• Subject of research: issues of optimal calculation of shells, as well as special tasks of special machine construction mechanics. The issues of calculation and optimal planning of slabs and membranes with discontinuous characteristics are discussed in the works; determination of tensile strength of elastic-plastic systems and anchor structures; Problems of the exact solution of some spatial problems of the theory of elasticity. The subject of scientific research is less researched engineering tasks, which are related to the calculation of rotating anchors, some of whose physical and geometrical parameters change in leaps and bounds. I. Kakutashvili uses the method of Academician Ilyushin to solve the mentioned issues.