Solutionto the homogeneous problem of the theoryof elasticity in the area of the cut boundaryin the plane domain РЕШЕНИЕ ОДНОРОДНОЙ ЗАДАЧИ ТЕОРИИ УПРУГОСТИ В ЗОНЕ ВЫРЕЗА ГРАНИЦЫ ПЛОСКОЙ ОБЛАСТИ

Vestnik MGSU

关键词: homogeneous problem of the theory of elasticity;    stress-strain state;    plane domain;    boundary value;    однородная задача теории упругости;    напряженно-деформированное состояние;    коэффициенты интенсивности;   

DOI  :  

来源: DOAJ

【 摘 要 】

The authors present their solution to the homogeneous boundary value problem of the theory of elasticity in the area of the cut boundary in the plane domain. The authors have derived the type of the stress-strain state in the small area of the peak of the cut area. The authors offer an asymptotic solution to the elastic homogeneous problem depending on intensity ratios as unknown constant values. The problem of research into the ratios of intensity is also relevant for the research into the stress-strain state of structures characterized by geometrical non-linearity of boundaries. In the article, the authors consider a plain problem of the theory of elasticity for a domain having an angular point (the case of concentrated forces in the vertex of an angle are not considered by the authors in this article). The authors consider a special case where the vertex angle is equal to 2π. The type of the stress-strain state derived for this case study coincides with the type of the stress-strain state considered in fracture mechanics. Identification of intensity ratios represents an independent problem of the stress-strain state in the area of the domain of the cut peak.
Приведен вывод коэффициентов интенсивности и собственных решений однородной краевой задачи теории упругости в зоне выреза границы плоской области. Полученное решение сопоставляется с решением упругой задачи в области математического выреза.

【 授权许可】

Unknown