Topology optimization has gained unprecedented attention due to its potential to automatically generate not only good but also optimal designs. Topology optimization to the design of continuum structures (Bendsøe and Kikuchi, 1988) has been successfully applied to many different types of structural design problems. Homogenization method was used by many authors (Suzuki and Kikuchi, 1991) in topology optimization. Many researchers extended topology optimization techniques to the optimization of continuum structures with local stress constraints (Duysinx and Bendsøe, 1998). Topology optimization techniques using compliant mechanism were studied extensively (Ananthasuresh et al., 1994; and Sigmund, 2001a and 2001b). The optimal stiffener design of shell structures with the small deformation was studied by Luo and Gea (1998) and Nishiwaki et al. (1998). Topology optimization for vibration problems was studied to maximize frequencies (Gea and Fu, 1997; Chen and Wu, 1998; and Pedersen, 2000). Extensive literature survey on topology optimization can be found in some works (Bendsøe, 1995). Many advances were made in finite element technology which have a direct impact on structural topology optimization, since most of the applications in topology optimization employ the finite element method as an analysis tool (Bletzinger and Ramm, 1993; Bendsøe et al., 1996; Mayer et al., 1996; Sigmund, 1997; Bendsøe and Sigmund, 1998; Maute et al., 1998; Buhl et al., 2000; Gea and Luo, 2001; Luzhong and Wei, 2001; Pedersen et al., 2001; and Antonio and Pascual, 2010). However, not much attention is paid to the actual finite element formulation in the application. In the present study, topology optimization of shell structure is performed using ANSYS—a commercial finite element software package. Also shell-93 element is used for discretization of the shell structure.
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