Abstract
Structural topology optimization (STO) is usually treated as a constrained minimization problem, which is iteratively addressed by solving the equilibrium equations for the problem under consideration. To reduce the computational effort, several reduced basis approaches that solve the equilibrium equations in a reduced space have been proposed. In this work, we apply functional principal component analysis (FPCA) to generate the reduced basis, and we couple FPCA with a gradient-based optimization method for the first time in the literature. The proposed algorithm has been tested on a large STO problem with 4.8 million degrees of freedom. Results show that the proposed algorithm achieves significant computational time savings with negligible loss of accuracy. Indeed, the density maps obtained with the proposed algorithm capture the larger features of maps obtained without reduced basis, but in significantly lower computational times, and are associated with similar values of the minimized compliance.
Highlights
The need for optimized solutions in structural applications has increased over the years and has become nowadays fundamental because of the limited availability of commodities, environmental impacts, increasingly stringent industrial time-to-market requests, and emerging manufacturing processes as additive manufacturing
We extend the use of functional principal component analysis (FPCA) in structural topology optimization (STO) by applying it to the class of gradientbased optimization methods, which are the most commonly used
We decided to embed FPCA rather than principal component analysis (PCA) in the optimization because of the results reported in Bianchini et al (2015), where FPCA has been employed for uncertainty quantification purposes
Summary
The need for optimized solutions in structural applications has increased over the years and has become nowadays fundamental because of the limited availability of commodities, environmental impacts, increasingly stringent industrial time-to-market requests, and emerging manufacturing processes as additive manufacturing. Almost all the proposed approaches are iterative, which means that the optimized mass distribution is determined by repeatedly performing structural finite element analyses (FEA) that involve the solution of the equilibrium equations for the problem under consideration. Basis approaches represent a valid solution to such an issue, because they allow to reduce the dimensionality of the structural problem, i.e., the number of equilibrium equations to solve and, the related computational effort. The novelty of our work is not to introduce a new numerical technique but to appropriately combine two consolidated STO methods in order to save computational time Such methods are the gradient-based optimization, (see for example Sigmund and Maute (2013)), and the reduced basis method (FPCA), able to reduce the dimensionality of the problem.
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