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Folded shells: A variational approach. (English) Zbl 0780.73043
Folded shells are characterized by the fact that their regular part is a smooth two-dimensional surface in \(\mathbb{R}^ 3\) and their singular part is a smooth curve in \(\mathbb{R}^ 3\). The theory starts from a three- dimensional elastic body passing to the limit “thickness \(\to 0\)”. The investigation is based on a variational method and results in the physical elucidation of the convergence of the minimizing sequence of the approximating problems to the solution of a limiting minimization problem. The case of a smooth curve in \(\mathbb{R}^ 2\) with a point in \(\mathbb{R}^ 2\) as its singular part is considered also. Two examples are presented.

MSC:
74K15 Membranes
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
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