
Minimum Weight Topology Optimization of 3D Continuum Structures with Stress Constraints using Isogeometric Analysis
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Topology optimization of structures is a relatively recent branch of structural optimization since the first proposals of Bendsoe and Kikuchi [1]. Since then, most approaches to this problem have been stated in terms of continuum formulations led by the SIMP constitutive model to deal with the concept of relative density. Moreover, the most common optimization approach for this formulation is usually posed in terms of minimum compliance with a volume constraint, unlike the most usual formulations in structural optimization branches such as size and shape optimization. Furthermore, material interpolation schemes are usually defined in terms of uniform relative density per element. This research is devoted to propose an alternative approach to the topology optimization problem that tries to find the minimum weight design considering stress constraints [2]. The proposed formulation includes isogeometric analysis for both structural analysis and material interpolation [3], allowing to obtain high definition solutions with a smaller number of design variables. An Overweight Constraint approach is also included to deal with stress constraints, and a penalized objective function is considered to promote binary distributions of material. The optimization model is solved using derivative-based optimization methods, and all necessary derivatives are calculated analytically. All these considerations are aimed at achieving the highest efficiency. Consequently, 3D practical application examples are solved to validate the developed formulation. References: [1] M. P. Bendsøe and N. Kikuchi, "Generating optimal topologies in structural design using a homogenization method", Comput. Methods Appl. Mech. Engrg. (1988) 71: 197-224. [2] D. Villalba, J. París, I. Couceiro, I. Colominas and F. Navarrina, "Topology optimization of structures considering minimum weight and stress constraints by using the Overweight Approach", Eng. Struct. (2022) 273: 115071. [3] T. Hughes, J. Cottrell and Y. Bazilevs, "Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement", Comput Methods Appl Mech Engrg. (2005) 194: 4135-4195.