Topology Optimization Framework Research Articles

Maximizing the decay of anti-plane shear waves in periodic pile barriers by topology optimization and its application in barrier design considering a moving load

Mitigating ambient vibrations using periodic pile barriers has gained significant attention in the past decade. The width of the bandgap and the attenuation coefficient are two important factors that determine the vibration reduction capabilities of periodic pile barriers. In certain situations, significant vertical anti-plane vibrations may occur, such as those generated by subways. Therefore, the focus of this article is to optimize the attenuation coefficients of anti-plane shear waves in periodic pile barriers. Firstly, a single-objective topology optimization framework is developed based on the Genetic Algorithm (GA) to maximize the attenuation coefficient of anti-plane shear waves in periodic pile barriers at a target frequency. The optimization considers the effects of the target frequency, elastic modulus of soil, and wave vector direction. A comparison between the optimized and traditional pile barriers is performed to demonstrate the superiority of the optimized design. Secondly, a multi-objective optimization framework is developed based on the non-dominated sorting GA II (NSGA-II) to investigate the relationship between the attenuation coefficient and the filling fraction, as well as the relationship between the attenuation coefficient and the bandgap width. The results indicate that a higher filling fraction results in a larger attenuation coefficient, while there is a tradeoff between the filling ratio and the bandgap width. Thirdly, an optimization framework is established considering the effect of a moving load, and the coverage rate of the target frequency range is defined to design periodic pile barriers. Finally, numerical simulations are conducted to validate the effectiveness of periodic pile barriers in mitigating vibrations when a finite number of pile rows is used.

Turbulent flow topology optimization in nuclear reactor pressure vessel via NURBS-based particle hydrodynamics (NBPH) topology optimization framework

Turbulent flow topology optimization in nuclear reactor pressure vessel via NURBS-based particle hydrodynamics (NBPH) topology optimization framework

On multiphysics concurrent multiscale topology optimization for designing porous heat-activated compliant mechanism under convection for additive manufacture

In this research, we investigated the use of concurrent multiscale topology optimization to design additively manufacturable lightweight porous compliant mechanisms that enable harnessing heat energy as the energy source to perform mechanical actions. By establishing two independent dimensionless representations of the design problem, i.e., macro and microscale domains, a concurrent multiscale topology optimization framework is implemented, and the effective properties of the microscale (i.e., elastic and heat conductivity tensors, as well as the thermal expansion coefficient) are calculated and used as the thermo-elastic modeling effective properties of the macroscale. For heat transfer physics, heat transport in solids, as well as heat convection, are simultaneously considered in this study. Sensitivity analysis on the suggested concurrent optimization scheme was derived to address the macro and microstructure coupling as well as the thermo-elastic physics coupling. Several numerical cases are studied with single and multiple microstructure systems. To investigate the macrostructure dependency on the microstructure systems, a study was performed for multiple microstructure subsystems. Incorporating several microstructures into a single macro design domain increased design freedom and improved the performance-to-weight ratio. Furthermore, and for achieving good additive manufacturability we investigated the connectivity of the multi-microstructure optimization and implement boundary competitivity technique to attain fully connected design for attaining good additive manufacturability.

Enhanced ship cross-section design methodology using peridynamics topology optimization

In this study, peridynamics topology optimization (PD-TO) framework is implemented to reduce the total weight of ship structures and increase their structural endurance against cracks. PD-TO is a general nonlocal optimization strategy that performs the minimization of strain energy density as the objective function and uses pre-defined volume fractions as optimization constraints. To analyze ship structures herein, both the optimality criteria (OC) algorithm and the proportional (PROP) approach are implemented into the PD-TO solver. As the initial design domain, a reference bulkhead geometry of trailing suction hopper dredger (ship) is modeled. This web frame is optimized according to critical wave/loading conditions such as hogging and sagging. Different volume fractions are investigated to obtain lighter designs based on OC and PROP methods. In addition, different cracked scenarios are created by locating the cracks into various positions on the reference ship cross-section. Optimized results for cracked cases shows that the proposed method can create alternative web frames for specific definitions of the possible damaged regions on the board. To prove the efficiency of the proposed method, maximum displacements and compliance of the reference and optimized structures are compared. The results proves that topologically optimized designs offered stiffer structures as compared to conventional designs under the same loading conditions. Finally, some of the optimized results are smoothed to demonstrate the practical utility of the PD-TO for manufacturing. Overall, it is revealed that the PD-TO can be effectively utilized to design marine structures to achieve a higher strength/weight ratio while considering critical operation conditions and possible damaged regions.

DL-MSTO+: A deep learning-based multi-scale topology optimization framework via positive definiteness ensured material representation network

A multi-scale approach to topology optimization has recently emerged due to its lightweight, robust, and multi-functional characteristics. Considering material diversity, an increasing number of materials leads to a computational burden due to numerous design variables and homogenization equations. This study proposes DL-MSTO+, a deep learning-based multi-scale topology optimization framework. The framework consists of two distinct deep neural networks for multi-scale topology optimization problems to reduce the dimensionality of design variables and predict homogenized material properties. First, a generator network learns the low-dimensional representation of a material microstructure in an unsupervised manner. Thus, the trained generator produces a micro-structural image from a low-dimensional vector. Second, a predictor network is trained in a supervised manner to predict the homogenized elasticity matrix for a given micro-structural image. Additionally, the predictor is specifically designed to ensure the positive definiteness of the predicted elasticity matrix. Lastly, the networks are integrated into the algorithm to improve the efficiency of multi-scale topology optimization. The numerical experiments demonstrate higher efficiency for the proposed algorithm than the conventional multi-scale approach. Moreover, the proposed method provides connectable multi-scale designs, and the low-dimensional latent representation enables semantic interpolation between solutions.

Efficient two-phase approach to reliability-based discrete variable topology optimization of continuum structures with multimodal distributions

In practical applications, some random variables follow multimodal distributions. However, conventional reliability analysis methods in reliability-based topology optimization (RBTO), such as the first order reliability method, often result in considerable computational errors when dealing with problems involving multimodal distributions. Consequently, the corresponding RBTO design is incredible. Moreover, the RBTO problem also faces the challenge of high computational cost. To this end, this paper proposes an efficient two-phase approach for RBTO of continuum structures with multimodal distributions combining sequential approximate integer programming with trust region (SAIP-TR) and direct probability integral method (DPIM). Firstly, DPIM is advanced to address the difficult problems of failure probability estimation and efficient sensitivity analysis under multimodal distributions. Secondly, a reliability-based discrete variable topology optimization framework based on SAIP-TR and DPIM is established, which yields clear topology configurations and facilitates engineering manufacturing. Owing to the merit of SAIP-TR, the original RBTO process is divided into two phases: the first phase performs deterministic topology optimization, and the second phase focuses on RBTO. Moreover, an adaptive selection strategy of representative points, considering structural compliance as performance function, is devised to further enhance computational efficiency. Finally, several examples illustrate high efficiency and accuracy of the proposed approach. The multimodal random variable and the random field are employed separately to describe global and local uncertainties in materials. In contrast, the optimized result considering global material uncertainty is more suitable for additive manufacturing. The proposed approach also presents potential in handling complex RBTO problems with random fields.

Vibroacoustic topology optimization for sound transmission minimization through sandwich structures

Recently, metamaterials, sandwich panels, and a combination of both have shown potential for creating lightweight, load-bearing structures with good noise and vibration suppression properties. However, designing these structures is difficult due to the complex vibroacoustic innate physics and the need to balance conflicting requirements. Structural optimization methods can help address this multi-functional, multi-physical design challenge. While much research has been conducted on optimizing the materials and sizes of plates and sandwich cores, the systematic topological design of fully coupled vibroacoustic cores has not yet been explored. To address this gap, this work presents a topology optimization framework for the vibroacoustic design of sandwich structure cores, with the goal of minimizing sound transmission while constraining volume and structural stiffness. The framework is used to conduct a systematic design analysis, focusing on the dynamic behavior of the optimized structures. The versatility of the methodology is demonstrated by analyzing different targeted frequency ranges, different angles of incidence and the trade-off between the acoustic and structural performance. The resulting designs are lightweight, load-bearing, and achieve high sound transmission loss performance, exceeding the mass law by 15–40 dB in targeted frequency ranges of 500Hz in the interval between 1000Hz and 3000Hz.

Design of heat exchangers via a bioinspired topology optimization framework with physics-informed underlying fields

Design of heat exchangers via a bioinspired topology optimization framework with physics-informed underlying fields

Topological design of open-cell microstructure with optimal effective thermal conductivity

The highly thermal conductive porous structure has many application scenarios, such as the skeletons embedded with phase change material. The additive manufacture technique combined with topology optimization motivates the design of microstructure of lattice material. A topology optimization framework based on isotropic material with penalization and finite element is developed. Aiming at extremely high thermal conductivity, the optimal lattices have closed pores. The conductivity is close to the theoretical Hashin-Strikman bound. In order to achieve the goal of open-cell lattice for heat and mass transport, a multi-objective function based on thermal conductivity and mass diffusivity is proposed. Optimization results reveal that various microstructure has optimal effective properties which are close to theoretical cross-property bound. In addition, the lattice materials are fabricated using selective laser melting. The experimental thermal conductivity results are in good agreement with the numerical simulation, with an error of less than 8%. The ability to fabricate the microstructure accurately provides an opportunity to use these lattice materials. This work provides a basis for designing lattice material, with better application in skeleton embedded with PCM, lattice channel, lattice heat sink, etc.

A strategy for avoiding spurious localized buckling modes in topology optimization

SummaryWe introduce a strategy preventing the occurrence of spurious modes in the spectrum computed by linearized buckling analysis in the context of topology optimization. Spurious buckling modes may appear in low density regions, a well‐known and largely discussed phenomenon. However, localized modes may also appear in solid areas, where stress concentrations occur. This second phenomenon, which is due to the inherent limitations of the linearized buckling analysis when used for complex stress states, is hardly addressed in the topology optimization literature. The remedy we propose makes use of elementary operations in the topology optimization framework: filtering and erosion, but now applied to the stress field. We show how this simple strategy helps mitigating the occurrence of spurious modes, in turn regularizing the optimization process towards high performance designs, which are then verified by nonlinear analysis.

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.

Enabling Quasi-Static Reconfigurable Networks With Robust Topology Engineering

Many optical circuit switched data center networks (DCN) have been proposed in the last decade to attain higher capacity and topology reconfigurability, though commercial adoption of these architectures have been minimal. One major challenge these architectures face is the difficulty of handling uncertain traffic demands using commercial optical circuit switches (OCS) with high switching latency. Prior works have generally focused on developing fast-switching OCS prototypes to quickly react to traffic variations through frequent reconfigurations. This approach, however, adds tremendous complexity overhead to the control plane, and raises the barrier for commercial adoption of optical circuit switched data center networks. We propose, a robust topology and routing optimization framework for reconfigurable optical circuit switched data centers. co-optimizes topology and routing based on a convex set of traffic matrices, and offers strict throughput guarantees for any future traffic matrices bounded by the convex set. For the bursty traffic demands that are unbounded by the convex set, we employ a desensitization technique to reduce performance hit. This enables to generate topology and routing solutions capable of handling unexpected traffic changes without relying on frequent topology reconfigurations. Our extensive evaluations based on Facebook’s production DCN traces show that, even with daily reconfigurations which could be realized by current commercial MEMS-based OCSs from Calient Technologies, achieves about 20% lower max link utilization, and about 32% lower average hop count compared to cost-equivalent static topologies. Our work shows that adoption of reconfigurable topologies in commercial DCNs is feasible even without fast OCSs.

A 3D Structure Mapping-Based Efficient Topology Optimization Framework

Abstract It is well known that the computational cost of classic topology optimization (TO) methods increases rapidly with the size of the design problem because of the high-dimensional numerical simulation required at each iteration. Recently, the technical route of replacing the TO process with artificial neural network (ANN) models has gained popularity. These ANN models, once trained, can rapidly produce an optimized design solution for a given design specification. However, the complex mapping relationship between design specifications and corresponding optimized structures presents challenges in the construction of neural networks with good generalizability. In this paper, we propose a new design framework that uses deep learning techniques to accelerate the TO process. Specifically, we present an efficient topology optimization (ETO) framework in which structure update at each iteration is conducted on a coarse scale and a structure mapping neural network (SMapNN) is constructed to map the updated coarse structure to its corresponding fine structure. As such, fine-scale numerical simulations are replaced by coarse-scale simulations, thereby greatly reducing the computational cost. In addition, fragmentation and padding strategies are used to improve the trainability and adaptability of SMapNN, leading to a better generalizability. The efficiency and accuracy of the proposed ETO framework are verified using both benchmark and complex design tasks. It has been shown that with the SMapNN, TO designs of millions of elements can be completed within a few minutes on a personal computer.

Supervised deep learning for the moving morphable components topology optimization framework

In the context of mechanical engineering design, the field of machine learning accelerated topology optimization is dominated by image-based models trained in a supervised manner on datasets with a limited diversity of boundary conditions. State-of-the-art methods show poor generalization capabilities and are strongly coupled to finite element mesh resolution, hindering scalability. In this paper, we leverage the explicit topology parameterization of the moving morphable components (MMC) framework to train a deep learning model that directly generates geometric design variables using a model architecture that is independent of the finite element mesh used for structural analysis. The developed model is trained on a large dataset of boundary conditions. Despite achieving state-of-the-art regression loss, evaluations reveal that direct-design approaches generate topologies with poor mechanical performance. Specifically, the model-generated topologies have, on average, a stiffness 11.48% lower than conventional MMC designs, as evidenced by in-distribution and out-of-distribution test samples. We demonstrate that this is due to the incompatibility between the regression loss function typically used in literature and the topology optimization objective of compliance minimization. To address this issue, we propose a novel acceleration approach that leverages the trained model to generate improved initial designs for conventional optimization. Specifically, the deep learning model is used to generate an initial design, which is then refined by conventional optimization to arrive at a final, optimal design. This approach shows a computation time-saving of 36.84% without sacrificing the final mechanical performance of the optimal topology compared to conventional optimization starting from a uniform initial layout.

Stress-based topology optimization for fiber composites with improved stiffness and strength: Integrating anisotropic and isotropic materials

Fiber-reinforced materials offer high stiffness- and strength-to-mass ratios to lightweight composite structures. To design stiff, strong, and lightweight fiber-reinforced composite structures, we propose a multimaterial anisotropic stress-constrained topology optimization framework that simultaneously optimizes geometry, distribution of anisotropic (i.e., orthotropic) and isotropic material phases, and local orientations of fiber reinforcements in the anisotropic phase. To achieve high performance in both stiffness and strength, we discover that both isotropic and anisotropic materials are needed: anisotropic materials are preferred in uniaxial members to increase stiffness, while isotropic materials are crucial at multi-axially stressed joints to enhance strength. We introduce multimaterial interpolation schemes to characterize both the stiffness and strength of composites made up of anisotropic and isotropic materials. The characterization of strength is enabled by a novel load factor-based yield function interpolation that consistently integrates anisotropic Tsai–Wu and isotropic von Mises yield criteria. We optimize stress-sensitive domains considering materials with various levels of stiffness and strength anisotropy as well as multiple load cases. The anisotropic stress constraints in the proposed framework effectively inform geometries to reduce stress concentration in fiber composites. The proposed framework provides a rational design paradigm for composite structures, capitalizing on dissimilar stiffness and strength properties of anisotropic and isotropic materials, to potentially benefit various engineering applications.

Topology Optimization of Self-supporting Porous Structures Based on Triply Periodic Minimal Surfaces

With the advent of additive manufacturing (AM), topology optimization (TO) has become increasingly important in structural design. A key component of structural design is generating the interior shape of an object under predefined force conditions and specific constraints. Fabricating such models by layer-based AM suffers from the problem of adding and removing interior supporting structures, which can produce artifacts in the final product. In this paper, we propose an algorithm to design a self-supporting porous structure by integrating overhang constraints into the topology optimization framework. A minimum thickness constraint is also built into the optimization process to automatically enforce printability of the resulting structures. We utilize triply periodic minimal surfaces (TPMSs) to represent interior structures which can be analyzed, optimized and stored directly using analytical functions. We apply several acceleration methods including super element strategy, multigrid algorithm and GPU-based solver to handle models comprising of several million of elements efficiently. Numerical results indicate that the optimized interior structures obtained by our approach exhibit improved printability as they largely satisfy manufacturing requirements on overhang angles and minimal thicknesses.

Topology Optimization of an Electromagnet Manipulator for 3-D Uniform Magnetic Field Generation

Magnetic manipulation is a method used for biomedical applications to remotely control micro-robots in a contactless manner. The electromagnet manipulator should control a magnetic field with 3 degrees of freedom inside a region of interest. In various case studies, this field results from the superposition of three decoupled uniform magnetic fields. Each of them is individually generated by a different pair of Helmholtz coils. Such an arrangement requires the pairs to be nested within each other, inevitably reducing the working area’s size and degrading the whole system’s performance and integration. The proposed work aims to design a novel electromagnetic manipulator with the help of computational design, to explore beyond the Helmholtz coils arrangement. A topology optimization framework is developed for this purpose. It investigates the distribution of coils that achieves the best field uniformity for a fixed footprint while keeping the different degrees of freedom balanced.

Topology optimization via implicit neural representations

Along with the rapid development of artificial intelligence (AI) technology, scientific research enters a new era of AI. Topology optimization (TO) and AI technology are recently showing a growing trend of cross development, which has received continuous attentions from relative researchers. In this paper, we introduce a concept of Implicit Neural Representations from AI into TO field and establish a novel TO framework which is named as TOINR. In TOINR, the Topology Description Function is the inherent combination factor, which is constructed by a Neural Network (NN) and determines the topology statuses of structural materials in the design domain. We adopt sine as a periodic activation function combined with MLP as the architecture of the NN. The inputs of NN are a predefined set of spatial points’ coordinates, while the outputs are the implicit representations of corresponding topological boundaries. Along with updating NN’s parameters (i.e., design variables), the structural topologies iteratively evolve according to the responses analysis results and optimization functions. A boundary-adaptive multi-resolution finite element analysis method is developed to improve the physical response accuracy. At each step of TOINR, we ensure the computational differentiability. Thus, the automatic differentiation is used in sensitivity analysis. The multi-penalty function approach is applied to handle objects with constraints. Besides, we design an adaptive adjustment scheme for learning rates to enhance the stability of the optimization process. Numerical examples illustrate that TOINR can stably obtain optimized structures for different problems with high performance and robustness.

Thermal-mechanical coupling topology optimization of multi-phase infill structures with a non-gradient porosity optimization method

Mechanical structures in the real world are often subject to different types of physics which affect their performance and reliability. Recent studies have revealed that porous structures can be an ideal solution for multiphysics problems due to their multifunctionality. In this paper, a full-scale topology optimization method of multi-phase infill structures, i.e. non-gradient porosity optimization method, is proposed to exploit the advantages of different phase materials and solve multiphysics problems efficiently. The method builds upon a unified multi-material density-based topology optimization framework to interpolate the thermal stress coefficient in order to characterize the dependence of the thermal stress load upon the design variables. To generate sparse but stable structures distributed in the interior of a given shape, the upper bound of the solid material volume fraction in the neighborhood of each element in the design domain is constrained. In particular, the influence radius of each element is considered as a separate variable to be optimized, which is calculated directly from field functions in finite element analysis (FEA) without additional sensitivity analysis. In the proposed method, the element pseudo-density and porosity are optimized simultaneously, which further expands the design space and improves the performance of infill structures. Subsequently, the improved weighting method is used to aggregate multiple objective functions. The whole analysis and optimization process are based on a full-scale FEA, thus avoiding scale separation and naturally ensuring the optimized spatial gradient infills to be connected smoothly. Numerical examples with different thermal and mechanical load conditions are presented to demonstrate the feasibility and effectiveness of the proposed method.

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.