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curved trapezoids; penalty method; hydrostatic pressure; cubic Hermite splines; piecewise linear finite elements; existence; convergence; shape optimization; weight minimization; finite elements
Extending the results of the previous paper [1], the authors consider elastic bodies with two design variables, i.e. "curved trapezoids" with two curved variable sides. The left side is loaded by a hydrostatic pressure. Approximations of the boundary are defined by cubic Hermite splines and piecewise linear finite elements are used for the displacements. Both existence and some convergence analysis is presented for approximate penalized optimal design problems.
[1] I. Hlaváček M. Křížek: Weight minimization of elastic bodies weakly supporting tension I. Appl. Math. 37(1992), 201-240. MR 1157456
[2] S. B. Stečkin J. N. Subbotin: Splajny v vyčisliteľnoj matematike. Nauka, Moskva, 1976. MR 0455278
[3] I. Hlaváček: Optimization of the shape of axisymmetric shells. Apl. Mat. 28 (1983), 269-294. MR 0710176
[4] I. Hlaváček: Inequalities of Korn's type, uniform with respect to a class of domains. Apl. Mat. 34 (1989), 105-112. MR 0990298 | Zbl 0673.49003
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