Nonlinear math model development and numerical model of strain deformed rock mass conditions prognosis
- Ph.D., Dr.Sci. professor Saint-Petersburg Mining University
Abstract
The article deals with the questions related to the development of math models of nonlinear strain deformed conditions of a laminar heterogeneous rock mass in the area of excavation in shallow formations. The non-linear relations between physical strains and deformations are added to the basic system of resolving differential equations in partial derivatives (equilibrium equations) and well-known Cauchy dependencies (formulas of connection between deformations and displacements). This ratio is defined by both the elastic potential and by exponential law of hardening or by linear hardening law. Within the framework of the accepted hypotheses of Genki – Ilyushin theory of small elastoplastic deformations some algorithms and calculating complexes of solutions of applied geomechanics problems have been developed. They include such numerical methods as finite difference method, finite element method, and boundary element method. Nonlinear boundary problem based on Newton – Kantorovich – Raphson linearization method comes to the iterative process of a linear boundary problems sequence solution.
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