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Existence of a solution for a nonlinearly elastic plane membrane “under tension”. (English) Zbl 0966.74043

The purpose of this paper is to establish existence results for nonlinear membrane-plate equations [D. D. Fox, A. Raoult and J. C. Simo, Arch. Ration. Mech. Anal. 124, No. 2, 157-199 (1993; Zbl 0789.73039)], and to obtain some properties of the solutions. The energy functional associated with the nonlinear membrane model is coercive but not sequentially weakly lower semicontinuous. This forbids to apply the classical theorem of the calculus of variations.

MSC:

74K15 Membranes
74B20 Nonlinear elasticity
74G25 Global existence of solutions for equilibrium problems in solid mechanics (MSC2010)
74G65 Energy minimization in equilibrium problems in solid mechanics
35Q72 Other PDE from mechanics (MSC2000)

Citations:

Zbl 0789.73039
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