Glaucio H. Paulino

Shun Wang, Eric de Sturler, Glaucio H. Paulino

We present an improved method for topology optimization with both adaptive mesh refinement and derefinement. Since the total volume fraction in topology optimization is usually modest, after a few initial iterations the domain of computation is largely void. Hence, it is inefficient to have many small elements, in such regions, that contribute significantly to the overall computational cost but contribute little to the accuracy of computation and design. At the same time, we want high spatial resolution for accurate three-dimensional designs to avoid postprocessing or interpretation as much as possible. Dynamic adaptive mesh refinement (AMR) offers the possibility to balance these two requirements. We discuss requirements on AMR for topology optimization and the algorithmic features to implement them. The numerical design problems demonstrate (1) that our AMR strategy for topology optimization leads to designs that are equivalent to optimal designs on uniform meshes, (2) how AMR strategies that do not satisfy the postulated requirements may lead to suboptimal designs, and (3) that our AMR strategy significantly reduces the time to compute optimal designs.

Harikrishnan Vijayakumaran, Jonathan B. Russ, Glaucio H. Paulino et al.

Additive manufacturing methods together with topology optimization have enabled the creation of multiscale structures with controlled spatially-varying material microstructure. However, topology optimization or inverse design of such structures in the presence of nonlinearities remains a challenge due to the expense of computational homogenization methods and the complexity of differentiably parameterizing the microstructural response. A solution to this challenge lies in machine learning techniques that offer efficient, differentiable mappings between the material response and its microstructural descriptors. This work presents a framework for designing multiscale heterogeneous structures with spatially varying microstructures by merging a homogenization-based topology optimization strategy with a consistent machine learning approach grounded in hyperelasticity theory. We leverage neural architectures that adhere to critical physical principles such as polyconvexity, objectivity, material symmetry, and thermodynamic consistency to supply the framework with a reliable constitutive model that is dependent on material microstructural descriptors. Our findings highlight the potential of integrating consistent machine learning models with density-based topology optimization for enhancing design optimization of heterogeneous hyperelastic structures under finite deformations.

Yuyu Zhang, Heng Chi, Binghong Chen et al.

A wide range of modern science and engineering applications are formulated as optimization problems with a system of partial differential equations (PDEs) as constraints. These PDE-constrained optimization problems are typically solved in a standard discretize-then-optimize approach. In many industry applications that require high-resolution solutions, the discretized constraints can easily have millions or even billions of variables, making it very slow for the standard iterative optimizer to solve the exact gradients. In this work, we propose a general framework to speed up PDE-constrained optimization using online neural synthetic gradients (ONSG) with a novel two-scale optimization scheme. We successfully apply our ONSG framework to computational morphogenesis, a representative and challenging class of PDE-constrained optimization problems. Extensive experiments have demonstrated that our method can significantly speed up computational morphogenesis (also known as topology optimization), and meanwhile maintain the quality of final solution compared to the standard optimizer. On a large-scale 3D optimal design problem with around 1,400,000 design variables, our method achieves up to 7.5x speedup while producing optimized designs with comparable objectives.