Theory of repeated superposition of large strains. Development of this theory for solution of multidisciplinary problems. Methods of implementation of this theory for strength analysis in new branches of industry

V. A. Levin

Čebyševskij sbornik, Tome 18 (2017) no. 3, pp. 524-542

Résumé

It is noted that the theory of repeatedly superimposed large strains permits one to formulate the problems in which the boundaries or boundary conditions are multiply changed step by step or continuously, including the changes of connectedness of the region occupied by the body and the changes of material properties of parts of the body. Every change leads to redistribution of large strains and stresses in the body. It is pointed out that the term “loading sequence” within the framework of this theory denotes the sequence of mechanical and non-mechanical actions on the body (article, element of construction, rock massif), changes of properties of a body part during loading (exploitation), addition or removal of parts of loaded bodies (including layered growth or forced origination of defects). The problem statement of the theory of repeatedly superimposed large strains is developed for two basic cases of interdisciplinary (coupled) problems. In the first case external non-mechanical actions on the body are taken into account: thermal, electromagnetic, chemical, radiation actions, solid-state phase transformations, and other actions that can not be described within the scope of solid body mechanics. This case involves the changes of material properties of the body or its part due to external actions. In the second case the interaction between deformable solids and other (external) surroundings is taken into account. It is noted that the industrial software implementation of interdisciplinary problems of the theory of repeatedly superimposed large strains in the FIDESYS program package in the first case requires the development of additional modules and (or) changes in computational kernels of the FIDESYS package. It is reported that for some problems in the first case the software is developed and scientifically approved within the framework of development roadmap of the FIDESYS package. In the second case, for industrial purposes, the implementation can be performed with proper quality and quickly enough by integration of the FIDESYS package with respective industrial packages that permits one to model the environment. Such integration is provided in the development roadmap of the package, and such works are carried out.

Détail

Keywords: theory of repeatedly superimposed large strains, mechanics of deformable solids, engineering software, computer-aided engineering, engineering analysis.