Finite element analysis of free material optimization problem. (English) Zbl 1099.65112

Mach, Jan

Appl. Math., Praha 49, No. 4, 285-307 (2004).

Summary: Free material optimization solves an important problem of structural engineering, i.e. to find the stiffest structure for given loads and boundary conditions. Its mathematical formulation leads to a saddle-point problem. It can be solved numerically by the finite element method. The convergence of the finite element method can be proved if the spaces involved satisfy suitable approximation assumptions. An example of a finite-element discretization is included.

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74G15	Numerical approximation of solutions of equilibrium problems in solid mechanics
74P05	Compliance or weight optimization in solid mechanics

Keywords:

structural optimization; topology optimization; finite elements

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