Quasidifferentiability and Nonsmooth Modelling in Mechanics, Engineering and Economics

1. Front Matter

   Pages i-xvii

   PDF

2. Nonsmooth Analysis

   • Vladimir F. Dem’yanov, Georgios E. Stavroulakis, Ludmila N. Polyakova, Panagiotis D. Panagiotopoulos

   Pages 1-48

3. Quasidifferentiable Functions and Sets

   • Vladimir F. Dem’yanov, Georgios E. Stavroulakis, Ludmila N. Polyakova, Panagiotis D. Panagiotopoulos

   Pages 49-91

4. Nonsmooth Mechanics I

   • Vladimir F. Dem’yanov, Georgios E. Stavroulakis, Ludmila N. Polyakova, Panagiotis D. Panagiotopoulos

   Pages 93-137

5. Nonsmooth Mechanics II

   • Vladimir F. Dem’yanov, Georgios E. Stavroulakis, Ludmila N. Polyakova, Panagiotis D. Panagiotopoulos

   Pages 139-176

6. Additional Topics

   • Vladimir F. Dem’yanov, Georgios E. Stavroulakis, Ludmila N. Polyakova, Panagiotis D. Panagiotopoulos

   Pages 177-203

7. Nonsmooth Optimization Algorithms

   • Vladimir F. Dem’yanov, Georgios E. Stavroulakis, Ludmila N. Polyakova, Panagiotis D. Panagiotopoulos

   Pages 205-252

8. Nonsmooth Computational Mechanics

   • Vladimir F. Dem’yanov, Georgios E. Stavroulakis, Ludmila N. Polyakova, Panagiotis D. Panagiotopoulos

   Pages 253-295

9. Nonsmooth Computational Mechanics

   • Vladimir F. Dem’yanov, Georgios E. Stavroulakis, Ludmila N. Polyakova, Panagiotis D. Panagiotopoulos

   Pages 297-344

10. Back Matter

    Pages 345-349

    PDF

Nonsmooth energy functions govern phenomena which occur frequently in nature and in all areas of life. They constitute a fascinating subject in mathematics and permit the rational understanding of yet unsolved or partially solved questions in mechanics, engineering and economics.
This is the first book to provide a complete and rigorous presentation of the quasidifferentiability approach to nonconvex, possibly nonsmooth, energy functions, of the derivation and study of the corresponding variational expressions in mechanics, engineering and economics, and of their numerical treatment. The new variational formulations derived are illustrated by many interesting numerical problems. The techniques presented will permit the reader to check any solution obtained by other heuristic techniques for nonconvex, nonsmooth energy problems. A civil, mechanical or aeronautical engineer can find in the book the only existing mathematically sound technique for the formulation and study of nonconvex, nonsmooth energy problems.
Audience: The book will be of interest to pure and applied mathematicians, physicists, researchers in mechanics, civil, mechanical and aeronautical engineers, structural analysts and software developers. It is also suitable for graduate courses in nonlinear mechanics, nonsmooth analysis, applied optimization, control, calculus of variations and computational mechanics.

• Calculus of Variations
• algorithm
• algorithms
• calculus
• mechanics
• modeling
• optimization
• stability

`... In view of the growing number of recent publications dealing with nonsmooth and set-valued modelling ... this book, which was written by a multidisciplinary group of authors, seems to be the first attempt to make nonsmooth modelling and set-valued techniques accessible to applied scientists by presenting the quasidifferentiable approach by means of concrete applications. ... The book provides significant help to scientists or graduate students who need an authoritative and understandable introduction to this field, and who would also, like to extend his/her ability to model nonsmooth complicated effects in his/her work. It may also serve as a reference book for advanced graduate courses in nonsmooth modelling, optimization and engineering. ... The book appears very attractive and it is certainly unique ...'
Daniel Goeleven in Mathematical Reviews, Issue 97h:49001

• Department of Mathematics, St. Petersburg State University, St. Petersburg, Russia

  Vladimir F. Dem’yanov, Ludmila N. Polyakova

• Lehr- und Forschungsgebiet für Mechanik; Lehrstuhl C für Mathematik, RWTH, Aachen, Germany

  Georgios E. Stavroulakis

• Department of Civil Engineering, Aristotle University, Thessaloniki, Greece

  Panagiotis D. Panagiotopoulos

• Faculty of Mathematics and Physics, RWTH, Aachen, Germany

  Panagiotis D. Panagiotopoulos

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