{"product_id":"mathematical-elasticity-philippe-g-ciarlet-9780444825704","title":"Mathematical Elasticity: Volume II: Theory of Plates Volume 27","description":"The objective of Volume II is to show how asymptotic methods, with the thickness as the small parameter, indeed provide a powerful means of justifying two-dimensional plate theories. More specifically, without any recourse to any \u003ci\u003ea priori\u003c\/i\u003e assumptions of a geometrical or mechanical nature, it is shown that in the linear case, the three-dimensional displacements, once properly scaled, converge in \u003ci\u003eH\u003c\/i\u003e\u003csup\u003e1\u003c\/sup\u003e towards a limit that satisfies the well-known two-dimensional equations of the linear Kirchhoff-Love theory; the convergence of stress is also established.\u003cp\u003eIn the nonlinear case, again after \u003ci\u003ead hoc\u003c\/i\u003e scalings have been performed, it is shown that the leading term of a formal asymptotic expansion of the three-dimensional solution satisfies well-known two-dimensional equations, such as those of the nonlinear Kirchhoff-Love theory, or the von K rm n equations. Special attention is also given to the first convergence result obtained in this case, which leads to two-dimensional large deformation, frame-indifferent, nonlinear membrane theories. It is also demonstrated that asymptotic methods can likewise be used for justifying other lower-dimensional equations of elastic shallow shells, and the coupled pluri-dimensional equations of elastic multi-structures, i.e., structures with junctions. In each case, the existence, uniqueness or multiplicity, and regularity of solutions to the limit equations obtained in this fashion are also studied.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Philippe G. Ciarlet\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 0444825703\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780444825704\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e North-Holland\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 07\/22\/1997\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 496\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 2.12lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 1.25d\u003c\/p\u003e","brand":"Philippe G. Ciarlet","offers":[{"title":"Hardcover","offer_id":44057314689279,"sku":"9780444825704","price":181.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_cdf23a0f-7a8c-4701-a5cb-1a5dfc028c4d.jpg?v=1685046263","url":"https:\/\/www.whiterainbookhouse.com\/products\/mathematical-elasticity-philippe-g-ciarlet-9780444825704","provider":"WR Book House","version":"1.0","type":"link"}