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Computer modeling of contact interaction between elastic bodies by combined adaptive numerical schemes

Work number - M 40 AWARDED

Authors: Prokopyshyn I. I., Styahar A. O., Yashchuk Yu. O.


Ivan Franko National University of Lviv


The series of works consists of 25 articles and 43 conference proceedings and materials, published within 8 years.

The aim of the series of scientific works is the development and justification of new mathematical models and efficient numerical methods for the problems of deformation of multielement mechanical structures that consist of massive and thin-walled elastic elements, coupled by perfect and unilateral contact conditions.

The scientific innovation of the research consists of obtaining new variational formulations of perfect and unilateral contact problems for the system of linear and nonlinear elastic bodies with thin inclusions, covers, and nonlinear surface layers. The theorems on existence and uniqueness of the solutions of variational problems are proved. New efficient domain decomposition algorithms for the solution of these problems,that include parallel Robin type algorithms in particular, are proposed, the theorems on the convergence of these algorithms are proved, and their numerical implementation is performed using finite and boundary element approximations. Moreover, a new method of error estimation based on comparison of the results obtained by finite and boundary element methods is developed and justified. With the help of this method, a new h-adaptive finite-boundary element scheme, that automatically reveals singularities of the solution, is constructed, and a parallel combined domain decomposition and h-adaptation algorithm for the contact problems is developed. The numerical analysis of a number of 2D problems of contact between several elastic bodies with nonlinear surface layers and of deformation of elastic bodies with thin inclusions and covers, that show the efficiency of proposed domain decomposition and h-adaptation methods and help to reveal new mechanical phenomena, is performed.

The results presented in the series of works are important for the study of practical problems of deformation of multielement elastic systems, arising in geomechanics, construction of buildings, mechanical engineering, biomechanics and other branches. Proposed numerical schemes allow to organize the parallelization of computations and to apply optimal mathematical models and methods in different subdomains (bodies). These schemes provide the economy of computing resources.