Author: Gerhard A. Holzapfel Publisher: ISBN: Category : Mathematics Languages : en Pages : 482
Book Description
Providing a modern and comprehensive coverage of continuum mechanics, this volume includes information on "variational principles"--Significant, as this is the only method by which such material is actually utilized in engineering practice.
Author: John D. Clayton Publisher: Springer Science & Business Media ISBN: 9400703503 Category : Science Languages : en Pages : 709
Book Description
This book describes behavior of crystalline solids primarily via methods of modern continuum mechanics. Emphasis is given to geometrically nonlinear descriptions, i.e., finite deformations. Primary topics include anisotropic crystal elasticity, plasticity, and methods for representing effects of defects in the solid on the material's mechanical response. Defects include crystal dislocations, point defects, twins, voids or pores, and micro-cracks. Thermoelastic, dielectric, and piezoelectric behaviors are addressed. Traditional and higher-order gradient theories of mechanical behavior of crystalline solids are discussed. Differential-geometric representations of kinematics of finite deformations and lattice defect distributions are presented. Multi-scale modeling concepts are described in the context of elastic and plastic material behavior. Representative substances towards which modeling techniques may be applied are single- and poly- crystalline metals and alloys, ceramics, and minerals. This book is intended for use by scientists and engineers involved in advanced constitutive modeling of nonlinear mechanical behavior of solid crystalline materials. Knowledge of fundamentals of continuum mechanics and tensor calculus is a prerequisite for accessing much of the text. This book could be used as supplemental material for graduate courses on continuum mechanics, elasticity, plasticity, micromechanics, or dislocation mechanics, for students in various disciplines of engineering, materials science, applied mathematics, and condensed matter physics.
Author: Jacques Besson Publisher: Springer Science & Business Media ISBN: 9048133564 Category : Science Languages : en Pages : 433
Book Description
In mechanical engineering and structural analysis there is a significant gap between the material models currently used by engineers for industry applications and those already available in research laboratories. This is especially apparent with the huge progress of computational possibilities and the corresponding dissemination of numerical tools in engineering practice, which essentially deliver linear solutions. Future improvements of design and life assessment methods necessarily involve non-linear solutions for inelastic responses, in plasticity or viscoplasticity, as well as damage and fracture analyses. The dissemination of knowledge can be improved by software developments, data base completion and generalization, but also by information and training. With such a perspective Non-Linear Mechanics of Materials proposes a knowledge actualization, in order to better understand and use recent material constitutive and damage modeling methods in the context of structural analysis or multiscale material microstructure computations.
Author: Adnan Ibrahimbegovic Publisher: Springer Science & Business Media ISBN: 9048123305 Category : Computers Languages : en Pages : 588
Book Description
This book offers a recipe for constructing the numerical models for representing the complex nonlinear behavior of structures and their components, represented as deformable solid bodies. Its appeal extends to those interested in linear problems of mechanics.
Author: Walter Lacarbonara Publisher: Springer Science & Business Media ISBN: 1441912762 Category : Science Languages : en Pages : 812
Book Description
This book reviews the theoretical framework of nonlinear mechanics, covering computational methods, applications, parametric investigations of nonlinear phenomena and mechanical interpretation towards design. Builds skills via increasing levels of complexity.
Author: Alexander L. Fetter Publisher: Courier Corporation ISBN: 048613699X Category : Science Languages : en Pages : 162
Book Description
In their prior Dover book, the authors provided a self-contained account of classical mechanics; this supplement/update offers a bridge to contemporary mechanics. Topics include nonlinear continuous systems. 2006 edition.
Author: Yury Vetyukov Publisher: Springer Science & Business Media ISBN: 3709117771 Category : Science Languages : en Pages : 280
Book Description
This book presents a hybrid approach to the mechanics of thin bodies. Classical theories of rods, plates and shells with constrained shear are based on asymptotic splitting of the equations and boundary conditions of three-dimensional elasticity. The asymptotic solutions become accurate as the thickness decreases, and the three-dimensional fields of stresses and displacements can be determined. The analysis includes practically important effects of electromechanical coupling and material inhomogeneity. The extension to the geometrically nonlinear range uses the direct approach based on the principle of virtual work. Vibrations and buckling of pre-stressed structures are studied with the help of linearized incremental formulations, and direct tensor calculus rounds out the list of analytical techniques used throughout the book. A novel theory of thin-walled rods of open profile is subsequently developed from the models of rods and shells, and traditionally applied equations are proven to be asymptotically exact. The influence of pre-stresses on the torsional stiffness is shown to be crucial for buckling analysis. Novel finite element schemes for classical rod and shell structures are presented with a comprehensive discussion regarding the theoretical basis, computational aspects and implementation details. Analytical conclusions and closed-form solutions of particular problems are validated against numerical results. The majority of the simulations were performed in the Wolfram Mathematica environment, and the compact source code is provided as a substantial and integral part of the book.
Author: Oliver M. O'Reilly Publisher: Springer ISBN: 331950598X Category : Mathematics Languages : en Pages : 434
Book Description
This book presents theories of deformable elastic strings and rods and their application to broad classes of problems. Readers will gain insights into the formulation and analysis of models for mechanical and biological systems. Emphasis is placed on how the balance laws interplay with constitutive relations to form a set of governing equations. For certain classes of problems, it is shown how a balance of material momentum can play a key role in forming the equations of motion. The first half of the book is devoted to the purely mechanical theory of a string and its applications. The second half of the book is devoted to rod theories, including Euler’s theory of the elastica, Kirchhoff ’s theory of an elastic rod, and a range of Cosserat rod theories. A variety of classic and recent applications of these rod theories are examined. Two supplemental chapters, the first on continuum mechanics of three-dimensional continua and the second on methods from variational calculus, are included to provide relevant background for students. This book is suited for graduate-level courses on the dynamics of nonlinearly elastic rods and strings.
Author: Gerhard A. Holzapfel
Author: John D. Clayton
Author: Jacques Besson
Author: Adnan Ibrahimbegovic
Author: Walter Lacarbonara
Author: Alexander L. Fetter
Author: Yury Vetyukov
Author: Oliver M. O'Reilly
Author: Javier Bonet
Author: Nikolai Mitrofanovich Krylov