Hereditary and Non-stationary Structural Optimization

In this Chapter we give a number of basic relations of the sensitivity analysis in the case of dependence of the deformed state of the body over the time. The given design problems with regard to the history of external influences and the effects of the stresses, as well as in the case of dependence of the stresses on the strain history, are given in the given section. This is the case with the equations of the hereditary theory of elasticity. In these problems the process of deformation of the body is reversed in time. The stresses are represented by the functions of the current coordinates. The necessary optimality condition expresses as the constancy of the trace of Noether’s tensor on the varying part of boundary.