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Franz-Theo Suttmeier describes a general approach to a posteriori error estimation and adaptive mesh design for finite element models where the solution is subjected to inequality constraints. This is an extension to variational inequalities of the so-called Dual-Weighted-Residual method (DWR method) which is based on a variational formulation of the problem and uses global duality arguments for deriving weighted a posteriori error estimates with respect to arbitrary functionals of the error. In these estimates local residuals of the computed solution are multiplied by sensitivity factors which are obtained from a numerically computed dual solution. The resulting local error indicators are used in a feed-back process for generating economical meshes which are tailored according to the particular goal of the computation. This method is developed here for several model problems. Based on these examples, a general concept is proposed, which provides a systematic way of adaptive error control for problems stated in form of variational inequalities.

Mathematics. --- Mathematics, general. --- Mathématiques --- Differential equations, Partial -- Numerical solutions. --- Error analysis (Mathematics). --- Finite element method. --- Variational inequalities (Mathematics). --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Applied Physics --- Variational inequalities (Mathematics) --- Error analysis (Mathematics) --- Differential equations, Partial --- Numerical solutions. --- Errors, Theory of --- Inequalities, Variational (Mathematics) --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Numerical analysis. --- Numerical Analysis. --- Numerical analysis --- Instrumental variables (Statistics) --- Mathematical statistics --- Statistics --- Calculus of variations --- Differential inequalities --- Isogeometric analysis --- Mathematical analysis --- Math --- Science

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The work deals with a systematic theoretical and problem-oriented treatment of fundamental topics in the wide area of error-controlled adaptive finite element methods for analyzing engineering structures with elastic and inelastic material behavior applied to engineering structures. Different types of error estimators are presented from both mathematical and engineering points of views: global estimators and goal-oriented estimators based on duality techniques, controlling h-, p-, and hp-adaptivity. Special features are: combined model and discretization adaptivity for thin-walled structures, hierarchic modeling in elasticity and related hp-adaptivity, error estimators of constitutive equations, adequate mesh refinement techniques and error-controlled adaptive elastic-plastic analysis of contact problems. The benefits are seen in new methods and results of leading researches in the field which provide deeper insight into recent developments of a posteriori error analysis and adaptivity.

Engineering. --- Numerical and Computational Methods in Engineering. --- Numerical Analysis. --- Numerical analysis. --- Ingénierie --- Analyse numérique --- Structural analysis (Engineering) --- Finite element method. --- Boundary element methods. --- Mathematical models. --- Structural analysis (Engineering) -- Mathematical models. --- Engineering & Applied Sciences --- Computer Science --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- BEM (Engineering analysis) --- BIE analysis --- BIE methods --- Boundary element analysis --- Boundary elements methods --- Boundary integral equation analysis --- Boundary integral equation methods --- Boundary integral methods --- Computational intelligence. --- Computational Intelligence. --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Mathematical analysis --- Construction --- Industrial arts --- Technology --- Numerical analysis --- Isogeometric analysis

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This textbook aims to be the bridge between plate theory and FE-software. Structural engineers must translate elastic analysis results into economic structure dimensions and reinforcement, which raises difficulties. Not all engineers are well enough equipped for the increasingly easy-to-use powerful programs. The problem is not lack of FE-knowledge, but rather ignorance of plate behaviour. Therefore, this book starts with classical plate theory for membrane and bending states, and proceeds to FE-practice. This volume can be used for university courses, serving as practical preparation for the engineering profession, and as a guide to structural designers.

Classical mechanics. Field theory --- Solid state physics --- Applied physical engineering --- Engineering sciences. Technology --- Artificial intelligence. Robotics. Simulation. Graphics --- Building design --- Building materials. Building technology --- Civil engineering. Building industry --- Architecture --- neuronale netwerken --- fuzzy logic --- cybernetica --- toegepaste mechanica --- bouwkunde --- architectuur --- KI (kunstmatige intelligentie) --- ingenieurswetenschappen --- bouw --- mechanica --- Finite element method --- Plates (Engineering) --- Structural analysis (Engineering) --- buigen --- dikke plaat --- discreet element method --- dunne plaat --- fem --- orthotrope plaat --- plaatmembraantheorie --- rechthoekige plaat --- sterkteleer --- FEM --- platen --- stabiliteit --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Numerical analysis --- Isogeometric analysis --- Architectural engineering --- Engineering, Architectural --- Structural mechanics --- Structures, Theory of --- Structural engineering --- Disks (Mechanics) --- Panels --- Structural plates --- Elastic plates and shells --- Shells (Engineering) --- Mathematical models --- Finite element method. --- Structural analysis (Engineering). --- Mathematical models.