The generalized problem for eigenvalues in problems of contact interaction with taking into account the material wear

Abstract

Solving of the problem of contact interaction of stiff punch with elastic half-plane with taking into
account the material wear has been reduced to a generalized problem for eigenvalue and
corresponding vectors. The peculiarities of the application of the main methods for finding
approximate eigenvalues and vectors for various input matrices and matrices with variable
dimensions are investigated. An algorithm for computing and software modules to implement the
mathematical models of the contact problems with deterioration using special functions and tools
of result visualization are constructed. An optimal number of eigenvalues for high-quality display
of graphs of contact pressure for different canonical forms of the punch is determined. The
analysis of modern applications, which can be reduced to solving a generalized problem for
eigenvalues (models for optimization and risk management in the networks transformation energy,
models for linear baroclinic instability in the Earth’ oceans) is carried out.