The problem of optimization of thick-walled sphere loaded by internal and external pressures was solved. The essence of the method consists in the variation of the modulus of elasticity. The problem of finding the distribution of the characteristics of material in which the stress state is given, is called the inverse problem. The idea of the inverse method was proposed by academician of RAACS prof.  V.I. Andreev. The analytical dependence of modulus of elasticity from the radius at which the calculated stress on the strength theory of Mor is constant throughout the thickness of the shell was found. This shell will be equally stressed. If the strength characteristics of the material do not depend on the modulus of elasticity it will also be equiresistant. By creation of indirect heterogeneity we reduced the maximum tensions in 1.6 times. It was also shown that in the case of a centrally symmetric problem the second theory of strength is a particular case of the strength theory of Mor.

Keywords: thick-walled spherical shell, optimization, strength theory of Mor, uniform strength, equal stress

We solved the problem of optimization of thick-walled prestressed concrete cylinder loaded by internal pressure. Preliminary stresses in such a cylinder are created by wounding with tension cables on the outer surface. The idea of the method is to find the law of variation of modulus of elasticity , in which the state of stress is given . The analytical dependence of modulus of elasticity of the radius at which the tensile stress in the entire thickness of the shell does not occure was found. By creation of indirect heterogeneity we reduced the consumption of rebar by 10%.  The direct problem - determining the stress- strain state of a cylinder with a constant modulus of elasticity was also resolved.

Keywords: thick-walled prestressed concrete cylinder, optimization, inverse problem, theory of elasticity, heterogeneity