A new method for calculating volumetric structural elements in the general case of their stress-strain state

Abstract

The parametric equations of the strength surface in the space of internal force factors (IFF) are given for 9 forces and 9 moments in homogeneous anisotropic bodies. As special cases, similar equations are given for isotropic bodies that resist tension and compression differently (and equally). A variant of the kinematic method of the theory of limit equilibrium is proposed. A rigid-plastic model of a deformable solid body is used. It is assumed that massive structural elements are destroyed by dividing into parts that deform relatively little (“absolutely rigid finite elements”, 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 active IFFs is taken into account. To determine the minimum kinematically possible load, the simplex linear programming (LP) method was used.