Weight minimization of elastic bodies under weakly supporting tension. II: Domains with two curved sides. (English) Zbl 0767.73048

Summary: Extending the results of the previous paper [see the foregoing entry], 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 convergence analysis is presented for approximate penalized optimal design problems.


74P99 Optimization problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
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[1] I. Hlaváček M. Křížek: Weight minimization of elastic bodies weakly supporting tension I. Appl. Math. 37(1992), 201-240. · Zbl 0767.73047
[2] S. B. Stečkin J. N. Subbotin: Splajny v vyčisliteľnoj matematike. Nauka, Moskva, 1976.
[3] I. Hlaváček: Optimization of the shape of axisymmetric shells. Apl. Mat. 28 (1983), 269-294.
[4] I. Hlaváček: Inequalities of Korn’s type, uniform with respect to a class of domains. Apl. Mat. 34 (1989), 105-112. · Zbl 0673.49003
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