Pierre Ladevèze – författare

Modeling and simulation are central to a mechanical engineer's activity. Increasingly complex models are being used routinely on a daily basis. This revolution is the result of the extraordinary progress in computer technology in terms of both hardware and software.This work deals with the control of the hypotheses leading from a mechanical model, usually coming from continuum mechanics, to a numerical model, i.e. the mastery of the mechanical computation process itself. Particular attention is given to structural analysis which, in this context, is the most advanced domain.A significant part of this work is dedicated to the application of error estimators to the control of the various parameters involved in a calculation, beginning with the parameters related to the mesh.

Mechanical Engineering, an engineering discipline borne of the needs of the in­ dustrial revolution, is once again asked to do its substantial share in the call for industrial renewal. The general call is urgent as we face profound issues of pro­ ductivity and competitiveness that require engineering solutions, among others. The Mechanical Engineering Series features graduate texts and research mono­ graphs intended to address the need for information in contemporary areas ofme­ chanical engineering. The series is conceived as a comprehensive one that covers a broad range of concentrations important to mechanical engineering graduate education and re­ search. We are fortunate to have a distinguished roster ofconsulting editors on the advisory board, each an expert in one ofthe areas ofconcentration. The names of the consulting editors are listed on the next page of this volume. The areas of concentration are applied mechanics, biomechanics, computational mechanics, dynamic systems and control, energetics, mechanics ofmaterials, processing, ther­ mal science, and tribology. Frederick A. Leckie,the series editor for applied mechanics, and I are pleased to presentthis volume in the Series: Nonlinear Computational Structural Mechan­ ics: New Approaches and Non-Incremental Methods of Calculation, by Pierre Ladeveze. The selection of this volume underscores again the interest of the Me­ chanical Engineering series to provide our readers with topical monographs as well as graduate texts in a wide variety of fields.

Mechanical Engineering, an engineering discipline borne of the needs of the in­ dustrial revolution, is once again asked to do its substantial share in the call for industrial renewal. The general call is urgent as we face profound issues of pro­ ductivity and competitiveness that require engineering solutions, among others. The Mechanical Engineering Series features graduate texts and research mono­ graphs intended to address the need for information in contemporary areas ofme­ chanical engineering. The series is conceived as a comprehensive one that covers a broad range of concentrations important to mechanical engineering graduate education and re­ search. We are fortunate to have a distinguished roster ofconsulting editors on the advisory board, each an expert in one ofthe areas ofconcentration. The names of the consulting editors are listed on the next page of this volume. The areas of concentration are applied mechanics, biomechanics, computational mechanics, dynamic systems and control, energetics, mechanics ofmaterials, processing, ther­ mal science, and tribology. Frederick A. Leckie,the series editor for applied mechanics, and I are pleased to presentthis volume in the Series: Nonlinear Computational Structural Mechan­ ics: New Approaches and Non-Incremental Methods of Calculation, by Pierre Ladeveze. The selection of this volume underscores again the interest of the Me­ chanical Engineering series to provide our readers with topical monographs as well as graduate texts in a wide variety of fields.

Mechanical Engineering, an engineering discipline borne of the needs of the in­ dustrial revolution, is once again asked to do its substantial share in the call for industrial renewal. The general call is urgent as we face profound issues of pro­ ductivity and competitiveness that require engineering solutions, among others. The Mechanical Engineering Series features graduate texts and research mono­ graphs intended to address the need for information in contemporary areas ofme­ chanical engineering. The series is conceived as a comprehensive one that covers a broad range of concentrations important to mechanical engineering graduate education and re­ search. We are fortunate to have a distinguished roster ofconsulting editors on the advisory board, each an expert in one ofthe areas ofconcentration. The names of the consulting editors are listed on the next page of this volume. The areas of concentration are applied mechanics, biomechanics, computational mechanics, dynamic systems and control, energetics, mechanics ofmaterials, processing, ther­ mal science, and tribology. Frederick A. Leckie,the series editor for applied mechanics, and I are pleased to presentthis volume in the Series: Nonlinear Computational Structural Mechan­ ics: New Approaches and Non-Incremental Methods of Calculation, by Pierre Ladeveze. The selection of this volume underscores again the interest of the Me­ chanical Engineering series to provide our readers with topical monographs as well as graduate texts in a wide variety of fields.

Modeling and simulation are central to a mechanical engineer's activity. Increasingly complex models are being used routinely on a daily basis. This revolution is the result of the extraordinary progress in computer technology in terms of both hardware and software.This work deals with the control of the hypotheses leading from a mechanical model, usually coming from continuum mechanics, to a numerical model, i.e. the mastery of the mechanical computation process itself.  Particular attention is given to structural analysis which, in this context, is the most advanced domain.A significant part of this work is dedicated to the application of error estimators to the control of the various parameters involved in a calculation, beginning with the parameters related to the mesh.

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.