A sequentially coupled shape and topology optimization method

Topology optimization is a widely-used technique for finding the most favorable, internal structural lay-out with a minimal weight under the specific loading and boundary conditions applied[1,2]. Accordingly, within a finite element setting this technique searches for the optimal relative density of a fixed, discretized spatial domain representing the actual structure. To enable more diversity within the design domain and to enlarge the search space of optimal structural configurations, in the present work a coupled method for topology optimization and shape optimization is proposed. The method incorporates the shape design variables into a SIMP (Simplified Isotropic Material with Penalization) topology optimization formulation, whereby the shape and topology optimization steps are performed in a sequential manner. The computational efficiency of the method is warranted by using Non-Uniform Rational B-Splines (NURBS) for describing the outer shape of the design domain, and by combining gradient-based optimization solvers with analytically derived shape and topology sensitivities. The coupled method has been implemented in a finite element framework to analyze 2D, 2.5D, and 3D structural design problems. The results of representative case studies clearly show that the features of the design domain can have a large influence on the final topology calculated. Additionally, the optimization sequence in the coupled method may affect the path followed within the design space; however, this typically only has a minor effect on the final computational result. [1] Bendsoe, M.P., Sigmund, O. (2004). Topology optimization by distribution of isotropic Material. In Topology Optimization (pp. 1-69). Springer, Berlin, Heidelberg. [2] Sigmund, O., Maute, K. (2013). Topology optimization approaches. Structural and Multidisciplinary Optimization, 48(6), 1031-1055.