Abstract
In this chapter of the book we present some chosen problems of adaptive hierarchical modelling and adaptive hp-analysis of problems of computational solid mechanics. We consider simple and complex structures, i.e. structures described by one mechanical model or more than one mechanical model, respectively. We are interested in three fundamental problems of solid mechanics: the equilibrium (static) problem, eigenvalue (free vibration) problem, and stationary forced vibration problem as well. In the context of static analysis, we consider problems faced while applying: the hierarchical models, hp-approximations, residual error estimation methods, and three- or four-step non- or iterative adaptive strategies, oriented on the target admissible value of the modelling and approximation errors. We also address possibilities and difficulties of generalization of the mentioned techniques onto free and forced vibration analyses. In this contribution we are interested mainly in still unresolved or open problems. We will show some ways, either potentially available or checked by us numerically, to cope with all the mentioned issues.
Published Version
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