Analysis of Thermoelastic Effects in Size-Dependent Mechanics

A new boundary element formulation is developed to analyze two-dimensional size-dependent thermoelastic response in linear isotropic couple stress materials. The model is based on the recently developed consistent couple stress theory, in which the couple-stress tensor is skew-symmetric. The size-dependency effect is specified by one characteristic parameter length scale l, while the thermal effect is quantified by the classical thermal expansion coefficient α and conductivity k. We discuss the boundary integral formulation and numerical implementation of this size-dependent thermoelasticity boundary element method (BEM). Then, we apply the resulting BEM formulation to a computational example to validate the numerical implementation and to explore thermoelastic couplings as the non-dimensional characteristic scale of the problem is varied. Interestingly, for a cantilever beam with a transverse temperature gradient, we find significantly reduced non-dimensional tip deflections as the beam depth h approaches the material characteristic length scale l. On the other hand, when l/h < 0.01, the classical size-independent deflections are recovered.