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Variational Formulation of Elastostatics
2013In this chapter the variational characterizations of a solution to a boundary value problem of elastostatics are recalled. They include the principle of minimum potential energy, the principle of minimum complementary energy, the Hu-Washizu principle, and the compatibility related principle for a traction problem.
Reza Eslami +5 more
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Differential Variational Formulations
1994D’Alembert† brought the problems of motion under the umbrella of problems of equilibrium. Using Euler’s linear momentum law (1.1.2), we have that, when a point mass is acted upon by a set of forces resulting in F, it will acquire a linear momentum B, such that $$F = \dot B$$ (2.1.1) Consider now an increment of work done by the force F, as ...
B. Tabarrok, F. P. J. Rimrott
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Extended variational formulation
1995The author shows how to transform a given problem, linear or nonlinear, into another one that has the same solution and admits a variational formulation with a (true) minimum. For the given problem there exists an infinity of equivalent problems, each with minimality property.
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Integral Variational Formulations
1994D’Alembert’s principle and Gauss’ principle of least constraint are examples of differential variational formulations. These formulations make independent statements at each instant of time during the motion. By contrast integral variational formulations, which we shall examine in this chapter, make a single, all inclusive, statement.
B. Tabarrok, F. P. J. Rimrott
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Variational Formulation of the Theory
1988Scholars of mechanics generally agree that variational principles provide one of the most elegant, systematic, and satisfying approaches to the study of finite-dimensional dynamical systems. The strength of the variational method lies in its generality.
Harley Cohen, Robert G. Muncaster
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Proceedings of the Physical Society, 1945
Formulae for calculating the effect in a complete optical instrument of small changes in the powers and separations of its component parts are collected together. The coefficients in these formulae need not be specially calculated, for they are already known if rays have been traced through the original system algebraically.
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Formulae for calculating the effect in a complete optical instrument of small changes in the powers and separations of its component parts are collected together. The coefficients in these formulae need not be specially calculated, for they are already known if rays have been traced through the original system algebraically.
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Variational Formulations and Their Solutions
For classical solutions, we saw in the previous chapter that we can go from a problem with second-order derivatives to a variational formulation with just first-order derivatives. By using the generalized integration-by-parts formulae, now we will justify this transition to the lower order derivatives in the general case.Patrick Ciarlet, Eric Lunéville
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Elasticity, Variational Formulations
2014The derivation of finite element equation of motion based on the variational formulation is presented in this chapter. The Hamilton principle for elastic continuum is derived and basic relations for the linear elasticity, the constitutive law, and the kinematical relations, are presented.
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Variational Formulation for the Multisymplectic Hamiltonian Systems
Letters in Mathematical Physics, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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