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Download Variational Prinicples in Thermo- and Magneto-Elasticity: by Heinz Parkus (auth.) PDF

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By Heinz Parkus (auth.)

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2) The basic simplifying assumption of piezoelectricity, [30] , now is that lAd << I'P ,d . 4) Under the additional assumptions of linear, isothermal constitutive equations, absence of volume charges and 42 Chap. v. , neglect of electric volume forces), Tiersten [30] has formulated a simple extension of Hamilton's principle as follows. 5) U(f .. ' - D· " ~ aH = aE. 7) D~,t. = 0 . Since a linear material is assumed H will have the form (5. 7) constitute a set of al- together 22 equations in 22 variables.

4) Chap. IV. Magnetoelasticity 34 where the space functions }... 1. are Lagrangian multipliers. We perform now the sequence of steps of the variation procedure. au a +au- {)M. ----OX· ax~ • axil' ~ aM~ ~~ uM~ ~ax. ~ ~ ~ m - ' f p. ~ , .. AII m ~ - ru. M. Y_v,.. Jl nx .. L obx~ nX :. ,. • '.. - u does not 0 H~,~oxJ. L ""()x. A •, .... dV Jv \~ ax. t'. ,.. L oM~ m ' .! bM. m • X. __ V • A C>M~. ' X. i. - ~ Brown's Principle 35 The variation of the magnetic self-energy is difficult. / dm J[:t v F = ({!

3] A. Castigliano : Theorie de l'equilibre des systemes elastiques. Turin 1879. [4] G. Kirchhoff : Mechanik. 11. und 28. Vorlesung. G. Teubner, Leipzig 1876. [5] E. Reissner : On a variational theorem in elasticity. J. Math. Phys. 29 (1950), 90. [6] E. Reissner : On a variational theorem for finite elastic deformations. J. Math. Phys. 32 (1953), 129. [7] H. Parkus : Thermoelasticity. , Waltham-Toronto-London 1968. [8] R. Trostel : Genaherte Berechnung von Warmespannungen mit Hilfe der Variationsprinzipien der Elastostatik.

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