Изучаются ограничения на параметры состояния в вершине кругового конуса под осесимметричной силовой и кинематической нагрузкой, а также когда вершина конуса-внутренняя точка. Результаты исследования найдут применение в постановках задач при изучении параметров состояния вблизи вершины конуса, в частности, при изучении взаимодействия конических инденторов с исследуемым образцом. Ключевые слова: особые точки, составной конус, круговой конус, внутренняя особая точка, концентрация напряжений, неклассические задачи, представительный объем.

The concept of a deformable body point is taken in the form of a continuum point and an elementary volume connected with it. The continuum point determines the spatial position of the deformable body point, and the elementary volume is the carrier of its material properties and stress-strain state characteristics. Based on this representation, restrictions on the state parameters at the edge points (singular points) of an isotropic body are constructed. These restrictions become preset conditions in singular points. The study covers possible interactions of the edge-forming surfaces with the external environment. It is shown that the restrictions formed at the edge points are usually more numerous than the restrictions at the regular point on the surface of a deformable body. This circumstance leads to a non-classical formulation of the mechanics problem for bodies with singular points. The combinations of geometric and material parameters of a structural component are discovered that determine the singular stresses behavior in elementary volumes with edge points. The load restrictions ensuring the compatibility of parameters defined at singular points are formulated. The attained results will apply to studying stress concentration in the vicinity of 3D-edges of structural components.

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