Isogeometric design of anisotropic shells: Optimal form and material distribution

Structural art: Past, present and future

“…An summary on recent topology optimization techniques and applications in a variety of disciplines can be found in [59]. Non-Uniform Rational B-Splines (NURBS)-based isogeometric analysis is another geometric numerical modelling technique that optimizes form and material distribution either separately or simultaneously [60][61][62][63]. Other recent case studies on form-finding techniques support a variety of design innovation in structural forms which could achieve efficiency, economy, and elegance [64][65][66][67][68][69].…”

Nitsche’s method for a coupling of isogeometric thin shells and blended shell structures

“…The valuable comments from the anonymous reviewers are highly appreciated. The membrane strain is defined in (14), and its derivative w.r.t. displacement variable u r is:…”

“…The NURBS patches for thin shells according to the Kirchhoff-Love theory [14][15][16] are end-point interpolatory providing only C 0 -continuity at the coupling interface which results in a hinge effect, i.e. bending moments are not transmitted properly, G 1 -continuity [17] can not be preserved, this is similar to the situation seen when a Kirchhoff-Love shell patch is coupled to a solid-like shell patch [18][19][20].…”

Isogeometric shape optimization of trimmed shell structures

“…Thus this method provides the possibility to resolve the drawbacks of the approaches based on the conventional FEM. The isogeometric approach has shown great successes on analysis and optimization of shell structures as well as on various other engineering fields with the affirmative features: isogeometric shell analysis (Kiendl and Bletzinger 2009;Kiendl et al 2010;Benson et al 2010Benson et al , 2011Benson et al , 2013Nguyen-Thanh et al 2011;Dornisch et al 2013;Echter et al 2013;Bouclier et al 2013a, b;Hosseini 2013;Hosseini et al 2014;Dornisch and Klinkel 2014), isogeometric shape or topology optimization of shell structures (Seo et al 2010b;Nagy et al 2013;Breitenberger et al 2013;Kiendl et al 2014).…”

“…This approach gives appropriate final designs, but the design domains of the shell structures are yet limited to untrimmed domains. Nagy et al (2013) introduced the isogeometric shape optimization for thinwalled composite shells. It optimizes the form and the material anisotropy distribution either separately or simultaneously.…”