Stress-constrained optimization using graded lattice microstructures
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RESEARCH PAPER
Stress-constrained optimization using graded lattice microstructures Dilaksan Thillaithevan1
· Paul Bruce1 · Matthew Santer1
Received: 18 February 2020 / Revised: 21 July 2020 / Accepted: 12 August 2020 © The Author(s) 2020
Abstract In this work, we propose a novel method for predicting stress within a multiscale lattice optimization framework. On the microscale, a scalable stress is captured for each microstructure within a large, full factorial design of experiments. A multivariate polynomial response surface model is used to represent the microstructure material properties. Unlike the traditional solid isotropic material with a penalization-based stress approach or using the homogenized stress, we propose the use of real microscale stress components with macroscale strains through linear superposition. To examine the accuracy of the multiscale stress method, full-scale finite element simulations with non-periodic boundary conditions were performed. Using a range of microstructure gradings, it was determined that 6 layers of microstructures were required to achieve periodicity within the full-scale model. The effectiveness of the multiscale stress model was then examined. Using various graded structures and two load cases, our methodology was shown to replicate the von Mises stress in the center of the unit lattice cells to within 10% in the majority of the test cases. Finally, three stress-constrained optimization problems were solved to demonstrate the effectiveness of the method. Two stress-constrained weight minimization problems were demonstrated, alongside a stress-constrained target deformation problem. In all cases, the optimizer was able to sufficiently reduce the objective while respecting the imposed stress constraint. Keywords Structural optimization · Homogenization · Stress constraint · Multiscale optimization · Additive manufacturing · Lattice microstructures
1 Introduction In engineering design, maximizing the strength-to-weight ratio of components has always been a primary objective. Reducing the weight of a component under stress constraints can often lead to a significant reduction in costs and increase the performance of the entire assembly. The design methodologies employed in the past were often limited by the manufacturing processes available at the time. Until recently, subtractive manufacturing, where components are manufactured by removing material from a solid block, imposed severe constraints on the design of com-
Responsible Editor: Seonho Cho Dilaksan Thillaithevan
[email protected] 1
Department of Aeronautics, Imperial College London, London, UK
ponents, limiting the potential performance improvements that could be made. With the advent of additive manufacturing (AM) processes (Ngo et al. 2018), where components are built layer-by-layer, many of these constraints have been lifted. This has led researchers to reformulate old design methodologies to suit the advantages posed by AM better. Examples of this are multiscale optimization methods. He
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