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

Hlaváček, Ivan; Křížek, Michal

Appl. Math., Praha 37, No. 4, 289-312 (1992).

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.

MSC:

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

Keywords:

curved trapezoids; penalty method; hydrostatic pressure; cubic Hermite splines; piecewise linear finite elements; existence; convergence

References:

[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