Ebook: Hemivariational Inequalities: Applications in Mechanics and Engineering

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 stress-strain 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 stress-strain 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.

---

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 stress-strain 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 stress-strain 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.

---

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 stress-strain 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 stress-strain 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.
Content:
Front Matter....Pages I-XVI
Front Matter....Pages 1-1
Elements of Nonsmooth Analysis....Pages 3-29
Front Matter....Pages 31-31
Nonsmooth Mechanics I....Pages 33-64
Nonsmooth Mechanics II....Pages 65-98
Hemivariational Inequalities....Pages 99-134
Multivalued Boundary Integral Equations....Pages 135-151
Front Matter....Pages 153-153
Static Hemivariational Inequalities....Pages 155-177
Eigenvalue and Dynamic Problems....Pages 179-221
Optimal Control and Identification Problems....Pages 223-236
Front Matter....Pages 237-237
On the Numerical Treatment of Hemivariational Inequalities....Pages 239-279
On the Approximation of Hemivariational Inequalities by Variational Inequalities....Pages 281-315
The Method of Substationary Point Search....Pages 317-344
On a Decomposition Method into Two Convex Problems....Pages 345-359
Dynamic Hemivariational Inequalities and Crack Problems....Pages 361-376
Applications of the Theory of Hemivariational Inequalities in Robotics....Pages 377-392
Addenda: Hemivariational Inequalities, Fractals and Neural Networks....Pages 393-415
Back Matter....Pages 417-451

---

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 stress-strain 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 stress-strain 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.
Content:
Front Matter....Pages I-XVI
Front Matter....Pages 1-1
Elements of Nonsmooth Analysis....Pages 3-29
Front Matter....Pages 31-31
Nonsmooth Mechanics I....Pages 33-64
Nonsmooth Mechanics II....Pages 65-98
Hemivariational Inequalities....Pages 99-134
Multivalued Boundary Integral Equations....Pages 135-151
Front Matter....Pages 153-153
Static Hemivariational Inequalities....Pages 155-177
Eigenvalue and Dynamic Problems....Pages 179-221
Optimal Control and Identification Problems....Pages 223-236
Front Matter....Pages 237-237
On the Numerical Treatment of Hemivariational Inequalities....Pages 239-279
On the Approximation of Hemivariational Inequalities by Variational Inequalities....Pages 281-315
The Method of Substationary Point Search....Pages 317-344
On a Decomposition Method into Two Convex Problems....Pages 345-359
Dynamic Hemivariational Inequalities and Crack Problems....Pages 361-376
Applications of the Theory of Hemivariational Inequalities in Robotics....Pages 377-392
Addenda: Hemivariational Inequalities, Fractals and Neural Networks....Pages 393-415
Back Matter....Pages 417-451
....