No abstract

Данная статья посвящена развитию метода граничных состояний на класс задач механики твердого деформируемого тела, включающих сингулярности физического характера. Сформировано множество специальных решений, соответствующих сосредоточенным силовым воздействиям на поверхности гладкого трехмерного тела. Каждое специальное решение включено в базисы пространств внутренних и граничных состояний. В качестве примеров эффективности использования специальных решений методом граничных состояний построены напряжённо-деформированные состояния тел шарообразной формы под воздействием сосредоточенных сил. This article is devoted to the development of the method of boundary states into a class of problems of mechanics of a solid deformable body, including singularities of a physical nature. Many special solutions have been formed corresponding to concentrated force actions on the surface of a smooth three-dimensional body. Each special solution is included in the bases of spaces of internal and boundary states. As examples of the effectiveness of using special solutions using the boundary state method, stress-strain states of spherical bodies are constructed under the influence of concentrated forces.

This paper presents an effective technique for solving some spatial problems in the theory of elasticity, particularly for a bounded set of point-like physical singularities. This technique development involves the advanced energy method of boundary states (MBS) for a class of solutions with singularities. A test problem for a single singularity such as the center of expansion complying with the proposed technique calculations reliability has been solved and analyzed. The use of the method of boundary states demonstrates the efficiency of the technique in solving problems with many centers of expansion and concentrated forces in an unbounded medium. The results of problem solving are displayed in a convenient graphical form.