Selected Topics in Boundary Integral Formulations for Solids and Fluids
July 9, 2001 — July 13, 2001
Coordinator:
- Vladimir Kompis (University of Zilina, Zilina, Slovakia)
The Finite Element (FEM) and Boundary Element Method (BEM) are very efficient tools for analysis of continuum mechanics problems. In the effort to develop more effective and reliable formulations, new approaches appear. The aim of the course is to present some current non-classical achievements in the BEM: non-singular Boundary Integral formulations, reciprocity based FEM, Boundary Contour (BCM) and Boundary Node Method (BNM), Dual Reciprocity BEM (DRBEM) and their applications in linear and non-linear Computational Mechanics.
In order to achieve more effective solutions in linear problems, new techniques will be presented: non-singular BEM/FEM formulations for both static and dynamic problems using Trefftz-(T-)functions and other regularization approaches; multi-domain reciprocity based formulations; BCM and BNM in analysis, sensitivity analysis, shape optimization, error analysis and adaptivity; stress smoothing by T-polynomials in the multi-domain solutions; hybrid BEM.
In non-linear problems, the solution of geometrical and material non-linearity will be presented using Lagrangian, Arbitrary Lagrangian-Eulerian (ALE) and rate formulations. In the time domain, the inverse transformation and convolution quadrature method applications will be shown. Also a hybrid micro-macro BEM formulation will be demonstrated.
Special applications will be presented in the solution of the problems of practical importance: design sensitivity of materially non-linear problems; metal forming; thermal aspects of machining; evolved damage in grinding; wave propagation in 3D visco-elastic continuum; noise radiation from rolling bodies caused by the vibration modes; acoustic radiation in closed and infinite domains; 3D problems of dynamic piezoelectricity; the Stefan problems; coupled heat, mass, momentum and solute transfer in solid-liquid systems; solution of industrial transport phenomena: solution of DC casting of aluminium alloys and continuous casting of steel.
The course is addressed to postgraduate students, academics, research engineers and practicing engineers interested in numerical methods, especially BEM/FEM, for the analysis of solids and fluids.