Transactions of Nanjing University of Aeronautics & Astronautics
MAC Models in Thermoelasticity
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Abstract:
There are two types of singularities in the linear thermoelasticity. The first one arises in the field of stresses if a force is applied to one point of the body. This singularity is physical and should be accepted. The second type of singularities is nonphysical and they arise in the fields of displacements and temperatures. There exist the nonlocal theories and gradient theories which have the goal to introduce the finite stresses instead of the infinite ones. The MAC model of the thermoelasticity is created to avoid the nonphysical singularities and it accepts the infinite stresses. MAC is the method of additional conditions, which allows introducing the new model to use the classical model, plus additional condition of the physical nonsingularity and/or condition of the good behavior of the solutions at infinity. The MAC Green′s functions for the heat conduction and for the elasticity could be introduced using the differential MAC models. The infinite and finite bodies are considered. The principle of superposition is applied to obtain the integral equations to solve the boundary value problems. The strength criteria based on finite stresses could be changed in this model because the infinite stresses are allowed. The strength criteria based on deformations are applicable. Classification of MAC models is given.
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