A Lagrangian approach to intrinsic linearized elasticity

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• 作者：Philippe G. Ciarlet ; Patrick Ciarlet Jr. ; Oana Iosifescu ; Stefan Sauter ; Jun Zou
• 刊名：Comptes Rendus Mathematique
• 出版年：2010
• 出版时间：May 2010
• 年：2010
• 卷：348
• 期：9-10
• 页码：587-592
• 全文大小：158 K

文摘

We consider the pure traction problem and the pure displacement problem of three-dimensional linearized elasticity. We show that, in each case, the intrinsic approach leads to a quadratic minimization problem constrained by Donati-like relations. Using the Babuška–Brezzi inf–sup condition, we then show that, in each case, the minimizer of the constrained minimization problem found in an intrinsic approach is the first argument of the saddle-point of an ad hoc Lagrangian, so that the second argument of this saddle-point is the Lagrange multiplier associated with the corresponding constraints.