Iterative finite element algorithm and its implementation for stress state of structural elements with singular points

The target of research is the stress-strain state (SSS) near and directly in the special points of structures with features in the form of flat composite wedges or spatial edges, which are the intersections of the forming bodies surfaces. Boundary conditions, continuity conditions of stresses and strains on the line (surface) connections of structural members and other constraints, posed by the problem statement into structural elements special points, form a mandatory algebraic equality (MAE), which represent a system of linear inhomogeneous algebraic equations. The MAE number, formulated at special points, exceeds the MAE number in ordinary (not special) points of the boundary, which limits the ability to build solutions meeting all of the UAR using usual solid mechanics methods. Therefore, the works purpose is to create an algorithm allowing constructing a solution consistent with all MAE formulated at special points. Substructure iterative mixed finite element method (FEM) is proposed. Substructures are parts of the computational area with continuous state parameters. The main results. The algorithm and software package for the stress state study near and directly in special points of construction elements are suggested. Depending on the considered flat or spatial structure geometric and material parameters properties, problems of elasticity and thermo elasticity are divided into types and subtypes, distinguished by the MAE number. Mixed finite element method version allows calculating nodal stress parameters without the differentiation of the approximate solution or without using any replenishment method. The iterative approach allows building a solution that is consistent with all MAE at special points. The procedure of the proposed algorithm and its Fortran-95 implementation is described. Features, associated with OpenMP technology used in the algorithm implementation are discussed.