{"product_id":"mathematical-elasticity-volume-2-theory-of-plates-studies-in-mathematics-and-its-application-0444825703","title":"Mathematical Elasticity, Volume 2: Theory of Plates (Studies in Mathematics and its Application)","description":"\u003cp\u003e\u003cstrong\u003eISBN:\u003c\/strong\u003e 0444825703\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eAuthor:\u003c\/strong\u003e Phililppe G. Ciarlet\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eCondition:\u003c\/strong\u003e New\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 a priori assumptions of a geometrical or mechanical nature, it is shown that in the linear case, the three-dimensional displacements, once properly scaled, converge in H1 towards a limit that satisfies the well-known two-dimensional equations of the linear Kirchhoff-Love theory; the convergence of stress is also established.In the nonlinear case, again after ad hoc 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":"Mia Karts","offers":[{"title":"Default Title","offer_id":51935283708192,"sku":"NEW0444825703","price":293.63,"currency_code":"USD","in_stock":false}],"url":"https:\/\/miakarts.com\/products\/mathematical-elasticity-volume-2-theory-of-plates-studies-in-mathematics-and-its-application-0444825703","provider":"Miakarts Books","version":"1.0","type":"link"}