English
Русский Method for calculating the strength of massive structural elements in the general case of their stress-strain state (kinematic method)
Abstract
A variant of the kinematic method of the theory of limit equilibrium is proposed; massive structural elements are considered, the material of which, in the general case, is anisotropic.
A rigid-plastic model of a deformable solid body is adopted. It is assumed that massive structural ele-ments are destroyed by dividing into parts that deform relatively little (“absolutely rigid finite ele-ments”, ARFE) and have 6 degrees of freedom in three-dimensional space. The process of destruction of the material goes along infinitely thin generalized destruction surfaces (GDS), on which the work of all acting internal force factors (IFF) is taken into account – 9 forces and 9 moments. Bodies made of homogeneous isotropic materials that resist tension and compression in different ways are considered. The strength surfaces in the IFF space are described by the corresponding parametric equations.
Using the equilibrium equation in the Lagrange form and the Mises maximum principle, as well as the proposed parametric equations of the limiting surface, the problem of determining the minimum value of the possible kinematic parameter of the load is reduced to a standard linear programming problem (LP), which is solved using the simplex method.
A rigid-plastic model of a deformable solid body is adopted. It is assumed that massive structural ele-ments are destroyed by dividing into parts that deform relatively little (“absolutely rigid finite ele-ments”, ARFE) and have 6 degrees of freedom in three-dimensional space. The process of destruction of the material goes along infinitely thin generalized destruction surfaces (GDS), on which the work of all acting internal force factors (IFF) is taken into account – 9 forces and 9 moments. Bodies made of homogeneous isotropic materials that resist tension and compression in different ways are considered. The strength surfaces in the IFF space are described by the corresponding parametric equations.
Using the equilibrium equation in the Lagrange form and the Mises maximum principle, as well as the proposed parametric equations of the limiting surface, the problem of determining the minimum value of the possible kinematic parameter of the load is reduced to a standard linear programming problem (LP), which is solved using the simplex method.