The aim of the work is to determine the axisymmetric stress-strain state of anisotropic bodies of revolution under the influence of an external load, and unbalanced and under conditions of temperature influences with missing internal heat sources.

This problem is provided by the development of the method of boundary states on the class of axisymmetric problems of thermoelasticity for anisotropic bodies of revolution. Development of the theory of constructing the bases of spaces of internal states, including displacement, deformation, stresses and temperature. The basis is formed on the basis of the general solution of the thermoelasticity problem for a transversely isotropic body of revolution and the formation of the relations determining the desired elastic state.

To determine the elastic axisymmetric state from the action of mass forces, it is assumed that the inverse method is extended to a class of problems for anisotropic bodies. By rheology, the inverse method is similar to the method of boundary states. The basis of the space of states is formed with the help of fundamental polynomials. After the orthogonalization of the basis, the desired state is determined by the Fourier series, the coefficients of which are definite integrals whose nuclei constitute the multiplication of temperatures.

The solution of the boundary value problem of mechanics is assumed to be a means of the method of boundary states. The basis of the space of internal states is formed according to the fundamental system of Weierstrass polynomials. The mechanical characteristics are expanded in a series of elements of the orthonormal basis, where the scalar products having the energy sense act as coefficients.

The final result is written as the sum of three independent states. The solution of the test problem for a circular cylinder from a rock with the corresponding conclusions is given, the design problem for a body of revolution is a stepped cylinder. Explicit and indirect signs of the convergence of the solution of problems and graphical visualization of the results are presented.

В работе представлена методика определения напряженно-деформированного состояния трансверсально-изотропных тел вращения под действием осесимметричных: внешних сил, объемных сил и распределения температуры внутри тела. Результирующее упругое состояние определяется как сумма упругих состояний от каждого воздействия.

Поставленная задача обеспечивается развитием метода граничных состояний для решения краевой задачи теории упругости и обратного метода для решения задачи термоупругости и задачи по определению состояния от действия массовых сил. Предложена методика формирования базиса внутренних состояний, составляющих фундамент методов. Предложены выражения для скалярных произведений и индуцированы соотношения для определения напряжений, деформаций и перемещений в каждой из задач.

Представлено строгое решение тестовой задачи для кругового цилиндра и приближенное решение расчетной задачи для тела ступенчатой цилиндрической формы.