Heterogeneous mathematical models in numerical analysis of structures

This paper presents a common approach to the numerical analysis of elasticity and heat conduction problems in computed structures. It is based on a combination of the linear elasticity theory with Timoshenkoʹs shell theory for elasticity problems, and of the classical heat conduction theory with a dimensionally reduced heat conduction model in thin bodies for heat conduction problems. Parts of the compound structure, which are described by different theories, are joined by special interface boundary conditions. Variational statements are formulated and their properties are investigated. Numerical solution of the posed problems is performed by either coupled direct boundary element and finite element methods or domain decomposition method. The obtained results demonstrate the effectiveness of the proposed techniques.