Structural Topology Optimization Method Research Articles

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.

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.

A new evolutionary topology optimization method for truss structures towards practical design applications

This paper presents a new topology optimization method and a comprehensive workflow for the practical design of truss structures. It begins with discussing practical design requirements for truss topology optimization and then introduces a technique for creating arbitrarily shaped ground structures suitable for complex geometries. To address limitations in current truss optimization methods, we propose a dual-material truss-bidirectional evolutionary structural optimization (DMT-BESO) method. This approach utilizes two materials that differ significantly in tensile and compressive allowable stresses and moduli of elasticity. The DMT-BESO method integrates the minimum energy principle with the full-stress design criterion, using bar cross-sectional areas as design variables to achieve simultaneous topology and size optimization. By considering stress constraints, this method ensures compliance with industry standards, enhancing both safety and material utilization. Additionally, a structural complexity control strategy is proposed to generate a near-optimal truss design and simplify the optimized design while maintaining efficiency, making it more suitable for practical applications. The effectiveness of the DMT-BESO method and its complexity control strategy is validated through numerical examples and the design of an arch bridge of composite materials.

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.

A one-time training machine learning method for general structural topology optimization

Machine learning (ML) methods have found some applications in structural topology optimization. In the existing methods, however, the ML models need to be retrained when the design domains and supporting conditions have been changed, posing a limitation to their wide applications. In this paper, we propose a one-time training ML (OTML) method for general topology optimization, where the self-attention convolutional long short-term memory (SaConvLSTM) model is introduced to update the design variables. An extension–division approach is used to enrich the training sets. By developing a splicing strategy, the training results of a small design space (i.e., a basic cell of either two- or three-dimensions) can be extended to tackling the optimization problem of a large design domain with arbitrary geometric shapes. Using the OTML method, the ML model needs to be trained for only one time, and the trained model can be used directly to solve various optimization problems with arbitrary shapes of design domains, loads, and boundary conditions. In the SaConvLSTM model, the material volume of the post-processed thresholded designs can be precisely controlled, though the control precision of the gray-scale designs might be slightly sacrificed. The effects of model parameters on the computational cost and the result quality are examined. Four examples are provided to demonstrate the high performance of this structural design method. For large-scale optimization problems, the present method can accelerate the structural form-finding process. This study holds a promise in the high-resolution structural form-finding and transdisciplinary computational morphogenesis.

Aircraft joint structure lightweight design

PurposeThe purpose of this article is to carry out a lightweight design of the joint structure according to the service condition of the joint.Design/methodology/approachThe finite element analysis techniques are used along with the variable density structure topology optimization method, the multi-island genetic algorithm for structural dimension optimization and the fatigue life analysis method.FindingsUtilizing the topology optimization method and size optimization method, the mass of the optimized model for the A100 material model is 9.67 kg. Compared to the pre-optimized model, the mass decreases by 8.23 kg, representing a weight reduction of 46.0% in the optimized model; the fatigue life of the aircraft joint is predicted to be a maximum of 1,460,017 cycles.Originality/valueThe originality of this study is that it provides new design ideas for the lightweight design of aircraft load-bearing structures.

A body-fitted adaptive mesh and Helmholtz-type filter based parameterized level-set method for structural topology optimization

A body-fitted adaptive mesh and Helmholtz-type filter based parameterized level-set method for structural topology optimization

Directed evolution-based non-gradient method for structural topology optimization

Existing non-gradient optimizers often rely on stochastic search strategies, which require a large number of finite element analyses to evaluate the objective function. In this study, a directed evolution-based non-gradient topology optimization method is proposed to reduce the high computational cost. A directed generation strategy of load path components is presented, based on the idea of fixed-point enumeration. This strategy determines the position and direction of components by locating the region with the maximum stress and enumerating samples with different orientations at each iteration step. Then, an element removal criterion is developed to gradually eliminate the redundant elements from the components. Consequently, an adaptive adjustment technique of component size is presented to overcome the numerical instability. The applicability and effectiveness of the proposed method are illustrated through numerical examples. The results show that the proposed method can reasonably generate structural load paths with exceptional efficiency compared to existing non-gradient algorithms.

Quantum computing intelligence algorithm for structural topology optimization

Structural topology optimization methods that are driven by the geometric features of components, such as the Moving Morphable Component (MMC), are widely explored due to their convenient interaction with design software. However, these methods exhibit significant sensitivity to the initial positioning of components, limiting their suitability for applications involving complex geometric boundaries. This study addresses these challenges by introducing a novel dual-layer optimization framework that employs a quantum computing-based intelligent optimization algorithm, Quantum-behaved Particle Swarm Optimization (QPSO). The potential drawbacks of the MMC method in engineering applications, particularly its sensitivity to initial conditions, are critically examined, leading to the proposal of a global-gradient hybrid framework for geometry feature-driven topology optimization. This proposed method demonstrates superior capability in optimizing material arrangements compared to the original MMC framework and enhances engineering applicability, making it more suitable for real-world applications. Through three representative examples, the limitations of the original MMC method are illustrated, and the advantages of the proposed dual-layer framework are highlighted. The results indicate that this method not only overcomes sensitivity issues but also stably identifies superior configurations, particularly for structures with complex geometric boundaries, providing models that facilitate interaction with CAD systems. This method offers a robust and precise approach for optimizing designs in various engineering fields.

Topology Optimization for Quasi-Periodic Cellular Structures Using Hybrid Moving Morphable Components and the Density Approach

Porous hierarchical structures are extensively utilized in engineering for their high specific strength, enhanced corrosion resistance, and multifunctionality. Over the past two decades, multiscale topology optimization for these structures has garnered significant attention. This paper introduces a novel hybrid MMCs (Moving Morphable Components)–density topology optimization method for quasi-periodic cellular structures. The term ‘quasi-periodic’ refers to microstructures whose different macroscopic points exhibit similar topologies with varying parameters. The primary concept involves using the MMC method to describe microstructural topology, while employing variable density to depict macro layouts. This approach leverages the advantage of MMCs in explicitly describing structural topology alongside the variable density of arbitrary microstructures. Sensitivity analyses of the optimization functions concerning design variables are shown, and a gradient optimization solver is employed to solve the optimization model. The examples effectively show the efficacy of the proposed method, illustrating that quasi-periodic cellular structures outperform single-scale solid structures.

MQ quasi-interpolation-based level set method for structural topology optimization

MQ quasi-interpolation-based level set method for structural topology optimization

Topology optimization framework for thermoelastic multiphase materials under vibration and stress constraints using extended solid isotropic material penalization

This paper proposes a multiphase material topology optimization (MMTO) method for thermal–mechanical structures that takes into account the effect of the temperature field under stress and frequency constraints. Thermoelastic coupling occurs when an engineering structure is concurrently subjected to thermal and mechanical loads. This work focuses on the following: (1) the derivation of three interpolation schemes that use stress, dynamic, and thermal loads based on the extended solid isotropic material penalization (SIMP) method; (2) the incorporation of stress and dynamic constraints of multi-material thermal-elastic structural designs; and (3) the effective control of the impact of thermal loads on structures based on stress and frequency levels. Numerical experiments show that a clear distinction exists in the final topologies for mechanical and thermal loads among materials. Coupled and uncoupled mechanical and thermal behaviors can be predicted using finite element models based on materials’ coefficients of thermal expansion. We see this method is capable of optimizing a structure’s strength and stability while solving the issue of a thermal environment. In addition, it allows for the precise management of stress and vibration levels when structures are not exposed to a thermal environment.

A topology, material and beam section optimization method for complex structures

This article presents an engineering method for optimizing the topology, materials and beam cross-sectional types of complex structures comprising bars, beams or shells, or their combinations. The optimization problem is established based on an extended ground structure where each location contains multiple components or cross-sectional beams with different materials. This problem is solved through explicit sequence approximate problems involving discrete 0/1 variables to determine the optimal topology, materials and beam section types of components, and continuous size variables. The 0/1 variables are determined with a genetic algorithm, in which size variables are optimized with a dual method after determining 0/1 variables in each generation. The final design is restricted to a condition where at most one component can exist per location, realized through modified operators in the genetic algorithm. Structural analyses are conducted before establishing approximate problems in iteration cycles. Numerical examples, including an engineering application, demonstrate the efficiency of this method.

Nonlinear electromechanical topology optimization method for stretchable electronic interconnect structures

Nonlinear electromechanical topology optimization method for stretchable electronic interconnect structures

Multiscale topology optimization of cellular structures with high thermal conductivity and large convective surface area

Cellular structures have excellent thermal performance due to their high specific surface areas and porosities. This paper proposes a multiscale topology optimization (MTO) method of cellular structures with high thermal conductivity and large convective surface area, which enables them to have rapid cooling capability. In the MTO of a cellular structure, the triply periodic minimal surface (TPMS) lattices are adopted and Kriging metamodels are constructed to predict their effective thermal conductivity tensors and surface areas. The thermal compliance of the cellular structure is firstly minimized under the given volume constraint by topology optimization. Then, maximizing the convective surface area of the cellular structure is considered as the objective to when imposing the optimized thermal compliance as the constraint. After conducting topology optimization, the cellular structure with high thermal conductivity and large convective surface area is achieved. Additionally, in the above MTO, isogeometric analysis (IGA) is employed to improve the accuracy of numerical analysis. A numerical example is provided to verify the effectiveness of the proposed method. By both simulation and experiment, the high thermal conductivity, large convective surface area and rapid cooling capability of the optimized cellular structure are verified.

A new efficient parametric level set method based on radial basis function-finite difference for structural topology optimization

To overcome a significant challenge in traditional parameterized level set methods based on globally supported radial basis functions, we propose employing a local differentiation construction of radial basis functions using finite difference, a technique previously applied to solving partial differential equations but novel in the context of topology optimization. We present a novel parameterized level set method for structural topology optimization of compliance minimization and compliant mechanism, with the main aim of reducing computational costs associated with fully dense matrices when approximating systems with a large number of collocation points. The new scheme implemented with rectangular mesh elements and polygonal mesh generation accommodates both rectangular and complex design domains. Numerical results are provided to demonstrate the algorithm's effectiveness.

An adaptive phase-field method for structural topology optimization

In this work, we develop an adaptive algorithm for the efficient numerical solution of the minimum compliance problem in topology optimization. The algorithm employs the phase field approximation and continuous density field. The adaptive procedure is driven by two residual type a posteriori error estimators, one for the state variable and the other for the first-order optimality condition of the objective functional. The adaptive algorithm is provably convergent in the sense that the sequence of numerical approximations generated by the adaptive algorithm contains a subsequence convergent to a solution of the continuous first-order optimality system. We provide several numerical simulations to show the distinct features of the algorithm.

Designing piezoelectric stretcher through multiphysics topology for enhanced photodynamic therapy in cancer treatment

This study presents an advancement in Photodynamic Therapy (PDT) by introducing piezoelectric stretchers designed to enhance tissue surface characteristics. With a focus on mitigating the impact of irregular tissue surfaces on light distribution, we propose a structural topology optimization method to design a stretcher that utilizes the piezoelectric effect for precise tissue stretching. The aim is to achieve uniform laser irradiance across treated tissue, thereby maximizing therapy efficiency. Our approach involves the formulation of finite element models that consider the piezoelectric effect and the elastic response in a multiphysics framework. Mesh convergence tests were conducted to strike a balance between accuracy and computational efficiency in evaluating the designed piezoelectric stretcher. The investigation into the application of piezoelectric stretchers for enhancing laser irradiance on non-uniform tissue reveals significant improvements in surface uniformity with increasing electric potential. Notably, the disparity between regions of high laser focusing and defocusing decreases as the stretcher expands, achieved through the application of higher voltages. The observed enhancement from no expansion to full expansion is quantified at 31 %. The implementation of electrically driven piezoelectric tissue expansion results in a more uniform tissue surface, leading to an augmentation of laser irradiance. In the absence of expansion, distinct areas of laser focus and near-zero irradiance are noted. Conversely, an increased potential yields a predominantly even surface, with 100 % extension achieving commendable laser irradiance uniformity.

Metaheuristic aided structural topology optimization method for heat sink design with low electromagnetic interference

This study investigates the application of the Metaheuristic Aided Structural Topology Optimization (MASTO) method as a novel approach to address the multiphysics design challenge of creating a heat sink with both high heat conductivity and minimal Electromagnetic Interference (EMI). A distinctive 2D layout with elongated fins is examined for electromagnetic traits, highlighting resonance-related EMI concerns. MASTO proves to be a valuable tool for navigating the complex design space, yielding thoughtfully optimized solutions that harmonize efficient heat dissipation with effective EMI control. By merging simulation findings with practical observations, this study underscores the potential of the MASTO method in achieving effective designs for intricate multiphysics optimization problems. Specifically, the method's capacity to address the complex interplay of heat transfer with convection and the suppression of electromagnetic emissions is showcased. Moreover, the study demonstrates the feasibility of translating these solutions into tangible outcomes through manufacturing processes.

Reinforcement layout design for deep beams based on bi-objective topology optimization

Determining an effective and efficient reinforcement layout for reinforced concrete deep beams is still a challenging problem. This paper proposes a bi-objective evolutionary structural topology optimization method for the reinforcement layout design. Based on a discrete model for steel bars, the optimization aims to achieve a uniform stress distribution of steel rebars while promoting the peak rebar stress. A lexicographic method is used to solve the bi-objective optimization. Two numerical examples are presented to demonstrate the proposed algorithm's feasibility, stability and universal applicability. It is shown the reinforcement stresses in both tension and compression zones are more uniformly distributed and, on average, closer to the yield strength than those of the single-objective optimization. Compared with the design based on the conventional strut-and-tie method, the deep beams optimized by the proposed method use less reinforcement steel, provide a higher ultimate load capacity, and, more interestingly, fail in a ductile failure mode.