Block-level elements in the design of heterogeneous materials and structures

Abstract

Block structure theory allowed us to develop a theory of hidden defects and for the first time to identify a new type of earthquakes that can be predicted. However, the possibilities of block structure and block elements theoryare not exhausted. Allowing to solve a wide range of boundary problems for systems of partial differential equations with high accuracy, these methods manage to build analytical representations of solutions of boundary problems and identify important properties of solutions, which is not always possible to do by numerical methods. For example, numerical method can help to obtain the solution of the boundary problem on the approximation on the basis of two deformable lithospheric plates and to detect the growth of stress concentration in the zone of convergence. However, it is impossible to obtain information about the singular stress concentration in this zone, as well as the dependence of the coefficient on the singularity of the input parameters of the boundary value problem. This issue can be resolved using the block element method by formation of appropriate block structures.