{"product_id":"mathematical-elasticity-volume-ii-theory-of-plates-volume-27-9780444825704","title":"Mathematical Elasticity: Volume II: Theory of Plates Volume 27","description":"\u003cp\u003e • Author(s): Philippe G. Ciarlet\u003cbr\u003e • Publisher: North-Holland\u003cbr\u003e • Publisher Imprint: North-Holland\u003cbr\u003e • BISAC: Mechanics - General\u003c\/p\u003e\u003cp\u003eThe 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.\u003c\/p\u003e\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 Kármán 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.\u003c\/p\u003e","brand":"North-Holland","offers":[{"title":"Hardcover","offer_id":47614706811031,"sku":"9780444825704","price":15765.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9780444825704.webp?v=1775095683","url":"https:\/\/atlanticbooks.com\/products\/mathematical-elasticity-volume-ii-theory-of-plates-volume-27-9780444825704","provider":"Atlantic Books","version":"1.0","type":"link"}