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Flows of Viscous Incompressible Fluids

J. N. REDDY

in An Introduction to Nonlinear Finite Element Analysis

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198525295
eISBN:
9780191711671
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525295.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Fluid mechanics is concerned with the motion of gases and liquids and their interaction with the surroundings. A fluid can either be inviscid (the viscosity is assumed to be zero) or incompressible ... More


Nonlinear Bending of Elastic Plates and Shells

J. N. REDDY

in An Introduction to Nonlinear Finite Element Analysis

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198525295
eISBN:
9780191711671
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525295.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Simple two-dimensional plate and shell theories can be developed to study the deformation and stresses in plate structures undergoing small strains, small to moderate rotations, and large ... More


Coarse-Grained Molecular Dynamics: Concurrent Multiscale Simulation at Finite Temperature Protect 1

Robert E. Rudd

in Multiscale Methods: Bridging the Scales in Science and Engineering

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199233854
eISBN:
9780191715532
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199233854.003.0005
Subject:
Mathematics, Applied Mathematics

Coarse-grained molecular dynamics (CGMD) is a computer modeling technique that couples conventional molecular dynamics (MD) in some spatial regions of the simulation to a more coarse-grained ... More


Finite Element Formulations of Solid Continua

J. N. REDDY

in An Introduction to Nonlinear Finite Element Analysis

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198525295
eISBN:
9780191711671
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525295.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In the linear description of the motion of solid bodies, the displacements and strains are assumed to be very small and the material is linearly elastic. In addition, the equilibrium equations are ... More


Nonlinear Analysis of Time-Dependent Problems

J. N. REDDY

in An Introduction to Nonlinear Finite Element Analysis

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198525295
eISBN:
9780191711671
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525295.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In this chapter, finite element models are used to solve time-dependent problems with nonlinearities and some standard time approximation schemes are described. All classes of nonlinear problems ... More


Material Nonlinearities and Coupled Problems

J. N. REDDY

in An Introduction to Nonlinear Finite Element Analysis

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198525295
eISBN:
9780191711671
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525295.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Nonlinearities arise from two independent sources: nonlinearity due to changes in the geometry or position of the material particles of a continuum, which is called the geometric nonlinearity, and ... More


Nonlinear Bending of Straight Beams

J. N. Reddy

in An Introduction to Nonlinear Finite Element Analysis, 2nd Edn: with applications to heat transfer, fluid mechanics, and solid mechanics

Published in print:
2014
Published Online:
June 2015
ISBN:
9780199641758
eISBN:
9780191789557
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641758.003.0005
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses two different theories to model the kinematic behaviour of beams – the Euler–Bernoulli beam theory and the Timoshenko beam theory – and their finite element models are ... More


Nonlinear Bending of Elastic Plates

J. N. Reddy

in An Introduction to Nonlinear Finite Element Analysis, 2nd Edn: with applications to heat transfer, fluid mechanics, and solid mechanics

Published in print:
2014
Published Online:
June 2015
ISBN:
9780199641758
eISBN:
9780191789557
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641758.003.0007
Subject:
Physics, Condensed Matter Physics / Materials

This chapter develops the classical plate theory (CPT) and first-order shear deformation plate theory (FSDT) based on assumed displacement fields and accounting for the von Káarmán nonlinearity. The ... More


One-Dimensional Problems Involving a Single Variable

J. N. Reddy

in An Introduction to Nonlinear Finite Element Analysis, 2nd Edn: with applications to heat transfer, fluid mechanics, and solid mechanics

Published in print:
2014
Published Online:
June 2015
ISBN:
9780199641758
eISBN:
9780191789557
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641758.003.0004
Subject:
Physics, Condensed Matter Physics / Materials

This chapter presents the weak-form Galerkin finite element model of a typical second-order nonlinear boundary-value problem in one dimension. It discusses iterative methods of solving nonlinear ... More


An Introduction to Nonlinear Finite Element Analysis, 2nd Edn: with applications to heat transfer, fluid mechanics, and solid mechanics

J. N. Reddy

Published in print:
2014
Published Online:
June 2015
ISBN:
9780199641758
eISBN:
9780191789557
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641758.001.0001
Subject:
Physics, Condensed Matter Physics / Materials

The development of realistic mathematical models that govern the response of systems or processes is strongly connected to the ability to translate them into meaningful discrete models that allow for ... More


Two-Dimensional Problems Involving a Single Variable

J. N. Reddy

in An Introduction to Nonlinear Finite Element Analysis, 2nd Edn: with applications to heat transfer, fluid mechanics, and solid mechanics

Published in print:
2014
Published Online:
June 2015
ISBN:
9780199641758
eISBN:
9780191789557
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641758.003.0006
Subject:
Physics, Condensed Matter Physics / Materials

This chapter presents the weak-form Galerkin finite element model of a generalized, nonlinear Poisson equation in two-dimensions for both steady-state and transient response. It discusses the ... More


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