Analytical and Numerical Methods for Analysis of Stress Singularity in Three-Dimensional Problems of Elasticity Theory

Abstract

AbstractDifferent variants of stress singularity analysis in three-dimensional problems of elasticity theory are considered. A complete system of eigensolutions is developed for different variants of circular conical bodies: solid cone, hollow cone, a composite cone under different variants of boundary conditions on the lateral surfaces. The applicability of the constructed eigensolutions for estimating the character of stress singularity at the vertices of conical bodies is considered. The numerical results presented in the study provide insight into the character of stress singularity at the vertices of solid and hollow cones under different variants of boundary conditions on the lateral surfaces. A method for constructing singular solutions for conical bodies is suggested and variants of its numerical realization based on the finite element method are considered. The results of conducted numerical experiments demonstrate the efficiency and reliability of the proposed method. The computation of eigenvalues allows us to determine the character of stress singularity in homogeneous and composite, circular and non-circular cones under different boundary conditions. The work presents an algorithm for the finite-element analysis of singular solutions to three-dimensional problems of elasticity theory for elastic bodies of isotropic, anisotropic, and functionally graded materials. The algorithm is based on determination of a power law relationship for stresses in the vicinity of singular points. The algorithm was verified by solving two- and three-dimensional problems and comparing the obtained results with those available in the literature.KeywordsSingular points2D and 3D problems of elasticity theoryStress singularityClosed-form solutionNumerical solutionsFinite element method