Nonlinear analysis of constructions from different materials based on unified plastic constitutive relations

In the paper the plastic constitutive relations based on the hypotheses of the plastic flow theory, unified for different materials, such as soil ground, concrete, metal etc. are proposed. These plastic constitutive relations are based on the hypotheses of the Mises-Schleicher-Botkin theory of failure. The strength characteristics of materials, determined by standard methods, are redefined for octahedral sites, they are invariants for. The problem is solved by the finite element method (FEM). The calculation model MFOE made up of singular finite elements (tetrahedral, triangular plates, rods). This fact increases the accuracy of the description of loading paths in finite elements and ensures a unique correspondence of the constitutive equations to elementary volumes of the construction. The use of singular finite elements is associated with a large amount of access memory for storing the stiffness matrix of the system. So, the range of practically solvable problems limits significantly. To eliminate this contradiction, the Newton’s iteration method – SOR method is developed for equilibrium equations solving in the design of finite elements structures. An iterative algorithm is obtained. It does not require assembly of the system stiffness matrix for its implementation. The volume of operational information is proportional to the number of finite elements in the system. Due to the traditional approach, which requires the assembly of the system stiffness matrix, the amount of operational information is proportional to the square of the degree of kinematic indeterminacy of the system. While using the iterative algorithm, the size of the stiffness matrix and the time of solving are reduced. The results of a nonlinear analysis of soil massifs and concrete structures are represented.