Panagiotopoulos, P. D. 1950
Overview
Works:  27 works in 132 publications in 4 languages and 2,783 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Honoree, Other 
Classifications:  QA316, 515.64 
Publication Timeline
.
Most widely held works by
P. D Panagiotopoulos
Inequality problems in mechanics and applications : convex and nonconvex energy functions by
P. D Panagiotopoulos(
Book
)
18 editions published between 1983 and 1989 in English and Russian and held by 226 WorldCat member libraries worldwide
In a remarkably short time, the field of inequality problems has seen considerable development in mathematics and theoretical mechanics. Applied mechanics and the engineering sciences have also benefitted from these developments in that open problems have been treated and entirely new classes of problems have been formulated and solved. This book is an outgrowth of seven years of seminars and courses on inequality problems in mechanics for a variety of audiences in the Technical University of Aachen, the Aristotle University of Thessaloniki, the University of Hamburg and the Technical University of Milan. The book is intended for a variety of readers, mathematicians and engineers alike, as is detailed in the Guidelines for the Reader. It goes without saying that the work of G. Fichera, J.L. Lions, G. Maier, J.J. Moreau in originating and developing the theory of inequality problems has considerably influenced the present book. I also wish to acknowledge the helpful comments received from C. Bisbos, J. Haslinger, B. Kawohl, H. Matthies, H.O. May, D. Talaslidis and B. Werner. Credit is also due to G. Kyriakopoulos and T. Mandopoulou for their exceptionally diligent work in the preparation of the fmal figures. Many thanks are also due to T. Finnegan and J. Gateley for their friendly assistance from the linguistic standpoint. I would also like to thank my editors in Birkhiiuser Verlag for their cooperation, and all those who helped in the preparation of the manuscript
18 editions published between 1983 and 1989 in English and Russian and held by 226 WorldCat member libraries worldwide
In a remarkably short time, the field of inequality problems has seen considerable development in mathematics and theoretical mechanics. Applied mechanics and the engineering sciences have also benefitted from these developments in that open problems have been treated and entirely new classes of problems have been formulated and solved. This book is an outgrowth of seven years of seminars and courses on inequality problems in mechanics for a variety of audiences in the Technical University of Aachen, the Aristotle University of Thessaloniki, the University of Hamburg and the Technical University of Milan. The book is intended for a variety of readers, mathematicians and engineers alike, as is detailed in the Guidelines for the Reader. It goes without saying that the work of G. Fichera, J.L. Lions, G. Maier, J.J. Moreau in originating and developing the theory of inequality problems has considerably influenced the present book. I also wish to acknowledge the helpful comments received from C. Bisbos, J. Haslinger, B. Kawohl, H. Matthies, H.O. May, D. Talaslidis and B. Werner. Credit is also due to G. Kyriakopoulos and T. Mandopoulou for their exceptionally diligent work in the preparation of the fmal figures. Many thanks are also due to T. Finnegan and J. Gateley for their friendly assistance from the linguistic standpoint. I would also like to thank my editors in Birkhiiuser Verlag for their cooperation, and all those who helped in the preparation of the manuscript
The boundary integral approach to static and dynamic contact problems : equality and inequality methods by
Heinz Antes(
Book
)
10 editions published in 1992 in English and held by 187 WorldCat member libraries worldwide
The fields of boundary integral equations and of inequality problems, or more gen erally, of nonsmooth mechanics, have seen, in a remarkably short time, a considerable development in mathematics and in theoretical and applied mechanics. The engineering sciences have also benefited from these developments in that open problems have been attacked succesfully and entirely new methodologies have been developed. The contact problems of elasticity is a class of problems which has offered many open questions to deal with, both to the research workers working on the theory of boundary integral equations and to those working on the theory of inequality problems. Indeed, the area of static and dynamic contact problems could be considered as the testing workbench of the new developments in both the inequality problems and in the boundary integral equations. This book is a first attempt to formulate and study the boundary integral equations arising in inequality contact problems. The present book is a result of more than two decades of research and teaching activity of the first author on boundary integral equations and, of the second author, on inequality problems, as well as the outgrowth of seminars and courses for a variety of audiences in the Technical University of Aachen, the Aristotle University of Thessa loniki, the Universities of Bochum, of Hamburg and Braunschweig, the Pontificia Univ. Catolica in Rio de Janeiro etc
10 editions published in 1992 in English and held by 187 WorldCat member libraries worldwide
The fields of boundary integral equations and of inequality problems, or more gen erally, of nonsmooth mechanics, have seen, in a remarkably short time, a considerable development in mathematics and in theoretical and applied mechanics. The engineering sciences have also benefited from these developments in that open problems have been attacked succesfully and entirely new methodologies have been developed. The contact problems of elasticity is a class of problems which has offered many open questions to deal with, both to the research workers working on the theory of boundary integral equations and to those working on the theory of inequality problems. Indeed, the area of static and dynamic contact problems could be considered as the testing workbench of the new developments in both the inequality problems and in the boundary integral equations. This book is a first attempt to formulate and study the boundary integral equations arising in inequality contact problems. The present book is a result of more than two decades of research and teaching activity of the first author on boundary integral equations and, of the second author, on inequality problems, as well as the outgrowth of seminars and courses for a variety of audiences in the Technical University of Aachen, the Aristotle University of Thessa loniki, the Universities of Bochum, of Hamburg and Braunschweig, the Pontificia Univ. Catolica in Rio de Janeiro etc
Mathematical theory of hemivariational inequalities and applications by
Z Naniewicz(
Book
)
9 editions published in 1995 in English and held by 175 WorldCat member libraries worldwide
9 editions published in 1995 in English and held by 175 WorldCat member libraries worldwide
Topics in nonsmooth mechanics(
Book
)
9 editions published between 1987 and 1988 in English and held by 146 WorldCat member libraries worldwide
9 editions published between 1987 and 1988 in English and held by 146 WorldCat member libraries worldwide
Hemivariational inequalities : applications in mechanics and engineering by
P. D Panagiotopoulos(
Book
)
12 editions published between 1993 and 2013 in English and Italian and held by 138 WorldCat member libraries worldwide
The aim of the present book is the formulation, mathematical study and numerical treatment of static and dynamic problems in mechanics and engineering sciences involving nonconvex and nonsmooth energy functions, or nonmonotone and multivalued stressstrain laws. Such problems lead to a new type of variational forms, the hemivariational inequalities, which also lead to multivalued differential or integral equations. Innovative numerical methods are presented for the treament of realistic engineering problems. This book is the first to deal with variational theory of engineering problems involving nonmonotone multivalue realations, their mechanical foundation, their mathematical study (existence and certain approximation results) and the corresponding eigenvalue and optimal control problems. All the numerical applications give innovative answers to as yet unsolved or partially solved engineering problems, e.g. the adhesive contact in cracks, the delamination problem, the sawtooth stressstrain laws in composites, the shear connectors in composite beams, the semirigid connections in steel structures, the adhesive grasping in robotics, etc. The book closes with the consideration of hemivariational inequalities for fractal type geometries and with the neural network approach to the numerical treatment of hemivariational inequalities
12 editions published between 1993 and 2013 in English and Italian and held by 138 WorldCat member libraries worldwide
The aim of the present book is the formulation, mathematical study and numerical treatment of static and dynamic problems in mechanics and engineering sciences involving nonconvex and nonsmooth energy functions, or nonmonotone and multivalued stressstrain laws. Such problems lead to a new type of variational forms, the hemivariational inequalities, which also lead to multivalued differential or integral equations. Innovative numerical methods are presented for the treament of realistic engineering problems. This book is the first to deal with variational theory of engineering problems involving nonmonotone multivalue realations, their mechanical foundation, their mathematical study (existence and certain approximation results) and the corresponding eigenvalue and optimal control problems. All the numerical applications give innovative answers to as yet unsolved or partially solved engineering problems, e.g. the adhesive contact in cracks, the delamination problem, the sawtooth stressstrain laws in composites, the shear connectors in composite beams, the semirigid connections in steel structures, the adhesive grasping in robotics, etc. The book closes with the consideration of hemivariational inequalities for fractal type geometries and with the neural network approach to the numerical treatment of hemivariational inequalities
Nonsmooth mechanics and applications by
Jean Jacques Moreau(
Book
)
10 editions published in 1988 in English and held by 136 WorldCat member libraries worldwide
10 editions published in 1988 in English and held by 136 WorldCat member libraries worldwide
From convexity to nonconvexity by
Robert P Gilbert(
Book
)
7 editions published in 2001 in English and held by 112 WorldCat member libraries worldwide
This collection of papers is dedicated to the memory of Gaetano Fichera, a great mathematician and also a good friend to the editors. Regrettably it took an unusual amount of time to bring this collection out. This was primarily due to the fact that the main editor who had collected all of the materials, for this volume, P. D. Panagiotopoulos, died unexpectedly during the period when we were editing the manuscript. The other two editors in appreciation of Panagiotopoulos' contribution to this field, believe it is therefore fitting that this collection be dedicated to his memory also. The theme of the collection is centered around the seminal research of G. Fichera on the Signorini problem. Variants on this idea enter in different ways. For example, by bringing in friction the problem is no longer selfadjoint and the minimization formulation is not valid. A large portion of this collection is devoted to survey papers concerning hemivariational methods, with a main point of its application to nonsmooth mechanics. Hemivariational inequali ties, which are a generalization of variational inequalities, were pioneered by Panagiotopoulos. There are many applications of this theory to the study of non convex energy functionals occurring in many branches of mechanics. An area of concentration concerns contact problems, in particular, quasistatic and dynamic contact problems with friction and damage. Nonsmooth optimization methods which may be divided into the main groups of subgradient methods and bundle methods are also discussed in this collection
7 editions published in 2001 in English and held by 112 WorldCat member libraries worldwide
This collection of papers is dedicated to the memory of Gaetano Fichera, a great mathematician and also a good friend to the editors. Regrettably it took an unusual amount of time to bring this collection out. This was primarily due to the fact that the main editor who had collected all of the materials, for this volume, P. D. Panagiotopoulos, died unexpectedly during the period when we were editing the manuscript. The other two editors in appreciation of Panagiotopoulos' contribution to this field, believe it is therefore fitting that this collection be dedicated to his memory also. The theme of the collection is centered around the seminal research of G. Fichera on the Signorini problem. Variants on this idea enter in different ways. For example, by bringing in friction the problem is no longer selfadjoint and the minimization formulation is not valid. A large portion of this collection is devoted to survey papers concerning hemivariational methods, with a main point of its application to nonsmooth mechanics. Hemivariational inequali ties, which are a generalization of variational inequalities, were pioneered by Panagiotopoulos. There are many applications of this theory to the study of non convex energy functionals occurring in many branches of mechanics. An area of concentration concerns contact problems, in particular, quasistatic and dynamic contact problems with friction and damage. Nonsmooth optimization methods which may be divided into the main groups of subgradient methods and bundle methods are also discussed in this collection
Minimax theorems and qualitative properties of the solutions of hemivariational inequalities by
D Motreanu(
Book
)
10 editions published in 1999 in English and held by 98 WorldCat member libraries worldwide
The present book is the first ever published in which a new type of eigenvalue problem is studied, one that is very useful for applications: eigenvalue problems related to hemivariational inequalities, i.e. involving nonsmooth, nonconvex, energy functions. New existence, multiplicity and perturbation results are proved using three different approaches: minimization, minimax methods and (sub)critical point theory. Nonresonant and resonant cases are studied both for static and dynamic problems and several new qualitative properties of the hemivariational inequalities are obtained. Both simple and double eigenvalue problems are studied, as well as those constrained on the sphere and those which are unconstrained. The book is selfcontained, is written with the utmost possible clarity and contains highly original results. Applications concerning new stability results for beams, plates and shells with adhesive supports, etc. illustrate the theory. Audience: applied and pure mathematicians, civil, aeronautical and mechanical engineers
10 editions published in 1999 in English and held by 98 WorldCat member libraries worldwide
The present book is the first ever published in which a new type of eigenvalue problem is studied, one that is very useful for applications: eigenvalue problems related to hemivariational inequalities, i.e. involving nonsmooth, nonconvex, energy functions. New existence, multiplicity and perturbation results are proved using three different approaches: minimization, minimax methods and (sub)critical point theory. Nonresonant and resonant cases are studied both for static and dynamic problems and several new qualitative properties of the hemivariational inequalities are obtained. Both simple and double eigenvalue problems are studied, as well as those constrained on the sphere and those which are unconstrained. The book is selfcontained, is written with the utmost possible clarity and contains highly original results. Applications concerning new stability results for beams, plates and shells with adhesive supports, etc. illustrate the theory. Audience: applied and pure mathematicians, civil, aeronautical and mechanical engineers
Finite element method for hemivariational inequalities : theory, methods, and applications by
J Haslinger(
Book
)
11 editions published between 1999 and 2011 in English and held by 96 WorldCat member libraries worldwide
"The present book gives a rigorous analysis of finite element approximation for a class of hemivariational inequalities of elliptic and parabolic type. Finite element models are described and their convergence properties are established. Discretized models are numerically treated as nonconvex and nonsmooth optimization problems. The book includes a comprehensive description of typical representants of nonsmooth optimization methods. Basic knowledge of finite element mathematics, functional and nonsmooth analysis is needed. The book is selfcontained. All necessary results from these disciplines are summarized in the introductory chapter." "Audience: Engineers and applied mathematicians at universities and working in industry. Also graduate level courses on advanced nonlinear computational mechanics, mathematics of finite elements and approximation theory."Jacket
11 editions published between 1999 and 2011 in English and held by 96 WorldCat member libraries worldwide
"The present book gives a rigorous analysis of finite element approximation for a class of hemivariational inequalities of elliptic and parabolic type. Finite element models are described and their convergence properties are established. Discretized models are numerically treated as nonconvex and nonsmooth optimization problems. The book includes a comprehensive description of typical representants of nonsmooth optimization methods. Basic knowledge of finite element mathematics, functional and nonsmooth analysis is needed. The book is selfcontained. All necessary results from these disciplines are summarized in the introductory chapter." "Audience: Engineers and applied mathematicians at universities and working in industry. Also graduate level courses on advanced nonlinear computational mechanics, mathematics of finite elements and approximation theory."Jacket
New developments in contact problems by
International Centre for Mechanical Sciences(
Book
)
7 editions published in 1999 in English and held by 84 WorldCat member libraries worldwide
The book gives an overview on formulation, mathematical analysis and numerical solution procedures of contact problems. In this respect the book should be of value to applied mathematicians and engineers who are concerned with contact mechanics
7 editions published in 1999 in English and held by 84 WorldCat member libraries worldwide
The book gives an overview on formulation, mathematical analysis and numerical solution procedures of contact problems. In this respect the book should be of value to applied mathematicians and engineers who are concerned with contact mechanics
Proceedings of the first International Symposium on Impact and Friction of Solids, Structures and Intelligent Machines : in
memoriam P.D. Panagiotopoulos (19501998), Ottawa Congress Centre, Ottawa, Canada, 2730 June 1998 by
Structures and Intelligent Machines International Symposium on Impact and Friction of Solids(
Book
)
5 editions published in 2000 in English and held by 57 WorldCat member libraries worldwide
This book deals with the dynamics of mechanical systems in presence of impact and friction. The contributors are an international group of engineers and scientists from industrial and academic institutions of more than 23 countries around the world concerned with the modeling, analysis, measurement and control of nonsmooth mechanical structures. Contact laws lead to mathematical models that are highly nonlinear and nonsmooth or discontinuous. Discontinuous and nonsmooth processes introduce problems with data processing techniques and analytical methods. Thanks to great advances in computer technology and computational analysis, as well as the introduction of new experimental devices such as the atomicforce microscope and the quartzcrystalmicrobalance probe, the study of impact and friction  one of the oldest problems in physics, is now in a phase of rapid and exciting development. The growing number of research breakthroughs have promoted the development of new technologies in the description and design of systems with impact and friction models to understand nature, structures, machines, transportation systems, and other processes. A fairly comprehensive picture of these new developments is presented in this book by researchers who are giving uptodate accounts of the present state of the field in many aspects. The book is essential for introducing readers in mechanical engineering, material science, applied mathematics, aerospace engineering, ocean engineering, biomechanics, and civil engineering to recent developments in nonsmooth mechanics. It is also useful for selfstudy purposes by professionals and practitioners in the field
5 editions published in 2000 in English and held by 57 WorldCat member libraries worldwide
This book deals with the dynamics of mechanical systems in presence of impact and friction. The contributors are an international group of engineers and scientists from industrial and academic institutions of more than 23 countries around the world concerned with the modeling, analysis, measurement and control of nonsmooth mechanical structures. Contact laws lead to mathematical models that are highly nonlinear and nonsmooth or discontinuous. Discontinuous and nonsmooth processes introduce problems with data processing techniques and analytical methods. Thanks to great advances in computer technology and computational analysis, as well as the introduction of new experimental devices such as the atomicforce microscope and the quartzcrystalmicrobalance probe, the study of impact and friction  one of the oldest problems in physics, is now in a phase of rapid and exciting development. The growing number of research breakthroughs have promoted the development of new technologies in the description and design of systems with impact and friction models to understand nature, structures, machines, transportation systems, and other processes. A fairly comprehensive picture of these new developments is presented in this book by researchers who are giving uptodate accounts of the present state of the field in many aspects. The book is essential for introducing readers in mechanical engineering, material science, applied mathematics, aerospace engineering, ocean engineering, biomechanics, and civil engineering to recent developments in nonsmooth mechanics. It is also useful for selfstudy purposes by professionals and practitioners in the field
Nonsmooth/nonconvex mechanics : modeling, analysis, and numerical methods by ASME Mechanics and Materials Conference(
Book
)
4 editions published in 2001 in English and held by 14 WorldCat member libraries worldwide
Nonsmoothness and nonconvexity arise in numerous applications of mechan ics and modeling due to the need for studying more and more complicated phe nomena and real life applications. Mathematicians have started to provide the necessary tools and theoretical results underpinning these applications. Ap plied mathematicians and engineers have begun to realize the benefits of this new area and are adopting, increasingly, these new tools in their work. New computational tools facilitate numerical applications and enable the theory to be tested, and the resulting feedback poses new theoretical questions. Because of the upsurge in activity in the area of nonsmooth and noncon vex mechanics, Professors Gao and Ogden, together with the late Professor P.D. Panagiotopoulos, had planned to organize a Minisymposium with the title Nonsmooth and Nonconvex Mechanics within the ASME 1999 Mechanics & Materials Conference, June 2730 1999, Blacksburg, Virginia. After the unex pected death of Professor Panagiotopoulos the first two editors invited the third editor (Professor Stavroulakis) to join them. A large number of mathematical and engineering colleagues supported our efforts by presenting lectures at the Minisymposium in which the available mathematical methods were described and many problems of nonsmooth and nonconvex mechanics were discussed. The interest of the many participants encourages us all to continue our research efforts
4 editions published in 2001 in English and held by 14 WorldCat member libraries worldwide
Nonsmoothness and nonconvexity arise in numerous applications of mechan ics and modeling due to the need for studying more and more complicated phe nomena and real life applications. Mathematicians have started to provide the necessary tools and theoretical results underpinning these applications. Ap plied mathematicians and engineers have begun to realize the benefits of this new area and are adopting, increasingly, these new tools in their work. New computational tools facilitate numerical applications and enable the theory to be tested, and the resulting feedback poses new theoretical questions. Because of the upsurge in activity in the area of nonsmooth and noncon vex mechanics, Professors Gao and Ogden, together with the late Professor P.D. Panagiotopoulos, had planned to organize a Minisymposium with the title Nonsmooth and Nonconvex Mechanics within the ASME 1999 Mechanics & Materials Conference, June 2730 1999, Blacksburg, Virginia. After the unex pected death of Professor Panagiotopoulos the first two editors invited the third editor (Professor Stavroulakis) to join them. A large number of mathematical and engineering colleagues supported our efforts by presenting lectures at the Minisymposium in which the available mathematical methods were described and many problems of nonsmooth and nonconvex mechanics were discussed. The interest of the many participants encourages us all to continue our research efforts
Ungleichungsprobleme in der Mechanik by
P. D Panagiotopoulos(
Book
)
3 editions published in 1977 in German and held by 8 WorldCat member libraries worldwide
3 editions published in 1977 in German and held by 8 WorldCat member libraries worldwide
Ungleichheitsprobleme in der Mechanik by
P. D Panagiotopoulos(
)
1 edition published in 1977 in German and held by 4 WorldCat member libraries worldwide
1 edition published in 1977 in German and held by 4 WorldCat member libraries worldwide
Applications of fractals in material science and engineering(
Book
)
2 editions published in 1997 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1997 in English and held by 2 WorldCat member libraries worldwide
Variational theory for liquid crystals with variable degree of orientation by
Z Naniewicz(
Book
)
2 editions published in 1997 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1997 in English and held by 2 WorldCat member libraries worldwide
Quasidifferentiability and nonsmooth modelling in mechanics, engineering, and economics by
Vladimir F Demyanov(
Book
)
2 editions published in 1996 in English and held by 1 WorldCat member library worldwide
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
2 editions published in 1996 in English and held by 1 WorldCat member library worldwide
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
Sports : Social Inclusion or Racism and Xenophobia? by Nikolaos Patsantaras(
)
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
Proceedings of the First International Symposium on Impact and Friction of Solids, Structures and Intelligent Machines: In
Memoriam P.D. Panagiotopoulos (19501998), Ottawa Congress Centre, Ottawa, Ca by
A Guran(
Book
)
1 edition published in 2000 in Undetermined and held by 1 WorldCat member library worldwide
1 edition published in 2000 in Undetermined and held by 1 WorldCat member library worldwide
Integrative ElternKindTherapie. Ein Modell zur Behandlung des Erziehungsprozesses A Model of Integrative ParentsChildTherapy
(IEKT) by
P. D Panagiotopoulos(
)
1 edition published in 1985 in German and held by 0 WorldCat member libraries worldwide
1 edition published in 1985 in German and held by 0 WorldCat member libraries worldwide
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Related Identities
 Guran, A. (Ardéshir) Author
 Naniewicz, Z. 1950 Author
 Moreau, Jean Jacques 1923 Other Author Editor
 International Centre for Mechanical Sciences
 Antes, Heinz Author
 Strang, Gilbert Other Editor
 Gilbert, Robert P. 1932 Author Editor
 Pardalos, P. M. (Panos M.) 1954 Editor
 Haslinger, J. Author
 Miettinen, Markku
Associated Subjects
Boundary element methods Calculus of variations Civil engineering Contact mechanics Dynamics Economics EconomicsMathematical models Engineering EngineeringMathematical models Engineering mathematics Finite element method Friction Functions, Special Hemivariational inequalities Impact Inequalities (Mathematics) Mathematical analysis Mathematical optimization Mathematics Maxima and minima Mechanics Mechanics, Analytic Mechanics, Applied Mechanics, AppliedMathematical models Nonsmooth optimization Nonstandard mathematical analysis Panagiotopoulos, P. D., Quasidifferential calculus Smoothness of functions Surfaces (Technology) Surfaces (Technology)Mathematical models Topological groups