DYNAMIC SHAPE CONTROL OF SOLIDS AND STRUCTURES BY THERMAL EXPANSION STRAINS

Abstract

The present article is concerned with the dynamic shape control of solids and structures by means of thermal expansion strains or, equivalently, by means of thermal expansion stresses. We study transient disturbances produced by imposed forces, and we wish to identify a transient temperature distribution that, when superimposed, leads to zero total displacements of the body. The derivation is based on the theorem of work expended and on Graffi's theorem. Using the anisotropic constitutive equations of linear thermoelasticity, we arrive at a dynamic extension of the principle of virtual forces and at a dynamic extension of Maysel's formula of thermoelasticity. Comparing these two convolution statements, it is found that, in order to make the total displacement zero everywhere in the body, the thermal expansion stress in the thermal problem should be the quasi-static stress minus the thermal expansion stress in the force problem. Any quasi-static stress due to a thermal loading may be added to the thermal expansion stress without changing the validity of this theorem. The practical application of this result is facilitated when the production of heat due to deformation may be neglected and when the applied forces are separable in space and time. The validity of the analytical solution is checked, by means of finite element computations.