A Method for the Design of Inhomogeneous Materials and Block Structures

Abstract

A new method for the design of inhomogeneous materials and block structures with complex physicomechanical properties is stated. This approach based on the method of a block element can conveniently complement different numerical approaches used for these purposes and reveal the boundary problem solution properties, which either are complicated or cannot be analyzed by other methods. It is proven that a crucial role in the construction of this new approach is played by packed block elements as topological manifolds with a boundary, which can form similar new topological manifolds as a result of conjugation. It is demonstrated how homeomorphisms, which represent the mappings of topological manifolds of block elements onto real number spaces and further enable the construction of quotient topologies, which “glue” together both block elements and boundary problem solution fragments on block elements as carriers, are constructed for these purposes.