Variational Models And Methods In Solid And Fluid Mechanics
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| Author | : Francesco dell'Isola |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 363 |
| Release | : 2012-01-15 |
| Genre | : Technology & Engineering |
| ISBN | : 3709109833 |
F. dell'Isola, L. Placidi: Variational principles are a powerful tool also for formulating field theories. - F. dell'Isola, P. Seppecher, A. Madeo: Beyond Euler-Cauchy Continua. The structure of contact actions in N-th gradient generalized continua: a generalization of the Cauchy tetrahedron argument. - B. Bourdin, G.A. Francfort: Fracture. - S. Gavrilyuk: Multiphase flow modeling via Hamilton's principle. - V. L. Berdichevsky: Introduction to stochastic variational problems. - A. Carcaterra: New concepts in damping generation and control: theoretical formulation and industrial applications. - F. dell'Isola, P. Seppecher, A. Madeo: Fluid shock wave generation at solid-material discontinuity surfaces in porous media. Variational methods give an efficient and elegant way to formulate and solve mathematical problems that are of interest to scientists and engineers. In this book three fundamental aspects of the variational formulation of mechanics will be presented: physical, mathematical and applicative ones. The first aspect concerns the investigation of the nature of real physical problems with the aim of finding the best variational formulation suitable to those problems. The second aspect is the study of the well-posedeness of those mathematical problems which need to be solved in order to draw previsions from the formulated models. And the third aspect is related to the direct application of variational analysis to solve real engineering problems.
| Author | : Alexander S. Kravchuk |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 337 |
| Release | : 2007-09-04 |
| Genre | : Technology & Engineering |
| ISBN | : 1402063776 |
The essential aim of this book is to consider a wide set of problems arising in the mathematical modeling of mechanical systems under unilateral constraints. In these investigations elastic and non-elastic deformations, friction and adhesion phenomena are taken into account. All the necessary mathematical tools are given: local boundary value problem formulations, construction of variational equations and inequalities and their transition to minimization problems, existence and uniqueness theorems, and variational transformations (Friedrichs and Young-Fenchel-Moreau) to dual and saddle-point search problems.
| Author | : Edgardo O. Taroco |
| Publisher | : John Wiley & Sons |
| Total Pages | : 606 |
| Release | : 2020-02-25 |
| Genre | : Mathematics |
| ISBN | : 1119600901 |
Introduces readers to the fundamentals and applications of variational formulations in mechanics Nearly 40 years in the making, this book provides students with the foundation material of mechanics using a variational tapestry. It is centered around the variational structure underlying the Method of Virtual Power (MVP). The variational approach to the modeling of physical systems is the preferred approach to address complex mathematical modeling of both continuum and discrete media. This book provides a unified theoretical framework for the construction of a wide range of multiscale models. Introduction to the Variational Formulation in Mechanics: Fundamentals and Applications enables readers to develop, on top of solid mathematical (variational) bases, and following clear and precise systematic steps, several models of physical systems, including problems involving multiple scales. It covers: Vector and Tensor Algebra; Vector and Tensor Analysis; Mechanics of Continua; Hyperelastic Materials; Materials Exhibiting Creep; Materials Exhibiting Plasticity; Bending of Beams; Torsion of Bars; Plates and Shells; Heat Transfer; Incompressible Fluid Flow; Multiscale Modeling; and more. A self-contained reader-friendly approach to the variational formulation in the mechanics Examines development of advanced variational formulations in different areas within the field of mechanics using rather simple arguments and explanations Illustrates application of the variational modeling to address hot topics such as the multiscale modeling of complex material behavior Presentation of the Method of Virtual Power as a systematic tool to construct mathematical models of physical systems gives readers a fundamental asset towards the architecture of even more complex (or open) problems Introduction to the Variational Formulation in Mechanics: Fundamentals and Applications is a ideal book for advanced courses in engineering and mathematics, and an excellent resource for researchers in engineering, computational modeling, and scientific computing.
| Author | : Kevin W. Cassel |
| Publisher | : Cambridge University Press |
| Total Pages | : 433 |
| Release | : 2013-07-22 |
| Genre | : Mathematics |
| ISBN | : 1107022584 |
This book reflects the strong connection between calculus of variations and the applications for which variational methods form the foundation.
| Author | : Jing Tang Xing |
| Publisher | : Academic Press |
| Total Pages | : 682 |
| Release | : 2019-08-30 |
| Genre | : Technology & Engineering |
| ISBN | : 0128193530 |
Fluid-Solid Interaction Dynamics: Theory, Variational Principles, Numerical Methods and Applications gives a comprehensive accounting of fluid-solid interaction dynamics, including theory, numerical methods and their solutions for various FSI problems in engineering. The title provides the fundamental theories, methodologies and results developed in the application of FSI dynamics. Four numerical approaches that can be used with almost all integrated FSI systems in engineering are presented. Methods are linked with examples to illustrate results. In addition, numerical results are compared with available experiments or numerical data in order to demonstrate the accuracy of the approaches and their value to engineering applications. The title gives readers the state-of-the-art in theory, variational principles, numerical modeling and applications for fluid-solid interaction dynamics. Readers will be able to independently formulate models to solve their engineering FSI problems using information from this book. - Presents the state-of-the-art in fluid-solid interaction dynamics, providing theory, method and results - Takes an integrated approach to formulate, model and simulate FSI problems in engineering - Illustrates results with concrete examples - Gives four numerical approaches and related theories that are suitable for almost all integrated FSI systems - Provides the necessary information for bench scientists to independently formulate, model, and solve physical FSI problems in engineering
| Author | : Francesco dell'Isola |
| Publisher | : Springer |
| Total Pages | : 954 |
| Release | : 2018-10-06 |
| Genre | : Science |
| ISBN | : 3319706926 |
This book presents the second volume of Piola’s original Italian text together with the English-language translation and comments, showing convincingly that Gabrio Piola’s work must still be regarded as a modern theory. Gabrio Piola’s work has had an enormous impact on the development of applied mathematics and continuum mechanics. As such, a committee of scientific experts took it upon themselves to translate his complete works. In a second step, they commented on Piola’s work and compared it to modern theories in mechanics in order to stress Piola’s impact on modern science and prove and confirm that he achieved significant milestones in applied mathematics.
| Author | : Francesco dell'Isola |
| Publisher | : Springer |
| Total Pages | : 816 |
| Release | : 2014-07-02 |
| Genre | : Science |
| ISBN | : 3319002635 |
Gabrio Piola works had an enormous impact on the development of applied mathematics and continuum mechanics. An excellent scientific committee who took it upon themselves to translate his complete works. In a second step, they commented Piola’s work and compared it to modern theories in mechanics in order to stress Piola’s impact on modern science and proofs that he has set milestones in applied mathematics. This book presents Piola's original Italian text together with ist translations and their comments. It shows impressively that Gabrio Piola’s work must still be regarded as a modern theory.
| Author | : O. C. Zienkiewicz |
| Publisher | : Elsevier |
| Total Pages | : 653 |
| Release | : 2005-08-09 |
| Genre | : Technology & Engineering |
| ISBN | : 0080455581 |
This is the key text and reference for engineers, researchers and senior students dealing with the analysis and modelling of structures – from large civil engineering projects such as dams, to aircraft structures, through to small engineered components. Covering small and large deformation behaviour of solids and structures, it is an essential book for engineers and mathematicians. The new edition is a complete solids and structures text and reference in its own right and forms part of the world-renowned Finite Element Method series by Zienkiewicz and Taylor. New material in this edition includes separate coverage of solid continua and structural theories of rods, plates and shells; extended coverage of plasticity (isotropic and anisotropic); node-to-surface and 'mortar' method treatments; problems involving solids and rigid and pseudo-rigid bodies; and multi-scale modelling. - Dedicated coverage of solid and structural mechanics by world-renowned authors, Zienkiewicz and Taylor - New material including separate coverage of solid continua and structural theories of rods, plates and shells; extended coverage for small and finite deformation; elastic and inelastic material constitution; contact modelling; problems involving solids, rigid and discrete elements; and multi-scale modelling
| Author | : Victor Berdichevsky |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 590 |
| Release | : 2009-09-18 |
| Genre | : Science |
| ISBN | : 354088467X |
Thereareabout500booksonvariationalprinciples. Theyareconcernedmostlywith the mathematical aspects of the topic. The major goal of this book is to discuss the physical origin of the variational principles and the intrinsic interrelations between them. For example, the Gibbs principles appear not as the rst principles of the theory of thermodynamic equilibrium but as a consequence of the Einstein formula for thermodynamic uctuations. The mathematical issues are considered as long as they shed light on the physical outcomes and/or provide a useful technique for direct study of variational problems. Thebookisacompletelyrewrittenversionoftheauthor’smonographVariational Principles of Continuum Mechanics which appeared in Russian in 1983. I have been postponing the English translation because I wished to include the variational pr- ciples of irreversible processes in the new edition. Reaching an understanding of this subject took longer than I expected. In its nal form, this book covers all aspects of the story. The part concerned with irreversible processes is tiny, but it determines the accents put on all the results presented. The other new issues included in the book are: entropy of microstructure, variational principles of vortex line dynamics, va- ational principles and integration in functional spaces, some stochastic variational problems, variational principle for probability densities of local elds in composites with random structure, variational theory of turbulence; these topics have not been covered previously in monographic literature.
| Author | : Thomas Richter |
| Publisher | : Springer |
| Total Pages | : 452 |
| Release | : 2017-08-26 |
| Genre | : Mathematics |
| ISBN | : 3319639706 |
This book starts by introducing the fundamental concepts of mathematical continuum mechanics for fluids and solids and their coupling. Special attention is given to the derivation of variational formulations for the subproblems describing fluid- and solid-mechanics as well as the coupled fluid-structure interaction problem. Two monolithic formulations for fluid-structure interactions are described in detail: the well-established ALE formulation and the modern Fully Eulerian formulation, which can effectively deal with problems featuring large deformation and contact. Further, the book provides details on state-of-the-art discretization schemes for fluid- and solid-mechanics and considers the special needs of coupled problems with interface-tracking and interface-capturing techniques. Lastly, advanced topics like goal-oriented error estimation, multigrid solution and gradient-based optimization schemes are discussed in the context of fluid-structure interaction problems.
