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Fully \(C^1\)-conforming subdivision elements for finite deformation thin-shell analysis. (English) Zbl 1039.74045
Summary: We extend the subdivision shell elements of F. Cirak et al. [ibid. 47, No. 12, 2039–2072 (2000; Zbl 0983.74063)] to the finite-deformation range. The assumed finite-deformation kinematics allows for finite membrane and thickness stretching, as well as for large deflections and bending strains. The interpolation of undeformed and deformed surfaces of the shell is accomplished through the use of subdivision surfaces. The resulting ‘subdivision elements’ are strictly \(C^1\)-conforming, contain three nodes and one single quadrature point per element, and carry displacements at the nodes only. The versatility and good performance of the subdivision elements is demonstrated with the aid of a number of test cases, including the stretching of a tension strip; the inflation of a spherical shell under internal pressure; the bending and inflation of a circular plate under the action of uniform pressure; and the inflation of square and circular airbags.

74S05 Finite element methods applied to problems in solid mechanics
74K25 Shells
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