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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.

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The plane-stress state in the vicinity of singular point, in a plate composed of two identical elements with interlayer such as glue is studied. The purpose of this study is determining characteristics of this solid mechanics problem and influence of material properties and interlayer thickness on stress concentration near the edge of the combining the elements (at the singular point). Analytical estimation of the restrictions count on the state parameters at the line edge of junction plate element and interlayer is conducted. It is shown that the count of independent restrictions depends on the material properties of the plate elements and is usually redundant (non-standard). Standard restrictions count is only an exceptional case, when certain combinations of plate elements material parameters take place. In this particular case the solution is named as a "basic-solution". For considered case of stress-strained plate basic-solution has uniform stress and piecewise-homogeneous strain state solution. With material parameters near the basic-solution the nonstandard problem is considered by iterative numerical-analytical method based on minimizing the residual divergence of all the boundary conditions at the singular point vicinity. A set of stress state problems is calculated. It is shown that the solution is practically independent of the interlayer thickness, but it depends drastically on the material properties of the elements. The more rigid material has the highest value concentration ratio.