Computational Mechanics with Model Adaptivity in Analysis and Design: Current Research and Perspectives

摘要

In this contribution, a brief review of error-controlled adaptive finite element methods available for approximate solutions of a given mathematical model is presented and the associated model error estimates are discussed. The second important matter is what physical/mathematical models—including various boundary layers and other disturbances—and which accuracy of the finite element solutions in which norm are prescribed and necessary for the safety and reliability of a certain engineering problem, for example in structural engineering, of course depending on materials, systems and the type as well as the magnitude of prescribed loadings (i.e. actions in a factorized concept) acting on a specific structure. It is hard to understand why the current regulations for structural engineering design in Europe—especially the European Standards (Eurocodes) and the German DIN Codes (DIN: Deutsches Institut fur Normung e. V.)—do not lay out any rules or bounds for the prescribed accuracy of the material and structural resistance, i.e. the validity of mechanical modeling and the accuracy of the associated numerical method, usually today the finite element method.