Research Article
Volume 3 Issue 2
Yu Axmedov and Sh Muradov*
August 01, 2023
DOI : 10.56831/PSEN-03-068
Abstract
Based on the generalization of the theory of generalization of polyhedra, a method for linearizing the yield conditions of an arbitrary form, for plastic shells by inscribed and circumscribed hyperpolyhedra, has been developed. The technique allows one to obtain hyperpolyhedra with an arbitrary number of faces. The linearization technique is used to construct an algorithm and a program for automatic approximation of convex hypersurfaces by inscribed and circumscribed hyperpolyhedra with any number of faces. Automatic linearization of plasticity conditions for rigid-plastic shells made it possible to construct an effective method and PPP for calculating lower estimates for the bearing capacity of shallow shells with rectangular plan. The possibility of increasing the efficiency of programs due to the optimal choice of the number of faces of hyperpolytopes is obtained - polyhedra with a minimum number of faces are found, leading to estimates of the bearing capacity with a given accuracy. On the basis of the kinematic method of the theory of limit equilibrium and the use of the generalized Ioganson's yield condition, a method has been developed for calculating the bearing capacity of plates of a complex shape.
Keywords: Geometric modelling; bearing capacity; yield conditions; approximation; hypersurface; polyhedron; equilibrium; hyperpolyhedron; seismic resistance; design; plasticity theory; design; geometric modelling; rigid plasticity; six-dimensional space; surface; linearization; ultimate load; deformation; optimization; coefficient
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