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Matériaux --- Modelisation --- Structure

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The papers in this volume start with a description of  the construction of reduced models through a review of Proper Orthogonal Decomposition (POD) and reduced basis models, including their mathematical foundations and some challenging applications, then followed by a description of a  new generation of simulation strategies based on the use of separated representations (space-parameters, space-time, space-time-parameters, space-space,…), which have led to what is known as Proper Generalized Decomposition (PGD) techniques. The models can be enriched by treating parameters as additional coordinates, leading to fast and inexpensive online calculations based on richer offline parametric solutions. Separated representations are analyzed in detail in the course, from their mathematical foundations to their most spectacular applications. It is also shown how such an approximation could evolve into a new paradigm in computational science, enabling one to circumvent various computational issues in a vast array of applications in engineering science.

Orthogonal decompositions. --- Decomposition (Mathematics) --- Mechanics, applied. --- Computer science. --- Computer aided design. --- Theoretical and Applied Mechanics. --- Computational Science and Engineering. --- Computer-Aided Engineering (CAD, CAE) and Design. --- CAD (Computer-aided design) --- Computer-assisted design --- Computer-aided engineering --- Design --- Informatics --- Science --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Mechanics. --- Mechanics, Applied. --- Computer mathematics. --- Computer-aided engineering. --- CAE --- Engineering --- Computer mathematics --- Electronic data processing --- Mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Data processing

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Mastering Calculations in Linear and Nonlinear Mechanics is concerned with the management of calculations in linear and nonlinear mechanics. In the last twenty years or so this constant preoccupation in industry as well as in research has gone through a revolution with the advent of truly quantitative tools. Particular attention is given to error estimators and indicators for structural analysis, as this domain is the most mature today. The accent is on the concept of error in constitutive relation. An important part of this work is also devoted to the utilization of the error estimators involved in a calculation, beginning with the parameters related to the mesh. Many of the topics are taken from the most recent research by the authors: local error estimators, extension of the concept of error in constitutive relation to nonlinear evolution problems and dynamic problems, adaptive improvement of calculations in nonlinear mechanics. This work is intended for all those interested in mechanics: students, researchers and engineers concerned with the construction of models as well as their simulation for industrial purposes.

Engineering. --- Computational intelligence. --- Structural mechanics. --- Mechanical engineering. --- Mechanical Engineering. --- Computational Intelligence. --- Structural Mechanics. --- Engineering, Mechanical --- Engineering --- Machinery --- Steam engineering --- Architectural engineering --- Engineering, Architectural --- Structural mechanics --- Structures, Theory of --- Structural engineering --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Construction --- Industrial arts --- Technology --- Mechanics, Applied --- Engineering mathematics. --- Mathematical models. --- Engineering analysis --- Mathematical analysis --- Mathematics --- Mechanics. --- Mechanics, Applied. --- Solid Mechanics. --- Applied mechanics --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory

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