Topology Optimization Method Research Articles

Multi-Objective Topology Optimization of Thin-Plate Structures Based on the Stiffener Size and Layout

To address the limitations of existing optimization methods that focus on single objectives or neglect stiffener features, a multi-objective topology optimization (MOTO) method is proposed based on the stiffener size and layout. By constraining the initial structural performance parameters, the optimal stiffener height is determined through size optimization. Based on the stiffener height, single-objective topology optimization is used to achieve the best material distribution. The stiffener width is treated as a design variable, while MOTO is performed on the load point displacement, first natural frequency, and mass, thereby yielding an optimal stiffener width and performance. Finally, a multi-dimensional analysis of the stiffener height, width, and dynamic and static characteristics of the stiffened thin-plate structure is conducted. The results indicate that the optimized stiffener layout is considerably improved. Compared to the initial structure, the maximum and average displacements of the load point are reduced by 23.26% and 8.62%, respectively. The first natural frequency increases by 3.81%, while the maximum resonance amplitude and overall structural mass decrease by 39.97% and 1.99%, respectively. The results indicate that the optimized structure achieves a lightweight design while maintaining better stiffness and low-frequency vibration resistance. The feasibility and effectiveness of the proposed method are validated.

Improvement of Heat Conduction in Triply Periodic Minimal Surface Heat Sinks Filled with Phase Change Materials

Recently phase change materials (PCMs) have received significant attention in the field of thermal management and energy storage systems. However, the thermal performance of PCMs is restricted by their low thermal conductivity. Triply periodic minimal surface (TPMS) is a novel surface with high strength, high specific surface area, and high connectivity, which can be applied in PCM heat sinks to enhance the local heat transfer rate. In this study, a topology optimization method for TPMS structures applied in PCM heat sinks with the objective of least dissipation of heat transport potential capacity is proposed. The optimized structure has a higher volume fraction of metal material near the heating surface while lower in the region away from the heating surface. Furthermore, the optimized structure accelerates the advancement of the melting interface. With a constant heat flux on the heating surface, the average temperature of the heating surface can be reduced by about 30 K compared to the uniform TPMS structure.

Designing brittle fracture-resistant structures:A tensile strain energy-minimized topology optimization

This research proposes a novel method for designing fracture-resistant structures. By analyzing the relationship between tensile strain energy and phase field brittle fracture, it has been found that minimizing tensile strain energy can delay fracture and enhance resistance. Capitalizing on this insight, a new topology optimization method is proposed. This method focuses on minimizing tensile strain energy to suppress the well-documented tension-dominated fracture behavior observed in phase field brittle fracture analysis. In contrast to traditional topology optimization methods based on von Mises stress, this method generates more robust structures under tension. Furthermore, the method can incorporate stress constraints to mitigate the potential for stress concentrations arising from geometric discontinuities. Numerical results demonstrate the effectiveness of the proposed method. Using phase-field modeling, the mechanical fracture properties of the optimized structures, including peak load, failure displacement, and absorbed elastic energy before fracture, are quantified. Furthermore, experimental tests are also conducted. Both numerical simulations and experimental results are consistently show that structures designed with minimized tensile strain energy exhibit superior fracture toughness. Furthermore, the method offers significant computational efficiency compared to conventional approaches due to its reliance solely on linear elasticity analysis within the optimization process.

Design of solid oxide fuel cell (SOFC) channel layout using the topology optimization method with a design variable propagation approach

Design of solid oxide fuel cell (SOFC) channel layout using the topology optimization method with a design variable propagation approach

Two-material structure non-probabilistic reliability-based topology optimization against geometric imperfections with bounded field model

In additive manufacturing processes for multi-material structures, geometric uncertainties such as boundary or interface size deviation inevitably occur in the structure because of processing errors and various other reasons; these uncertainties induce performance fluctuations and affect the reliability of the structure. Considering the limited number of samples in practical engineering projects, a novel method of two-material structure non-probabilistic reliability-based topology optimization (TNRBTO) against geometric uncertainty is proposed to improve structure reliability under conditions in which the geometric uncertainty is characterized by an uncertainty threshold field function and further described by a non-probabilistic bounded field model. TNRBTO is a nested optimization model in which the inner-loop is used for reliability evaluation and the outer loop is used to determine the optimal two-material topology via the material-field series-expansion (MFSE) topology optimization method. The sensitivity information for the TNRBTO model is obtained via adjoint sensitivity analysis, and a gradient-based optimization algorithm based on the method of moving asymptotes (MMA) is used to solve the optimization problem. Numerical examples verified the effectiveness of the TNRBTO model against the geometric uncertainty that exist in two-material structures with bounded field model.

An adaptive material-field series-expansion method for structural topology optimization

The material-field series-expansion (MFSE) method reduces the dimension of design variables in density-based topology optimization and avoids the checkerboard patterns. However, the constant correlation function of the MFSE method only accounts for the spatial dependency between material field points. Accordingly, the expanded material field using the constant correlation function has an obscure topology, which increases the iterations and computation burden of the MFSE method. This paper proposes an adaptive correlation function that considers the spatial dependency and the values of material field points simultaneously. It describes the correlation between material field points more accurately. As a result, the expanded material field based on the adaptive correlation function has a clearer topology than the constant correlation function. Moreover, the adaptive material-field series-expansion (AMFSE) method with dual-loop optimization is introduced leveraging the adaptive correlation function. The outer loop updates the adaptive correlation functions and expanded material fields. The inner loop searches for the optimal solution of the current topology optimization model based on the expanded material field. Finally, several examples of static compliance and dynamic modal loss factor topology optimization validate the effectiveness and applicability of the AMFSE method. Results show that the AMFSE method converges faster with fewer iterations than the MFSE method, despite it increasing the computing time of matrix decomposition in the outer loops. Therefore, the AMFSE method is suitable for topology optimization with complex responses such as modal loss factors to decrease the iterations and computation burden simultaneously.

Multiscale topology optimization for designing locally resonant acoustic metamaterials with specified low-frequency bandgaps

Locally resonant acoustic metamaterials (LRAMs) have significant potential to isolate low-frequency vibrations and noise, whereas designing them with specified bandgaps is challenging. Compared to the monoscale method, the multiscale method can design microstructures that form equivalent materials to act as scatterers, coatings, and matrices. This may aid in obtaining LRAMs that are sometimes difficult to achieve with the monoscale method. Therefore, a multiscale topology optimization method is presented to design LRAMs with bandgaps that meet specified frequency constraints. Since bandgap optimizations are complicated, many local minimum solutions may exist when using sensitivity-based methods. To mitigate this issue, a macro-parameter optimization stage using a genetic algorithm (GA) is added between the macro and micro optimizations in this top-down multiscale framework. As a result, the method comprises three optimization stages: macro-bandgap optimization, macro-parameter optimization, and micro-optimization. Since the macrostructures consist of multiple microstructures and the microstructures consist of multiple materials, a parameterized level-set-based multi-material topology method is adopted to obtain topologies on both scales. The effectiveness of the proposed method is demonstrated through numerical examples of two optimization problems. The first is to obtain LRAMs with the maximum bandgap width while ensuring their bandgaps encompass specified frequency ranges. The other is to obtain LRAMs with specified bandgaps. Successfully obtained LRAMs with specified bandgaps demonstrate the application prospects of this method in designing structures and devices to address issues related to vibrations and noise.

Numerical study of Mg(OH)2/MgO thermochemical heat storage reactor coupled with parabolic dish solar system

Systems coupling Mg(OH)2/MgO thermochemical reactor with parabolic dish solar collector (PDSC) have a potential application prospect in solar seasonal heat storage. However, their working mechanism has not been systematically studied and not well understood either. In this study, Mg(OH)2-based thermochemical reactor, which was coupled with PDSC, was numerically studied for the first time using a three-dimensional model. The various working conditions and influencing factors of PDSC system were investigated, and a comprehensive analysis and optimization for the heat storage performance of the reactor such as the reaction time and energy storage rate were conducted. Effects of the fluid inflow temperature, velocity, and fluid pipe distribution on heat storage performance were also unfolded. For instance, when the heating pipe was arranged at 70 mm from the central axis, the reaction time was 15.9 % less than that of evenly arranged at R/2 from the center. Moreover, fins were added to the reactor and the fin shape was optimized using the density-based topology optimization method. It was found that the reaction time was reduced by 42.4 % and was only 12614 s.

Research on structural improvement of microchannel heat sink by using topology optimization method based on ε-constraint model

Research on structural improvement of microchannel heat sink by using topology optimization method based on ε-constraint model

Topology optimization method for light-weight design of three-dimensional continuous fiber-reinforced polymers (CFRPs) structures

Topology optimization method for light-weight design of three-dimensional continuous fiber-reinforced polymers (CFRPs) structures

Topology optimization for 3D fluid diode design considering wall-connected structures

This paper proposes a density-based topology optimization method for the three-dimensional design of fluid diodes considering wall-connected structures based on the fictitious physical modeling approach. The optimum design problem of fluid diodes is formulated as maximizing the energy dissipation in the reverse flow subject to the upper bound constraint of the energy dissipation in the forward flow. A fictitious physical model and a geometric constraint are constructed to detect and restrict the “floating” solid domains, which are not connected to the outer boundaries. The sensitivities of cost functions are derived and computed based on the continuous adjoint method. The finite volume method is employed to discretize the governing and adjoint equations to mitigate the huge computational costs of three-dimensional fluid analysis. Numerical investigations are presented to validate the fictitious physical model and the geometric constraint for excluding “floating” islands. Finally, topology optimization for fluid diodes with and without the geometric constraint is performed, and the result demonstrates that the proposed method is capable of generating fluid diodes with wall connectivity, while maintaining a good functional performance.

Experimental demonstration of a topology optimization method to generate a capacity-specific device with cavitation resistance for control valve applications

Experimental demonstration of a topology optimization method to generate a capacity-specific device with cavitation resistance for control valve applications

Multiscale concurrent topology optimization of transient thermoelastic structures

Previous multiscale concurrent topology optimization methods for thermoelastic structures were primarily based on static loading and steady-state heat transfer conditions, which do not account for transient effects associated with time-dependent loads. To address this limitation, this paper establishes a novel generic multiscale concurrent topology optimization method that incorporates transient thermoelastic coupling based on transient heat conduction and structural dynamics. In this study, first, a transient multiscale thermoelastic sensitivity equation is innovatively derived through adjoint sensitivity analysis. The effectiveness of this equation is then demonstrated through comparative cases involving transient heat conduction, structural dynamics, and transient thermoelastic (including multimaterial and 3D problems) optimization. Furthermore, the research finds that the topology optimization of transient thermoelastic structures also presents transient effects at microscale. This method demonstrates good versatility and applicability across various optimization cases. The method has great potential in the integrated design of materials and structures involving coupling between time-dependent thermal loads and time-dependent mechanical loads.

Performance comparison of battery cold plates designed using topology optimization across laminar and turbulent flow regime

Liquid cooling with cold plates offers an efficient solution for battery thermal management. However, conventional cold plates in turbulent regime often result in inadequate temperature uniformity within battery modules and generate significant pressure drops. In this study, we employ the turbulent conjugate heat transfer topology optimization method based on the k-ε turbulent model for cold plate design. Then we derive two novel cold plate designs based on the laminar and turbulent topology optimization method, respectively, and the effectiveness of the two design methods are compared. A multi-objective function which minimizes pressure drop and average temperature is established to balance the thermal and hydraulic performance of the cold plates. The electrochemical-thermal coupled model is utilized to simulate heat production of the battery pack. The fluid flow and heat transfer performance of turbulent topology-optimized cold plate (TTCP) during constant rate discharging is analyzed and compared with that of laminar topology-optimized cold plate (LTCP), serpentine cold plate (SCP), and rectangular cold plate (RCP). Numerical simulation results show that TTCP gives the best overall cooling results among all the designs despite a slight disadvantage against LTCP at very low flow rates. At high-speed turbulent flow (8.488 × 10−2 kg/s), the performance evaluation criterion (PEC) number improvements for TTCP, LTCP, and SCP compared with RCP are 86.7 %, 78.5 %, and 85.4 %, respectively. Hence, cold plate topology optimization using turbulent conditions and methods is recommended for power battery systems, especially those with fast charging/discharging requirements.

A fast calculation method for dynamic topology optimization based on hybrid spectral element method

In this study, a Hybrid Spectral Element Method (HSEM) integrated with Equivalent Static Load (ESL) in the frequency domain is suggested. This integration aims to enhance the computational efficiency of dynamic topology optimization. In comparison with existing techniques, the proposed HSEM transforms the governing equation of dynamic analysis into a spectral element equation within the frequency domain by utilizing the Fast Fourier Transform (FFT) algorithm. This approach enables the representation of both structural displacements and external loads in spectral forms, potentially leading to a reduction in the number of dimensions compared to traditional time-interval-based methods. By using spectral representation, a low-dimensional ESL set can be constructed in the frequency domain for model reduction. To validate the effectiveness of the suggested proposed method, extensive analyses and comparisons using various two-dimensional (2D) and three-dimensional (3D) examples are carried out. The obtained results demonstrate a substantial improvement in computational efficiency, both during the dynamic analysis phase and the quasi-static topology optimization phase, while maintaining high levels of accuracy. Moreover, even as the scale of the model increases, our method maintains its advantage in computational efficiency. In the test examples, a maximum speedup ratio of up to 6.54 times was observed, indicating the significant potential of the proposed HSEM-ESL approach in enhancing the performance of dynamic topology optimization tasks.

Topology-optimized phoxonic crystals with simultaneous acoustic and photonic helical edge states

Sonic and photonic topological insulators that host topological edge states offer promising potentials for the resilient control of acoustic and electromagnetic waves, respectively. Despite the great progress on sonic or photonic topological insulators, the research of their integration, i.e., the phoxonic topological insulator, is less explored. In this work, we propose a phoxonic topological insulator that hosts acoustic and dual-polarization photonic helical edge states simultaneously. In specific, we first design a glide-symmetric phoxonic crystal with concurrent sonic and dual-polarization photonic bandgaps via the topology optimization method. Then by choosing two different unit cells from the optimized phoxonic crystal and assembling them to create a domain-wall interface, a phoxonic topological insulator that supports two pairs of gapless helical edge states within both the sonic and photonic bandgaps is constructed. Pseudospin-locked unidirectional transmissions and robust manipulations of helical edge states are demonstrated for acoustic and dual-polarization electromagnetic waves simultaneously in the proposed phoxonic topological insulator. The designed phoxonic topological insulator opens new avenues for developing topological photoacoustic devices, enabling the reliable management of both acoustic and electromagnetic waves, as well as the investigation of their interplay. Published by the American Physical Society 2024

A Harmonic Response Topology Optimization Method Based on Hybrid Cellular Automata

Abstract Hybrid cellular automaton (HCA) method is a topology optimization method with high convergence efficiency. Harmonic response topology optimization problem has been widely researched and common frequency-domain methods have been applied to solve this problem. Despite this, little work has so far been undertaken to utilize the HCA method to improve the calculation efficiency of harmonic response topology optimization. In this article, we present a methodology that applies the HCA method to solve harmonic response topology optimization problem. Mode displacement method (MDM), mode acceleration method (MAM), and full method (FM) are common frequency-domain methods that are utilized as harmonic response analysis methods in this study. The examples under rotating loads demonstrate that feasibility of this methodology at one specific frequency excitation and multiple frequencies excitation. This article presents and implements a high convergence efficiency method for harmonic response topology optimization, and this method can converge in 20–30 iterations. This method can extend the application range of the HCA method and improve the optimization efficiency of harmonic response topology optimization.

Nickel–titanium alloy porous scaffolds based on a dominant cellular structure manufactured by laser powder bed fusion have satisfactory osteogenic efficacy

Nickel–titanium (NiTi) alloy is a widely utilized medical shape memory alloy (SMA) known for its excellent shape memory effect and superelasticity. Here, laser powder bed fusion (LPBF) technology was employed to fabricate a porous NiTi alloy scaffold featuring a topologically optimized dominant cellular structure that demonstrates favorable physical and superior biological properties. Utilizing a porous structure topology optimization method informed by the stress state of human bones, two types of cellular structures—compression and torsion—were designed, and porous scaffolds were produced via LPBF. The physical properties of the porous NiTi alloy scaffolds were evaluated to confirm their biocompatibility, while their osteogenic efficacy was investigated through both in vivo and in vitro experiments, with comparisons made against a traditional octahedral unit cell structure. NiTi alloy porous scaffolds can be nearly net-shaped via LPBF and exhibit favorable physical properties, including a low elastic modulus, high hydrophilicity, a specific linear expansion rate, as well as superelastic and shape memory effects. These scaffolds demonstrate excellent biocompatibility, support in vitro osteogenesis, and possess significant in vivo bone ingrowth capabilities. When compared to titanium alloys, NiTi alloys show comparable osteogenic properties in vitro but superior bone ingrowth properties in vivo. Additionally, among octahedral-type, torsion-type, and topologically optimized compression-type porous scaffolds, the latter demonstrates enhanced bone ingrowth properties. LPBF technology is effective for manufacturing porous NiTi alloy scaffolds with fine pore structures and excellent mechanical properties. The scaffolds based on topologically optimized dominant cellular structures facilitate satisfactory and efficient bone formation.

Employing topology optimization method to create optimum telecommunication tower design structure

Recently, the employment of topology optimization (TO) in structural engineering design has gained a significant structural performance, also, TO is employed by designers for developing aesthetically and efficient buildings. In this work, TO is employed to design novel and rigged structures of communication towers. The way that the TO algorithm works is to intelligently create the 3D model by preserving architectural features with tradeoffs between the stiffness and weight ratio. The present work focuses on the investigation of creating optimal self-supported communication towers. Results concerning the prime observation of optimization analyses and the potential benefits of TO in designing telecommunication tower lattices are drawn.

Topology optimization of a superconducting photonic crystal power beam splitter

The design of photonic crystals using novel materials holds significant importance in constructing high-performance, next-generation photonic crystal devices. In this study, aiming at the requirements for enhanced transmission and selectivity, we utilized a topology optimization method based on the method of moving asymptotes (MMA) to realize a high-temperature superconducting photonic crystal power splitter with low transmission loss and selectivity effects, which allows for flexible control and manipulation of optical signals. The method addresses the shortcomings of traditional scanning techniques, such as low efficiency and high resource consumption, by allowing for multi-parameter optimization. This improvement enhances the precision and effectiveness of the numerical computational iterative process. The research offers insights into the design of novel optical devices.