Multiphysics Topology Optimization Research Articles

An approach for topology optimization of heat sinks for two-phase flow boiling: Part 1 – Model formulation and numerical implementation

Two-phase flow boiling in heat sinks and cold plates is attractive for various thermal management applications due to high effective heat capacity rates and high heat transfer coefficients compared to single-phase operation. In addition, multi-physics topology optimization is sought for generation of high performance thermal management components. Yet, the design of heat sinks using topology optimization has been restricted to single-phase flow physics, due to incompatibility between available two-phase flow models and traditional single-phase topology optimization approaches. Interface-capturing two-phase flow models are too computationally expensive for optimization; mixture and two-fluid models that treat the liquid and vapor phases as an interpenetrating continuum with interfacial transport phenomena captured through empirical correlations are computationally tractable for heat-sink-scale optimization. However, the penalization approaches commonly used to define the structures formed during topology optimization results in arbitrary fin and channel geometries for which a universal two-phase flow correlation is not available. To enable coupling with two-phase mixture models, this work leverages a homogenization approach to topology optimization wherein heat sink designs are represented using spatially varying microstructures with optimized dimensions. A predefined microstructure geometry is chosen for which two-phase flow correlations exist and therefore topology optimization can be performed. This work is the first to develop a topology optimization algorithm using a mixture model for simulating two-phase flow boiling to design heat sinks and cold plates. Part 1 of this study develops and implements the algorithm to investigate topology optimized heat sinks at various heat inputs, topology optimization grid sizes, and maximum vapor quality constraints. Topology optimized heat sinks designed for single-phase versus two-phase flow are compared. There are significant differences in hydraulic and thermal responses of the single-phase and two-phase designs due to high effective heat capacity rates and high heat transfer coefficients of flow boiling. A companion paper (Part 2) focuses on manufacturing, model calibration, and experimental validation of the topology optimized heat sinks under two-phase flow boiling. The algorithm demonstrated in this work extends the capabilities of topology optimization to two-phase flow physics, and thereby enables the design of various two-phase flow components such as evaporators, condensers, heat sinks, and cold plates.

Multiphysics Topology Optimization of SynRMs Considering Control Performance and Machinability

Multiphysics Topology Optimization of SynRMs Considering Control Performance and Machinability

Multiphysics topology optimization of aluminium and copper conductors for automotive electrical machines

Multiphysics topology optimization of aluminium and copper conductors for automotive electrical machines

Design Synthesis of a 4D-Printed Self-Tying Knot With Programmable Morphology

Abstract Smart materials provide a means by which we can create engineered mechanisms that artificially mimic the adaptability, flexibility, and responsiveness found in biological systems. Previous studies have developed material-based actuators that could produce targeted shape changes. Here, we extend this capability by introducing a novel computational and experimental method for design and synthesis of a material-based mechanism capable of achieving complex pre-programmed motion. By combining active and passive materials, the algorithm can encode the desired movement into the material distribution of the mechanism. We use multimaterial, multiphysics topology optimization to design a set of kinematic elements that exhibit basic bending and torsional deflection modes. We then use a genetic algorithm to optimally arrange these elements into a sequence that produces the desired motion. We also use experimental measurements to accurately characterize the angular deflection of the 3D-printed kinematic elements in response to thermomechanical loading. We demonstrate this new capability by de novo design of a 3D-printed self-tying knot. This method advances a new paradigm in mechanism design that could enable a new generation of material-driven machines that are lightweight, adaptable, robust to damage, and easily manufacturable by 3D printing.

Arbitrary curvature programming of thermo-active liquid crystal elastomer via topology optimization

Plants can change their morphology upon environmental variations such as temperature. Inspired by plants’ morphological adaptability, we present a computational inverse design framework for systematically creating optimized thermo-active liquid crystal elastomers (LCEs) that spontaneously morph into arbitrary programmed geometries upon temperature changes. The proposed framework is based on multiphysics topology optimization and a statistical mechanics-based LCE model to realize arbitrary curvature programming for LCE composites under large deformations. We propose a curvature-based optimization formulation that enables rotation-invariant and size-insensitive programmability of LCE, accounting for its highly nonlinear deformed shape. We demonstrate that the programmed LCE composites can accurately morph into a wide range of complex target shapes and curvatures, such as those of numbers, letters, flowers, and various objects. The resulting optimized designs exhibit highly irregular material distributions, which surpass intuition-based designs, and precisely produce desired deformed geometries upon temperature increase. The computational inverse design technique holds promise for a wide array of applications requiring function- and performance-driven design of active materials.

Inverse design of magneto-active metasurfaces and robots: Theory, computation, and experimental validation

Magneto-active structures can undergo rapid and reversible deformations under untethered magnetic fields. The capability to design such structures to achieve programmable shape morphing in three dimensions (3D) under magnetic actuation is highly desirable for many applications. In this work, we develop a multi-physics topology optimization framework for the inverse design of magneto-active metasurfaces that can undergo programmable shape morphing in 3D under external magnetic fields. These metasurfaces remain planar in their initial configurations and are deformed into complex 3D target shapes. The proposed framework accounts for large-deformation kinematics and optimizes both the topologies and magnetization distributions of metasurfaces in conjunction with the directions and magnitudes of the external magnetic fields. We demonstrate the framework in the design of kirigami metasurfaces, bio-inspired robots with “swimming”, “steering”, “walking”, and “climbing” motions, and multi-modal magnetic actuators, and the optimized designs show high precision and performance in achieving complex 3D deformations. We also use a hybrid fabrication procedure to manufacture representative designs and conduct experimental tests to validate their programmed 3D deformations, with results showing good agreement with simulation predictions. We envision that the proposed framework could lead to a systematic and versatile approach for the design of magneto-active metasurfaces for robotics applications.

On concurrent multiscale topology optimization for porous structures under hygro‐thermo‐elastic multiphysics with considering evaporation

AbstractLightweight polymeric and natural composite materials are extensively used in modern structures, especially with the demands for environmentally friendly products as well as lowering energy consumption. Furthermore, a high performance‐to‐weight ratio can be attained by utilizing porous composites. However, hygral and thermally induced loads are limiting the robustness of polymeric and natural composite materials, therefore; in this research, concurrent multiscale multiphysics topology optimization is used to design lightweight porous composite structures that have resilience toward mechanical as well as hygral and thermal loads. By establishing two independent representations of the design problem, that is, macro and microscale domains, a concurrent topology optimization framework is implemented, and the effective properties of the microscale (i.e., elastic, thermal conductivity, moisture diffusivity tensors, and hygral as well as thermal expansion coefficients) are calculated and used as the hygro‐thermo‐elastic properties of the macroscale using in‐house MATLAB codes. For hygral physics, moisture transport, as well as evaporation, are simultaneously considered in this study. A sensitivity analysis was conducted on the multiphysics concurrent optimization scheme in order to account for the coupling of macro and microstructure, as well as hygro‐thermo‐elastic physics. Multiple numerical cases were examined, which included different loading and boundary conditions, as well as various spatial configurations. The results showed attaining a high stiffness‐to‐weight ratio for the multiscale optimized porous structure compared to the single‐scale solid structure. Furthermore, a study was conducted on multiple microstructure subsystems to examine the impact of microstructure systems on macrostructure dependence. By combining several microstructures into a single macro design domain, design flexibility was enhanced and the performance‐to‐weight ratio was improved. The study was expanded to include the evaluation of hygro‐thermo‐elastic multiscale multiphysics with an evaporation problem, which was demonstrated through several numerical examples. The introduced formulations showed a successful application of the concurrent multiscale optimization formulations and good coupling on the macro and microscale. Also, the formulations demonstrated a strong influence between the macro and the microscale of the design problem for the topology optimization methods. The successful application of the concurrent multiscale optimization method in this research highlights its potential for designing more efficient and effective structures in the future.

Reaction–diffusion equation driven topology optimization of high-resolution and feature-rich structures using unstructured meshes

Motivated by the need for porous structures in the design of biodegradable implants, as well as for the diverse and competitive designs in architecture, this paper builds upon the recent advances in the single-scale (macroscopic) topology optimization (TO) approach and proposes a level-set method (LSM) for the design of lattice structures. The key idea is to introduce the maximum length-scale constraint, realized by a PDE filter, into the reaction–diffusion equation (RDE)-based LSM which can end up with feature-rich shape, starting from scratch. Then, the proposed TO technique is coupled with distributed computing algorithms based on PETSc, interfaced in the open-source software FreeFEM using unstructured meshes, to deliver both two- and three-dimensional designs with complex-shape geometry. The parallel efficiency is validated by solving large-scale 3D benchmarks with 20 million tetrahedral elements on a cloud-based cluster. Furthermore, we integrate local mesh refinement (h-adaptation scheme) into this workflow, allowing one to reach high-resolution and feature-rich 3D designs on a desktop, paving the way to future investigations, aimed at including the maximum length-scale constraint in large-scale multiphysics topology optimization at a reasonable cost.

Comprehensive performance enhancement of conformal cooling process using thermal-load-based topology optimization

Conformal cooling technology is widely used in the thermal management for injection molding process. However, the overall design of cooling channel layout needs to be optimized due to non-uniform thermal load, limited design freedom and other factors. This paper presents a novel procedure for conformal cooling channel design by using thermal-load-based topology optimization. Unlike previous approaches that focused on optimizing the channel configuration or geometric parameters, the current work applies multiphysics topology optimization on the entire cooling area. The objective is to obtain the optimal channel layout with both low pressure drop and high heat transfer rate. A serious of optimized planar results are converted to three-dimensional channels that conform to the specific injection casting and are applied to injection molding process in a simulation software environment. For a given thin-plate casting, compared with the conventional parallel cooling process, the steady state average temperature and maximum temperature difference are decreased by 0.53 K and 2.20 K, respectively, and the pressure drop of coolant is decreased by 25.40%. For castings where non-uniform thermal loads are considered, the average temperature and pressure drop are decreased up to 1.45 K and 27.55%, respectively. The results for both sheet castings and cylindrical castings have demonstrated the stability, flexibility, and rationality of the proposed procedure. In addition, the conceptual design of cooling channels based on thermal load is expected to be applied to more potential thermal engineering fields.

Multiphysics topology optimization of a multifunctional structural battery composite

Multiphysics topology optimization of a multifunctional structural battery composite

Genotype-Phenotype Mapping for Applied Evolutionary Multi-Objective and Multi-Physics Topology Optimization

We present a multi-objective topology optimization method based on the Non-Sorting Genetic Algorithm II (NSGA-II). The presented approach is a tool for early-stage engineering applications capable of providing insights into the complex relationship between structural features and the performance of a design without a priori assumptions about objective space. Mass reduction, linear elastic deformation, and stationary thermal conduction are considered simultaneously with three additional constraints. The specifically developed genotype-phenotype mapping ensures the practical benefit of obtained design propositions and significantly reduces computational effort to generate a dense set of Pareto solutions. The mapping procedure smooths probabilistically generated structures, removes unconnected material, and refines the spatial discretization for the subsequently used finite element solver. We present sets of Pareto optimal solutions to large three-dimensional design problems with multiple objectives and multiple near-application constraints that are feasible design propositions for engineering design. Geometrical features present in the obtained Pareto set are discussed.

Multi-Head Self-Attention Generative Adversarial Networks for Multiphysics Topology Optimization

Machine learning surrogates for topology optimization must generalize well to a large variety of boundary conditions and volume fractions to serve as a stand-alone model. However, when analyzing design performance using physics-based analysis, many of the recently published methods suffer from low reliability, with a high percentage of the generated structures performing poorly. Disconnected regions of solid material between boundary conditions lead to unstable designs with significant outliers skewing the performance on test data. In this work, multi-head self-attention generative adversarial networks are introduced as a novel architecture for multiphysics topology optimization. This network contains multi-head attention mechanisms in high-dimensional feature spaces to learn the global dependencies of data (i.e., connectivity between boundary conditions). The model is demonstrated on design of coupled thermoelastic structures and its performance is evaluated with respect to the physics-based objective function used to generate training data. The proposed network achieves over a 36 times reduction in mean objective function error and an eight times reduction in volume fraction error compared to a baseline approach without attention mechanisms.

Implementation of Thermomechanical Multiphysics in a Large-Scale Three-Dimensional Topology Optimization Code

<div class="section abstract"><div class="htmlview paragraph">Due to the inherent computational cost of multiphysics topology optimization methods, it is a common practice to implement these methods in two-dimensions. However most real-world multiphysics problems are best optimized in three-dimensions, leading to the necessity for large-scale multiphysics topology optimization codes. To aid in the development of these codes, this paper presents a general thermomechanical topology optimization method and describes how to implement the method into a preexisting large-scale three-dimensional topology optimization code. The weak forms of the Galerkin finite element models are fully derived for mechanical, thermal, and coupled thermomechanical physics models. The objective function for the topology optimization method is defined as the weighted sum of the mechanical and thermal compliance. The corresponding sensitivity coefficients are derived using the direct differentiation method and are verified using the complex-step method. The design variables are updated using the method of moving asymptotes so that the objective function is minimized resulting in maximum performance of the structure. Solution of the linear systems of equation is scaled across several supercomputer nodes using the Portable, Extensible Toolkit for Scientific Computation (PETSc) developed by Argonne National Laboratory. The finite element models, sensitivity analysis, optimization algorithm, and solver are all implemented in a freeware, density-based, topology optimization code (written in C++) that has been modified for thermomechanical problems. As such, the implementation of the thermomechanical model is provided. The code is applied to solve an example problem under thermal, mechanical, and thermomechanical boundary conditions. The resulting topologies and field variables are shown with a corresponding discussion.</div></div>

A New Development of a Shadow Density Filter for Manufacturing Constraint and Its Applications to Multiphysics Topology Optimization

Abstract The present research develops a new shadow filter and presents its usage for structural topology optimization (TO) considering the molding manufacturability. It is important to consider manufacturing methods in designing products. Some geometrical features not allowing molded parts should be removed. In addition, it has been an important issue to efficiently impose these manufacturing constraints in TO. For this purpose, the present research emulates implementation of shadowing of products and applies the shadow images as pseudo-density variables in TO. The use of this shadow density filter ensures that the optimized layouts comply with the conditions of the manufacturing constraints. Various manufacturing conditions can be imposed depending on the direction and the position of the light. Several numerical examples of compliance minimization problem, conjugate heat transfer problem, and fluid–structure interaction problem are solved to demonstrate the validity and effectiveness of the present shadow density filters, and their performances are compared.

Multiphysics topology optimization scheme considering the evaporation cooling effect

In this research, a new topology optimization scheme considering the evaporation cooling effect that cools air through the evaporation of liquid is presented. To efficiently cool down hot surfaces or products, it is a viable approach to use the evaporating cooling effect when water absorbs a large amount of heat on evaporating. To numerically consider the evaporating cooling effect, the three nonlinear governing equations, i.e., Navier–Stokes equation, heat transfer equation, and moisture transportation, should be coupled and analyzed; Air movement, temperature convection, and moisture transportation should be mutually coupled and analyzed. Due to the movement of air, the moisture inside porous media evaporates and the velocities, temperature, and moisture distributions of porous media are subject to be changed. From a topology optimization point of view, the material properties as well as the governing equations are interpolated with respect to the design variables defined at each finite element. After solving topology optimization problems, it is possible to find out the optimal distributions of porous media to control the states of the system. Through several numerical examples, the validity of the present topology optimization method is illustrated.

Three-dimensional topology optimization of thermal-fluid-structural problems for cooling system design

In the present study, a topology optimization method of thermal-fluid-structural problems is researched to design the three-dimensional heat sink with load-carrying capability. The optimization is formulated as a mean temperature minimization problem controlled by Navier-Stokes (N-S) equations as well as energy balance and linear elasticity equations. In order to prevent an unrealistic and low load-carrying design, the power dissipation of the fluid device and the normal displacement on the load-carrying surface are taken as constraints. A parallel solver of multi-physics topology optimization problems is built-in Open Field Operation And Manipulation (OpenFOAM) software. The continuous adjoint method is adopted for the sensitivity analysis to make the best use of built-in solvers. With the developed tool, the three-dimensional (3D) thermal-fluid topology optimization is studied. It is found that the Darcy number, which is suitable for fluid design, may cause severe problems in thermal-fluid optimization. The structural features of 3D thermal-fluid-structural problems are also investigated. The “2D extruded designs” are helpful to improve the structural stiffness, and channels with a larger aspect ratio in high-temperature areas improve the cooling performance.

Multi-physics topology optimization of functionally graded controllable porous structures: Application to heat dissipating problems

Graded porous structures can improve the design performance with a smooth transition of material properties over the domain. We present a multi-physics topology optimization approach for designing functionally graded porous structures. As an application, we present a formulation to optimize heat dissipating structures to enhance structural and thermal performance. The pore size, resolution, and porosity of the structures can be controlled to obtain optimized mechanical and thermal performances. Several controlling schemes are introduced which can tailor the design of the porous structures. Design approaches based on the functional variation of porosity, pore size and sensitivity-based porosity control are employed. Numerical examples with different structural loads, thermal loads and boundary conditions are presented to verify the formulation and show the efficacy of the implementation. We also investigate the effect of the controlling parameters on the overall design. The proposed formulation shows good promise to design functionally graded porous structures with targeted porosity in multi-physics systems.

Multi-physics bi-directional evolutionary topology optimization on GPU-architecture

Topology optimization has proven to be viable for use in the preliminary phases of real world design problems. Ultimately, the restricting factor is the computational expense since a multitude of designs need to be considered. This is especially imperative in such fields as aerospace, automotive and biomedical, where the problems involve multiple physical models, typically fluids and structures, requiring excessive computational calculations. One possible solution to this is to implement codes on massively parallel computer architectures, such as graphics processing units (GPUs). The present work investigates the feasibility of a GPU-implemented lattice Boltzmann method for multi-physics topology optimization for the first time. Noticeable differences between the GPU implementation and a central processing unit (CPU) version of the code are observed and the challenges associated with finding feasible solutions in a computational efficient manner are discussed and solved here, for the first time on a multi-physics topology optimization problem. The main goal of this paper is to speed up the topology optimization process for multi-physics problems without restricting the design domain, or sacrificing considerable performance in the objectives. Examples are compared with both standard CPU and various levels of numerical precision GPU codes to better illustrate the advantages and disadvantages of this implementation. A structural and fluid objective topology optimization problem is solved to vary the dependence of the algorithm on the GPU, extending on the previous literature that has only considered structural objectives of non-design dependent load problems. The results of this work indicate some discrepancies between GPU and CPU implementations that have not been seen before in the literature and are imperative to the speed-up of multi-physics topology optimization algorithms using GPUs.

Multiphysics topology optimization for piezoelectric acoustic focuser

The application of piezoelectric materials allows many advantages such as reducing the number of parts and manufacturing cost of a mechanical system. Despite these merits, the performance predictions and optimization of piezoelectric-material-based devices are challenging because of the mutual coupling between electricity and mechanics. The analysis and the optimization become more challenging when acoustics are to be coupled with piezoelectric-material-based devices. In the present study, the mutual couplings among electric, mechanics, and acoustics are simulated and its applications for the topology optimization of an acoustic energy focuser are presented. Owing to the local optima issue, some blurred and unsuccessful layouts are obtained. To overcome this issue and impose the manufacturing constraint, a modified morphology density filter is also developed. With the presented approach, it is possible to determine some optimized piezoelectric rings to focus acoustic energy. Compared with the existing design methods, some better designs in terms of objective value can be obtained by the present approach.

Multiobjective and multi-physics topology optimization using an updated smart normal constraint bi-directional evolutionary structural optimization method

To date the design of structures using topology optimization methods has mainly focused on single-objective problems. Since real-world design problems typically involve several different objectives, most of which counteract each other, it is desirable to present the designer with a set of Pareto optimal solutions that capture the trade-off between these objectives, known as a smart Pareto set. Thus far only the weighted sums and global criterion methods have been incorporated into topology optimization problems. Such methods are unable to produce evenly distributed smart Pareto sets. However, recently the smart normal constraint method has been shown to be capable of directly generating smart Pareto sets. Therefore, in the present work, an updated smart Normal Constraint Method is combined with a Bi-directional Evolutionary Structural Optimization (SNC-BESO) algorithm to produce smart Pareto sets for multiobjective topology optimization problems. Two examples are presented, showing that the Pareto solutions found by the SNC-BESO method make up a smart Pareto set. The first example, taken from the literature, shows the benefits of the SNC-BESO method. The second example is an industrial design problem for a micro fluidic mixer. Thus, the problem is multi-physics as well as multiobjective, highlighting the applicability of such methods to real-world problems. The results indicate that the method is capable of producing smart Pareto sets to industrial problems in an effective and efficient manner.