Finite Element Methods for Elasticity with Error-Controlled Discretization and Model Adaptivity
| العنوان: | Finite Element Methods for Elasticity with Error-Controlled Discretization and Model Adaptivity |
|---|---|
| المؤلفون: | Marcus Rüter, Erwin Stein |
| المصدر: | Encyclopedia of Computational Mechanics ISBN: 0470846992 Encyclopedia of Computational Mechanics |
| بيانات النشر: | John Wiley & Sons, Ltd, 2017. |
| سنة النشر: | 2017 |
| مصطلحات موضوعية: | Mathematical optimization, Discretization, Finite element limit analysis, Estimator, Mixed finite element method, 02 engineering and technology, 01 natural sciences, Finite element method, 010101 applied mathematics, 020303 mechanical engineering & transports, 0203 mechanical engineering, Applied mathematics, Meshfree methods, Elasticity (economics), 0101 mathematics, Mathematics, Extended finite element method |
| الوصف: | The essential topics of the finite element method for linear and finite elastic deformations of solids are presented in this chapter from both the mechanical and mathematical point of view. As a starting point, the nonlinear, and linearized theory of elasticity are derived in a rigorous way, followed by the classical variational principles of elasticity, which are the basis for the finite element method in its various forms. More precisely, the discrete variational approach of the (one-field) Dirichlet minimization principle of the total potential energy is presented, followed by concise representations of the (two-field) Hellinger–Reissner stationary dual-mixed principle and the (three-field) Hu–Washizu stationary mixed principle, including the main features of the associated finite element methods. The main objective of this chapter is the systematic treatment of error estimation procedures and adaptivity for the linearized and finite elasticity problem covering both global and goal-oriented a posteriori error estimators. The three basic classes, that is, residual-, hierarchical-, and averaging-type error estimators are presented and applied to a fracture mechanics problem as an example. A further challenging topic is the combination of error-controlled adaptive finite element solutions with hierarchical model and dimension adaptivity of the underlying mathematical model, especially for thin-walled structures where model expansion is necessary in subdomains with boundary layers and other disturbances. Keywords: finite elasticity; linearized elasticity; finite element methods; mixed methods; a posteriori error estimation; goal-oriented error estimation; model error estimation |
| ردمك: | 978-0-470-84699-5 0-470-84699-2 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d2d9657a2215a0b1d738474f5ee2dae2 https://doi.org/10.1002/9781119176817.ecm2025 |
| رقم الأكسشن: | edsair.doi.dedup.....d2d9657a2215a0b1d738474f5ee2dae2 |
| قاعدة البيانات: | OpenAIRE |
| ردمك: | 9780470846995 0470846992 |
|---|