An efficient threshold dynamics method for topology optimization for fluids

We propose an efficient threshold dynamics method for topology optimization for fluids modeled with the Stokes equation. The proposed algorithm is based on minimization of an objective energy function that consists of the dissipation power in the fluid and the perimeter approximated by nonlocal energy, subject to a fluid volume constraint and the incompressibility condition. We show that the minimization problem can be solved with an iterative scheme in which the Stokes equation is approximated by a Brinkman equation. The indicator functions of the fluid-solid regions are then updated according to simple convolutions followed by a thresholding step. We demonstrate mathematically that the iterative algorithm has the total energy decaying property. The proposed algorithm is simple and easy to implement. A simple adaptive time strategy is also used to accelerate the convergence of the iteration. Extensive numerical experiments in both two and three dimensions show that the proposed iteration algorithm converges in much fewer iterations and is more efficient than many existing methods. In addition, the numerical results show that the algorithm is very robust and insensitive to the initial guess and the parameters in the model.Comment: 23 pages, 24 figure

Thermo-fluid Topology Optimization and Experimental Study of Conformal Cooling Channels for 3D Printed Plastic Injection Molds

With the advent of additive manufacturing, innovative design methods, such as network-based techniques, and structural topology optimization have been used to generate complex and highly efficient cooling systems in recent years. However, methods that incorporate coupled thermal and fluid analysis remain scarce. In this paper, a coupled thermal-fluid topology optimization algorithm is introduced for the design of conformal cooling channels. The problem is formulated based on a coupling of Navier- Stokes equations and convection-diffusion equation. The problem is solved by gradient-based optimization after analytical sensitivity derived using adjoint method. With this method, the channel position problem is replaced to a material distribution problem. The material distribution directly depends on the effect of flow resistance, heat conduction, natural and forced convection. The algorithm leads to a two-dimensional conceptual design having optimal heat transfer and balanced flow, which is further transformed into three-dimensional cooling channel design. Here, a comprehensive study is presented, starting from design, simulation, 3D printing process and experimental testing of an injection mold with conformal cooling channels in industrial production environment. A traditional mold model is provided by an industrial collaborator. To enhance the overall thermo-fluid performance of the mold and improve final product quality, a redesign of this mold core is done with conformal cooling channels inside. The final design is 3D printed in pre-alloyed tool-steel powder Maraging Steel using Truprint 3000 metal 3D printing machine. The printed core required some heat treatment and finishing processes and added features to be incorporated to make it production ready. Once all the preparation was complete, the core was tested experimentally in a multicavity injection molding machine in real industrial environment at our industrial partner’s production facility. This paper describes all the steps starting from design, analysis, die 3D printing and finally ending at final experimental testing, as well as recommendations for tool designer and injection molding industry to implement additive manufacturing for their benefit. This paper is not just focused on a specific aspect such as design, simulation or manufacturing, but rather a comprehensive paper presenting a case study on implementation of topology optimization and additive manufacturing in real life industrial production scenario

Topology optimisation of natural convection problems

This paper demonstrates the application of the density-based topology optimisation approach for the design of heat sinks and micropumps based on natural convection effects. The problems are modelled under the assumptions of steady-state laminar flow using the incompressible Navier-Stokes equations coupled to the convection-diffusion equation through the Boussinesq approximation. In order to facilitate topology optimisation, the Brinkman approach is taken to penalise velocities inside the solid domain and the effective thermal conductivity is interpolated in order to accommodate differences in thermal conductivity of the solid and fluid phases. The governing equations are discretised using stabilised finite elements and topology optimisation is performed for two different problems using discrete adjoint sensitivity analysis. The study shows that topology optimisation is a viable approach for designing heat sink geometries cooled by natural convection and micropumps powered by natural convection.Comment: Submitted to the 'International Journal for Numerical Methods in Fluids' on 28th of August 2013 - currently under revie

A topology optimization method in rarefied gas flow problems using the Boltzmann equation

This paper presents a topology optimization method in rarefied gas flow problems to obtain the optimal structure of a flow channel as a configuration of gas and solid domains. In this paper, the kinetic equation, the governing equation of rarefied gas flows, is extended over the entire design domain including solid domains assuming the solid as an imaginary gas for implicitly handling the gas-solid interfaces in the optimization process. Based on the extended equation, a 2D flow channel design problem is formulated, and the design sensitivity is obtained based on the Lagrange multiplier method and adjoint variable method. Both the rarefied gas flow and the adjoint flow are computed by a deterministic method based on a finite discretization of the molecular velocity space, rather than the DSMC method. The validity and effectiveness of our proposed method are confirmed through several numerical examples

4D topology optimization: Integrated optimization of the structure and self-actuation of soft bodies for dynamic motions

Topology optimization is a powerful tool utilized in various fields for structural design. However, its application has primarily been restricted to static or passively moving objects, mainly focusing on hard materials with limited deformations and contact capabilities. Designing soft and actively moving objects, such as soft robots equipped with actuators, poses challenges due to simulating dynamics problems involving large deformations and intricate contact interactions. Moreover, the optimal structure depends on the object's motion, necessitating a simultaneous design approach. To address these challenges, we propose "4D topology optimization," an extension of density-based topology optimization that incorporates the time dimension. This enables the simultaneous optimization of both the structure and self-actuation of soft bodies for specific dynamic tasks. Our method utilizes multi-indexed and hierarchized density variables distributed over the spatiotemporal design domain, representing the material layout, actuator layout, and time-varying actuation. These variables are efficiently optimized using gradient-based methods. Forward and backward simulations of soft bodies are done using the material point method, a Lagrangian-Eulerian hybrid approach, implemented on a recent automatic differentiation framework. We present several numerical examples of self-actuating soft body designs aimed at achieving locomotion, posture control, and rotation tasks. The results demonstrate the effectiveness of our method in successfully designing soft bodies with complex structures and biomimetic movements, benefiting from its high degree of design freedom.Comment: 36 pages, 27 figures; for supplementary video, see https://youtu.be/sPY2jcAsNY