Numerical Solution of Plane Elasticity Problems by a Finite Difference Method
| Author | : Donald Craig Shumate |
| Publisher | : |
| Total Pages | : 130 |
| Release | : 1965 |
| Genre | : Elasticity |
| ISBN | : |
Numerical Solution Of Plane Elasticity Problems By A Finite Difference Method
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Numerical Analysis of Plane Elastic-Plastic Boundary Value Problems: Theory and Application to Single Crystal Beam
| Author | : Martin A. Eisenberg |
| Publisher | : |
| Total Pages | : 71 |
| Release | : 1970 |
| Genre | : |
| ISBN | : |
A technique for the solution of a large class of plane elastic-plastic problems is presented and applied to the bending of a simply supported singled crystal beam. The solution of elastic-perfectly plastic problems is accomplished by means of an iterative scheme for the location of the elastic-plastic interface at given load levels. This necessitates the solution of the plane elasticity problem in domains with irregular boundaries and numerical methods are thus dictated. An appropriate finite difference method and computer code are described. This method and code can be readily extended to include effects of elastic anisotropy and non-homogeneity. (Author).
A Numerical Method for the Solution of Problems in Three Dimensional Elasticity
| Author | : Hotten Arthur Elleby |
| Publisher | : |
| Total Pages | : 250 |
| Release | : 1964 |
| Genre | : Elasticity |
| ISBN | : |
Numerical Methods for Exterior Problems
| Author | : Long'an Ying |
| Publisher | : World Scientific |
| Total Pages | : 282 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 9812772561 |
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
Numerical Solution of Differential Equations
| Author | : Zhilin Li |
| Publisher | : Cambridge University Press |
| Total Pages | : 305 |
| Release | : 2017-11-30 |
| Genre | : Mathematics |
| ISBN | : 1107163226 |
A practical and concise guide to finite difference and finite element methods. Well-tested MATLAB® codes are available online.
Numerical Solution of Partial Differential Equations by the Finite Element Method
| Author | : Claes Johnson |
| Publisher | : Courier Corporation |
| Total Pages | : 290 |
| Release | : 2012-05-23 |
| Genre | : Mathematics |
| ISBN | : 0486131599 |
An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.
The Cell Method
| Author | : Elena Ferretti |
| Publisher | : Momentum Press |
| Total Pages | : 282 |
| Release | : 2014-02-02 |
| Genre | : Technology & Engineering |
| ISBN | : 1606506064 |
The Cell Method (CM) is a computational tool that maintains critical multidimensional attributes of physical phenomena in analysis. This information is neglected in the differential formulations of the classical approaches of finite element, boundary element, finite volume, and finite difference analysis, often leading to numerical instabilities and spurious results. This book highlights the central theoretical concepts of the CM that preserve a more accurate and precise representation of the geometric and topological features of variables for practical problem solving. Important applications occur in fields such as electromagnetics, electrodynamics, solid mechanics and fluids. CM addresses non-locality in continuum mechanics, an especially important circumstance in modeling heterogeneous materials. Professional engineers and scientists, as well as graduate students, are offered: • A general overview of physics and its mathematical descriptions; • Guidance on how to build direct, discrete formulations; • Coverage of the governing equations of the CM, including nonlocality; • Explanations of the use of Tonti diagrams; and • References for further reading.
Elasticity in Engineering Mechanics
| Author | : Arthur P. Boresi |
| Publisher | : John Wiley & Sons |
| Total Pages | : 640 |
| Release | : 2000 |
| Genre | : Science |
| ISBN | : 9780471316145 |
"Arthur Boresi and Ken Chong's Elasticity in Engineering Mechanics has been prized by many aspiring and practicing engineers as an easy-to-navigate guide to an area of engineering science that is fundamental to aeronautical, civil, and mechanical engineering, and to other branches of engineering. With its focus not only on elasticity theory but also on concrete applications in real engineering situations, this work is a core text in a spectrum of courses at both the undergraduate and graduate levels, and a superior reference for engineering professionals."--BOOK JACKET.
