Mathematical Elasticity

Mathematical Elasticity
Author: Philippe G. Ciarlet
Publisher: SIAM
Total Pages: 521
Release: 2022-01-22
Genre: Mathematics
ISBN: 1611976782
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The first book of a three-volume set, Three-Dimensional Elasticity covers the modeling and mathematical analysis of nonlinear three-dimensional elasticity. It includes the known existence theorems, either via the implicit function theorem or via the minimization of the energy (John Ball’s theory). An extended preface and extensive bibliography have been added to highlight the progress that has been made since the volume’s original publication. While each one of the three volumes is self-contained, together the Mathematical Elasticity set provides the only modern treatise on elasticity; introduces contemporary research on three-dimensional elasticity, the theory of plates, and the theory of shells; and contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study. These classic textbooks are for advanced undergraduates, first-year graduate students, and researchers in pure or applied mathematics or continuum mechanics. They are appropriate for courses in mathematical elasticity, theory of plates and shells, continuum mechanics, computational mechanics, and applied mathematics in general.

Three-Dimensional Elasticity

Three-Dimensional Elasticity
Author: Philippe G. Ciarlet
Publisher: Elsevier
Total Pages: 500
Release: 1994-01-19
Genre: Mathematics
ISBN: 9780444817761
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This volume is a thorough introduction to contemporary research in elasticity, and may be used as a working textbook at the graduate level for courses in pure or applied mathematics or in continuum mechanics. It provides a thorough description (with emphasis on the nonlinear aspects) of the two competing mathematical models of three-dimensional elasticity, together with a mathematical analysis of these models. The book is as self-contained as possible.

Three-Dimensional Elasticity

Three-Dimensional Elasticity
Author:
Publisher: Elsevier
Total Pages: 495
Release: 1988-04-01
Genre: Technology & Engineering
ISBN: 0080875416
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This volume is a thorough introduction to contemporary research in elasticity, and may be used as a working textbook at the graduate level for courses in pure or applied mathematics or in continuum mechanics. It provides a thorough description (with emphasis on the nonlinear aspects) of the two competing mathematical models of three-dimensional elasticity, together with a mathematical analysis of these models. The book is as self-contained as possible.

Numerical Solution of Three-Dimensional Elasticity

Numerical Solution of Three-Dimensional Elasticity
Author: E. L. Marvin
Publisher:
Total Pages: 13
Release: 1967
Genre:
ISBN:
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The research reported here was undertaken to develop an alternative method for solving three-dimensional elasticity boundary value problems that might prove less expensive than the three-dimensional finite elements approach. Such a new approximate solution procedure, if successful, would also provide a means for checking the results obtained by finite elements analysis. A computer program called 3DELAS1, which may be used to solve displacement boundary value problems for generally shaped finite solids, has been developed as a part of this research.

Three-Dimensional Problems of Elasticity and Thermoelasticity

Three-Dimensional Problems of Elasticity and Thermoelasticity
Author: V.D. Kupradze
Publisher: Elsevier
Total Pages: 951
Release: 2012-12-02
Genre: Science
ISBN: 0080984630
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North-Holland Series in Applied Mathematics and Mechanics, Volume 25: Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity focuses on the theory of three-dimensional problems, including oscillation theory, boundary value problems, and integral equations. The publication first tackles basic concepts and axiomatization and basic singular solutions. Discussions focus on fundamental solutions of thermoelasticity, fundamental solutions of the couple-stress theory, strain energy and Hooke’s law in the couple-stress theory, and basic equations in terms of stress components. The manuscript then examines uniqueness theorems and singular integrals and integral equations. The book ponders on the potential theory and boundary value problems of elastic equilibrium and steady elastic oscillations. Topics include basic theorems of the oscillation theory, existence of solutions of boundary value problems, integral equations of the boundary value problems, and boundary properties of potential-type integrals. The publication also reviews mixed dynamic problems, couple-stress elasticity, and boundary value problems for media bounded by several surfaces. The text is a dependable source of data for mathematicians and readers interested in three-dimensional problems of the mathematical theory of elasticity and thermoelasticity.

Numerical Methods for Exterior Problems

Numerical Methods for Exterior Problems
Author: Long'an Ying
Publisher: World Scientific
Total Pages: 282
Release: 2006
Genre: Mathematics
ISBN: 9812772561
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Preface -- 1. Exterior problems of partial differential equations. 1.1. Harmonic equation-potential theory. 1.2. Poisson equations. 1.3. Poisson equations-variational formulation. 1.4. Helmholtz equations. 1.5. Linear elasticity. 1.6. Bi-harmonic equations. 1.7. Steady Navier-Stokes equations-linearized problems. 1.8. Steady Navier-Stokes equations. 1.9. Heat equation. 1.10. Wave equation. 1.11. Maxwell equations. 1.12. Darwin model -- 2. Boundary element method. 2.1. Some typical domains. 2.2. General domains. 2.3. Subdivision of the domain. 2.4. Dirichlet to Neǔmann operator. 2.5. Finite part of divergent integrals. 2.6. Numerical approximation. 2.7. Error estimates. 2.8. Domain decomposition. 2.9. Boundary perturbation -- 3. Infinite element method. 3.1. Harmonic equation-two dimensional problems. 3.2. General elements. 3.3. Harmonic equation-three dimensional problems. 3.4. Inhomogeneous equations. 3.5. Plane elasticity. 3.6. Bi-harmonic equations. 3.7. Stokes equation. 3.8. Darwin model. 3.9. Elliptic equations with variable coefficients. 3.10. Convergence -- 4. Artificial boundary conditions. 4.1. Absorbing boundary conditions. 4.2. Some approximations. 4.3. Bayliss-Turkel radiation boundary conditions. 4.4. A lower order absorbing boundary condition. 4.5. Liao extrapolation in space and time. 4.6. Maxwell equations. 4.7. Finite difference schemes. 4.8. Stationary Navier-Stokes equations -- 5. Perfectly matched layer method. 5.1. Wave equations. 5.2. Bérenger's perfectly matched layers. 5.3. Stability analysis. 5.4. Uniaxial perfectly matched layers. 5.5. Maxwell equations. 5.6. Helmholtz equations -- 6. Spectral method. 6.1. Introduction. 6.2. Orthogonal systems of polynomials. 6.3. Laguerre spectral methods. 6.4. Jacobi spectral methods. 6.5. Rational and irrational spectral methods. 6.6. Error estimates