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Virtual work

About: Virtual work is a research topic. Over the lifetime, 2446 publications have been published within this topic receiving 53086 citations. The topic is also known as: Principle of virtual work.


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Book
29 Mar 1991
TL;DR: In this article, the authors present a general solution based on the principle of virtual work for two-dimensional linear elasticity problems and their convergence rates in one-dimensional dimensions. But they do not consider the case of three-dimensional LEL problems.
Abstract: Mathematical Models and Engineering Decisions. Generalized Solutions Based on the Principle of Virtual Work. Finite Element Discretizations in One Dimension. Extensions and Their Convergence Rates in One Dimension. Two-Dimensional Linear Elastostatic Problems. Element-Level Basis Functions in Two Dimensions. Computation of Stiffness Matrices and Load Vectors for Two Dimensional Elastostatic Problems. Potential Flow Problems. Assembly, Constraint Enforcement, and Solution. Extensions and Their Convergence Rates in Two Dimensions. Computation of Displacements, Stresses and Stress Resultants. Computation of the Coefficients of Asymptotic Expansions. Three-Dimensional Linear Elastostatic Problems. Models for Plates and Shells. Miscellaneous Topics. Estimation and Control of Errors of Discretization. Mathematical Models. Appendices. Index.

2,748 citations

Journal ArticleDOI
TL;DR: In this article, a unified treatment of thermoelasticity by application and further developments of the methods of irreversible thermodynamics is presented, along with a new definition of the dissipation function in terms of the time derivative of an entropy displacement.
Abstract: A unified treatment is presented of thermoelasticity by application and further developments of the methods of irreversible thermodynamics. The concept of generalized free energy introduced in a previous publication plays the role of a ``thermoelastic potential'' and is used along with a new definition of the dissipation function in terms of the time derivative of an entropy displacement. The general laws of thermoelasticity are formulated in a variational form along with a minimum entropy production principle. This leads to equations of the Lagrangian type, and the concept of thermal force is introduced by means of a virtual work definition. Heat conduction problems can then be formulated by the methods of matrix algebra and mechanics. This also leads to the very general property that the entropy density obeys a diffusion‐type law. General solutions of the equations of thermoelasticity are also given using the Papkovitch‐Boussinesq potentials. Examples are presented and it is shown how the generalized coordinate method may be used to calculate the thermoelastic internal damping of elastic bodies.

2,287 citations

Journal ArticleDOI
TL;DR: In this paper, a one-dimensional large-strain beam theory for plane deformations of plane beams, with rigorous consistency of dynamics and kinematics via application of the principle of virtual work is presented.
Abstract: The paper formulates a one-dimensional large-strain beam theory for plane deformations of plane beams, with rigorous consistency of dynamics and kinematics via application of the principle of virtual work. This formulation is complemented by considerations on how to obtain constitutive equations, and applied to the problem of buckling of circular rings, including the effects of axial normal strain and transverse shearing strain.

623 citations

Journal ArticleDOI
TL;DR: In this article, a new formulation of the field theory of dielectric solids is proposed, which does not start with Newton's laws of mechanics and Maxwell-Faraday theory of electrostatics, but produces them as consequences.
Abstract: Two difficulties have long troubled the field theory of dielectric solids. First, when two electric charges are placed inside a dielectric solid, the force between them is not a measurable quantity. Second, when a dielectric solid deforms, the true electric field and true electric displacement are not work conjugates. These difficulties are circumvented in a new formulation of the theory in this paper. Imagine that each material particle in a dielectric is attached with a weight and a battery, and prescribe a field of virtual displacement and a field of virtual voltage. Associated with the virtual work done by the weights and inertia, define the nominal stress as the conjugate to the gradient of the virtual displacement. Associated with the virtual work done by the batteries, define the nominal electric displacement as the conjugate to the gradient of virtual voltage. The approach does not start with Newton's laws of mechanics and Maxwell–Faraday theory of electrostatics, but produces them as consequences. The definitions lead to familiar and decoupled field equations. Electromechanical coupling enters the theory through material laws. In the limiting case of a fluid dielectric, the theory recovers the Maxwell stress. The approach is developed for finite deformation, and is applicable to both elastic and inelastic dielectrics. As applications of the theory, we discuss material laws for elastic dielectrics, and study infinitesimal fields superimposed upon a given field, including phenomena such as vibration, wave propagation, and bifurcation.

485 citations

Book
01 Jan 1988
TL;DR: In this article, the equations of equilibrium and the principle of virtual work for three-dimensional elasticity have been discussed and the boundary value problems of 3D elasticity has been studied.
Abstract: Part A Description of Three-Dimensional Elasticity 1 Geometrical and other preliminaries 2 The equations of equilibrium and the principle of virtual work 3 Elastic materials and their constitutive equations 4 Hyperelasticity 5 The boundary value problems of three-dimensional elasticity Part B Mathematical Methods in Three-Dimensional Elasticity 6 Existence theory based on the implicit function theorem 7 Existence theory based on the minimization of the Energy Bibliography Index

475 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202356
2022121
202175
202066
201998
201890