A Topology-Preserving Level Set Method for Shape Optimization

The objective of this paper is to introduce and demonstrate a robust methodology for solving multi-constrained 3D topology optimization problems. The proposed methodology is a combination of the topological level-set formulation, augmented Lagrangian algorithm, and assembly-free deflated finite element analysis (FEA). The salient features of the proposed method include: (1) it exploits the topological sensitivity fields that can be derived for a variety of constraints, (2) it...

The objective of this paper is to introduce and demonstrate a robust method for multi-constrained topology optimization. The method is derived by combining the topological sensitivity with the classic augmented Lagrangian formulation. The primary advantages of the proposed method are: (1) it rests on well-established augmented Lagrangian formulation for constrained optimization, (2) the augmented topological level-set can be derived systematically for an arbitrary set of load...

We consider regularization methods based on the coupling of Tikhonov regularization and projection strategies. From the resulting constraint regularization method we obtain level set methods in a straight forward way. Moreover, we show that this approach links the areas of asymptotic regularization to inverse problems theory, scale-space theory to computer vision, level set methods, and shape optimization.

In this paper we present GridapTopOpt, an extendable framework for level set-based topology optimisation that can be readily distributed across a personal computer or high-performance computing cluster. The package is written in Julia and uses the Gridap package ecosystem for parallel finite element assembly from arbitrary weak formulations of partial differential equation (PDEs) along with the scalable solvers from the Portable and Extendable Toolkit for Scientific Computing...

In this work we consider topology optimization of systems, which are governed by the external Bernoulli free boundary problem. We utilize the so-called pseudo-solid approach to solve the governing free boundary problems during the optimization. To define design domains we utilize a level set representation parameterized by radial basis functions. This design parametrization allows topological changes in the design domain.

The ability to efficiently solve topology optimization problems is of great importance for many practical applications. Hence, there is a demand for efficient solution algorithms. In this paper, we propose novel quasi-Newton methods for solving PDE-constrained topology optimization problems. Our approach is based on and extends the popular solution algorithm of Amstutz and Andr\"a (A new algorithm for topology optimization using a level-set method, Journal of Computational Ph...

We propose a new algorithm for the design of topologically optimized lightweight structures, under a minimum compliance requirement. The new process enhances a standard level set formulation in terms of computational efficiency, thanks to the employment of a strategic computational mesh. We pursue a twofold goal, i.e., to deliver a final layout characterized by a smooth contour and reliable mechanical properties. The smoothness of the optimized structure is ensured by the emp...

This paper proposes a level set-based method for optimizing shell structures with large design changes in shape and topology. Conventional shell optimization methods, whether parametric or nonparametric, often only allow limited design changes in shape. In the proposed method, the shell structure is defined as the isosurface of a level set function. The level set function is iteratively updated based on the shape sensitivity on the surface mesh. Therefore, the proposed method...

This paper is concerned with topology optimization based on a level set method using (doubly) nonlinear diffusion equations. Topology optimization using the level set method is called level set-based topology optimization, which is possible to determine optimal configurations that minimize objective functionals by updating level set functions. In this paper, as an update equation for level set functions, (doubly) nonlinear diffusion equations with reaction terms are derived, ...

This article proposes a new discrete framework for approximating solutions to shape optimization problems under convexity constraints. The numerical method, based on the support function or the gauge function, is guaranteed to generate discrete convex shapes and is easily implementable using standard optimization software. The framework can handle various objective functions ranging from geometric quantities to functionals depending on partial differential equations. Width or...