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

Currently actively developing direction of seismic protection, the identified using absorbing screens made in the form of sandwich structures. The present paper presents a design руктивная scheme of energy absorbing panel, which allows you to raise, if used, seismic stability of constructions.

Keywords: Dynamic loading, uprugoplastichesky deformation, deformation chart, power absorption

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

Currently actively developing direction of seismic protection, the identified using absorbing screens made in the form of sandwich structures with упругопластическими energy-absorbing elements. In this article, on the basis of the conducted research and analysis, the formulas for the calculation of power characteristics of belt elastic element.

Keywords: Dynamic loading, uprugoplastichesky deformation, deformation chart, power absorption

Method of successive approximations was used to solve the problem of optimization of multispan continuous beam. Cross section of a beam was a welded I-beam.  By the variation of the width of the shelf we ensured that the maximum equivalent stress for energy theory of strength in each section is the same throughout. The solution is made numerically using complex MatLab. Bearing capacity of beams with variable stiffness along the length increased in 2 times in comparison with the beam with constant stiffness and the same mass. The proposed method can be applied to frames, taking into account the contribution of longitudinal forces in the equal stresses. Another effective way to change stiffness is to change the height of the wall of I-beam. In practice curvilinear shape of beams or shelves are not used because of complexity of manufacturing. They are replaced by the discrete form of cross section.

Keywords: multispan beams, work method, optimization, uniform strength, welded I-beam, variable stiffness