Topology Optimization Scheme Research Articles

Topology optimization of controllable porous microstructure with maximum thermal conductivity

Porous structures are lightweight and thus possess tailorable thermophysical properties through topological design. A multi-constraint topology optimization scheme is developed for designing 2D periodic lattice material with controllable porosity and optimal thermal conductivity. The porosity, pore size and specific surface area are modulated by imposing local density constraints, and thus the structure-determined thermal conductivity can be systematically investigated. The isotropic porous structures after optimization show effective thermal conductivity close to the Hashin-Shtrikman theoretical bound. The specific surface area of base cell is enlarged with imposing local density constraint. In addition, microstructure with anisotropic thermal conductivity can be also obtained. The samples of lattice structure are additively manufactured via selective laser melting, and the thermal conductivities are experimentally validated with deviation within 10 %. The proposed porous structures with targeted porosity have potential application in skeleton embedded with phase change materials.

A level set reliability-based topology optimization (LS-RBTO) method considering sensitivity mapping and multi-source interval uncertainties

With the diversification of engineering structure performance requirements and the continuous development of structural design refinement, structural design methods are facing more and more factors to be considered. It is necessary to develop advanced design technology. In this paper, a sensitivity mapping technique is proposed to improve the effect of topology optimization based on a gradient optimization algorithm. The applicability of this technology is analyzed. In addition, considering the influence of multi-source uncertainties in the whole life cycle of the structure, a reliability-based topology optimization strategy based on the level set method is proposed. The sensitivity of displacement constraint and reliability constraint with pseudo time is derived. Numerical examples and Monte Carlo verification results fully illustrate the applicability, effectiveness, and efficiency of the proposed method. This method has been successfully applied to the topology optimization design of the rocket skid structure.

Topological Design Optimization Approach for Winding Oil Flow Paths in Oil-Natural Air-Natural Transformers Based on a Fluidic-Thermal Coupled Model

Power transformers are a critical component in transmission and distribution systems. To limit the temperature rise to extend the life-cycle while operating with enough reliability and controllability of a transformer, the design of the cooling system has attracted extensive research attention. In this paper, a topology optimization (TO) methodology is presented for designing the coolant flow paths in a prototype oil-natural air-natural (ONAN) power transformer to maximize the winding heat dissipation capacity without any compromise on the flow resistance. First, the thermal and fluid flow characteristics in both the winding and the radiator of the prototype transformer are numerically investigated through a fluidic-thermal coupled field approach. The preliminary cooling effectiveness of the oil circulation system is initialized. Second, a material-density-based TO scheme is employed to realize the optimal design of the oil baffle structures. In the TO optimization, artificial Darcy frictional forces are applied to the solidified cells to block their internal flows in the fluidic calculations, while the thermal conduction coefficients in those cells are enhanced to separate the baffles from the flowing oil in thermal analyses. Finally, the fluidic and thermal coupled fields of the prototype transformer winding region with structurally optimized oil baffles are numerically investigated to validate the TO effectiveness.

Research on the spatial structure of environmental art design based on topology optimization and morphology optimization

Abstract In this paper, firstly, a mathematical model of spatial structure topology optimization is constructed, and sensitivity analysis, approximate model fitting and optimization finding strategy for topology optimization in environmental art design are carried out. Secondly, morphological optimization is carried out from the morphological model of spatial structure and the urban thermal environment through urban environmental art design and morphological optimization. Finally, the optimization of structural morphology is explored under static multiple working conditions and single-objective optimization, considering the dynamic frequency of the structure. The results show that as the optimization proceeds, the total strain energy, axial strain energy and bending strain energy of the space structure increase to 0.45, 0.52 and 0.5 of the initial structure, respectively. At the 9th iteration of optimization, the performance is at its peak. The load-carrying capacity is 1.59 times that of the 35th step and 1.5 times that of the initial structure. The research results of this paper can provide references and guidance for structural design and optimization in the fields of environmental art design and urban planning.

Exploring the influence of initial design domain dependencies in concurrent multiscale topology optimization for heat conductivity maximization

Advancements in additive manufacturing have led to the widespread adoption of topology and shape optimization in the design process across various industrial applications. Topology optimization has emerged as a promising approach for creating ultra-lightweight structures with exceptional functionality. By designing porous structures and addressing the layout of pores, concurrent multiscale topology optimization schemes offer a means to achieve such outcomes. This paper focuses on the development of a multiscale topology optimization tool and presents a numerical investigation of the initial design domain's impact on maximizing heat conductivity through concurrent multiscale topology optimization. The study highlights the significant influence of the initial design domain in the microscale on the final microscale design. Moreover, modifying the initial micro design domain has a direct impact on the macro design domain. The findings underscore the importance of considering the initial design domain when aiming to maximize heat conductivity through concurrent multiscale topology optimization. To facilitate the replication of the results presented in this paper, comprehensive details regarding parameter settings and implementation aspects are provided.

A BEM broadband topology optimization strategy based on Taylor expansion and SOAR method—Application to 2D acoustic scattering problems

AbstractIn this article, an innovative method is proposed for broadband topology optimization of sound‐absorbing materials adhering to the surface of a sound barrier structure. Helmholtz equation for the acoustic problems is solved using the boundary element method, while sensitivities of the objective function with respect to a large number of design variables are calculated via a sensitivity analysis method originated from the adjoint variable method (AVM), and the optimal solution is obtained by the method of moving asymptotes (MMA). Since the traditional single‐frequency topology optimization is frequency dependent, that is, the optimal solution at a certain frequency may not be optimal at other frequencies, broadband topology optimization of sound‐absorbing materials is conducted in this work. To address the problem of tremendous computational cost due to repetitive calculations at each discrete frequency point during broadband optimization, Taylor expansion of the Hankel function is performed to decouple the frequency dependent and independent terms in the BEM equations. For large‐scale problems, a reduced‐order model that retains the essential structures and key properties of the original model is built using the second‐order Arnoldi (SOAR) method. The accuracy and feasibility of the proposed algorithms are finally validated via some two‐dimensional numerical examples.

Statistical topology optimization scheme for structural damage identification

Statistical topology optimization (TO) scheme, which statistically records and analyzes local optima at random frequencies of the excitation force, is developed for material damage and open crack. To identify the alternations of stiffness, mass, and strength due to the damages, the structural responses of healthy and suspicious systems can be compared and optimized by TO for fault identification. Owing to the local optima problem in TO, slight modifications in responses caused by relatively minimal damage, and inadequate comparison of insufficient vibration information, the application of TO to a damage identification problem is often complicated. To overcome this complication, this study establishes a new approach that records local optima (layouts) and performs a statistical process (clustering and averaging of layouts). To illustrate the concept of the present scheme, several examples with material damage and open crack are solved.

Non-probabilistic reliability-based topology optimization (NRBTO) scheme for continuum structures based on the strength constraint parameterized level set method and interval mathematics

In this paper, a study on non-probabilistic reliability-based topology optimization (NRBTO) scheme for continuum structures based on the parameterized level set method (PLSM) is conducted. The P-norm is used to replace the local stress constraint with a single comprehensive stress constraint that approximates the maximum stress to optimize the structure model with minimum volume. In the interval-set model, the stress constraint is transformed into the non-probabilistic reliability-based scheme and the reliability is evaluated by the optimization feature distance (OFD). In the NRBTO scheme, the unknown-but-bounded (UBB) uncertainties of the material and external load of the optimized structure are considered. By interpolating the level set function (LSF) with the multiquadric (MQ) splines, the partial differential equation (PDE) is transformed into an ordinary differential equation (ODE). In addition, the interval parameter vertex method is employed to obtain the stress constraint interval, and the shape derivative and adjoint vector methods are used to obtain the evolution velocity field of LSF. The optimality criterion (OC) method is used to solve the optimization problem. Finally, three examples are given, and the optimization model of stiffness constraint is introduced, which not only verifies the applicability of the topology optimization scheme based on non-probabilistic reliability but also compares the difference between the topology optimization with strength constraint and the topology optimization with stiffness constraint.

Multigrid reduced-order topology optimization scheme for structures subjected to stationary random excitations

Multigrid reduced-order topology optimization scheme for structures subjected to stationary random excitations

A versatile Topology Optimization Strategy for Devising Low‐Dimensional Architectures with Boosted Photocatalytic Activity

AbstractConstructing low‐dimensional heterojunctions via hybridizing 0D, 1D, and 2D building blocks is an effective means to devise higher‐order architectures with excellent photocatalytic reaction activities. Developing a versatile topology optimization strategy paves the way for guiding the rational structural design of a wide range of heterostructures. Herein, taking the ZnO‐CdS hybrids with mixed topology structures (including 0D‐1D, 0D‐0D, and 1D‐1D composites) as a model system, the work unveils a ubiquitous, yet unrecognized, topology dependence of photocatalytic performances and the 0D‐1D topology combination coupled with an annealing treatment gives rise to an optimal photocatalytic redox activity, far exceeding those of 0D‐0D and 1D‐1D counterparts. The 0D‐1D topology integrates the structural merits of both constituent units, where the 1D unit acts as a rigid matrix to allow the uniform dispersity of 0D units for exposing abundant active sites, and a mobile 0D unit contributes to the interfacial reconstruction for forming charge‐migration‐expediated heterointerfaces via thermal‐induced grain rotations. Such thermal‐annealing‐coupled topology optimization methodology shows applicability for a large spectrum of low‐dimensional heterojunctions, offering a prototype for the precise structural design of low‐dimensional heterojunctions with enhanced catalytic performance.

Multi-material topology optimization for maximizing structural stability under thermo-mechanical loading

Mechanical structures are often simultaneously subjected to thermal and mechanical loading, both of which can lead to buckling failure. Developing efficient structural forms with better capacity for stability is important to keep structures safe. This study aims to optimize structural buckling capacity by using a density-based topology optimization scheme. Instead of treating the mechanical and thermal loadings as a single coupled part in the linearized buckling analysis, the effects of mechanical and thermal loadings are decoupled, which allows to separately analyze and optimize buckling aspects induced by mechanical or thermal loading. Two optimization models based on the decoupled analysis models are developed to respectively maximize the critical load factor of buckling induced by mechanical loading under a specified thermal loading and buckling induced by thermal loading under a specified mechanical loading. Further, based on a three-phase material model, a multi-material topology optimization scheme is employed to optimize the buckling capacity of active structures made of structural and actuating materials and prestressed structures containing prestressed components. The actuation effects are mimicked by the thermal loading of active material. The sensitivities of the objective functions and constraints are derived through the adjoint technique, and the method of moving asymptotes (MMA) is employed to solve the topology optimization problems. Numerical examples are adopted to verify the effectiveness of the proposed approach.

A level set driven concurrent reliability-based topology optimization (LS-CRBTO) strategy considering hybrid uncertainty inputs and damage defects updating

With the diversification of engineering structure performance requirements and the continuous development of structural design refinement, it puts forward higher requirements for lightweight design of structures in terms of concurrent design and reliability design. It is necessary to develop advanced design technology. This paper focuses on the influence of multi-source hybrid uncertainties and defect damage in the design process and proposes a concurrent reliability-based topology optimization design method. Based on the collocation method, the propagation analysis of hybrid uncertainties is realized. A performance reduction method considering defect damage is proposed. Furthermore, the parameter iteration strategy of the optimization criterion method is improved. Based on the sensitivity analysis of a series of parameters, the gradient optimization algorithm is used to solve the optimization model. Finally, three numerical examples are given to illustrate the effectiveness and necessity of the proposed method.

Multiscale topology optimization of biodegradable metal matrix composite structures for additive manufacturing

Recent advances in biomedical engineering have promoted the development of innovative metal implants that have integrated mechanical and biodegradable properties. Most of the existing implant designs were created by using a trial-and-error approach, which depends on the designer's experience. Alternatively, inverse design approaches, such as topology optimization, have evolved into an efficient design solution to optimize the structural and material layout within a given design domain. Here we introduce a novel topology optimization scheme to support the microstructural design of biodegradable metal matrix composite structures (BM−MCS). The effect of material degradation on the mechanical performance of the structure is considered by integrating a degradation simulation algorithm into the structural finite element (FE) analysis. The objective function is to minimize the structural compliance at macroscale in a certain number of time steps to realize sufficient structural integrity in the initial bone healing stage, and the different stiffness reduction properties can be adjusted by changing the volume ratio of the two base constitutive biodegradable materials. The sensitivity of the above objective function concerning design variables was derived with considering the time-dependent degradation of the biodegradable material. Several numerical design examples were presented and benchmarked with classical designs. Finally, several prototypes were fabricated by integrating additive manufacturing with casting technology. Collectively, this demonstrates the feasibility and effectiveness of the proposed inverse design method for additive manufacturing.

A feature-driven robust topology optimization strategy considering movable non-design domain and complex uncertainty

With the diversification of engineering structure performance requirements and the continuous development of refinement of processing and manufacturing, structural design is faced with more and more factors to be considered. By quantifying the important features of non-design domain location and parameter uncertainty, a feature-driven robust topology optimization strategy considering movable non-design domain and complex uncertainty is proposed. Firstly, the influence of non-design domain on structural topology is quantified by a shape description function. The slight boundary discontinuity caused by non-design domain is further solved. In addition, the mathematical properties of structural response about uncertainty are analyzed, and vertex method and subinterval dimension-wise method are adopted to quantify the influence of uncertainties. Finally, the sensitivity of the robust optimization model is derived based on the shape derivative principle, which provides the basis for the implementation of gradient based optimization algorithm. Three examples illustrate the effectiveness, necessity and influence of important parameters of the topology optimization method considering movable non-design domain and complex uncertainty from different aspects.

Topology Optimization Design of Scramjet Structures With Forced Convective Heat Transfer on Unstructured Meshes

Abstract A topology optimization strategy with coupled fluid–solid interaction was proposed to maximize the cooling efficiency of a kind of structure applied for scramjets. The Galerkin finite element method (FEM) is used to solve the forced convective heat transfer, and the rational approximation of material properties (RAMP) method combined with the globally convergent method of moving asymptotes (GCMMA) method are used to solve the topological optimization models with different boundary conditions and objective functions. Examples are provided to demonstrate the validity and effectiveness of the optimization strategy. The optimal flow passages of scramjet structures are achieved successfully. Compared with a baseline structure with rectangular straight passages, the optimized flow passages significantly reduce the averaged bulk temperature and pressure loss, and the bulk temperature is more uniform to avoid the occurrence of concentrated high-temperature areas. With the Reynolds number changing from 1000 to 1750, the heat transfer performance of the three-dimensional topology-optimized structure increases by 16.79% to 20.82%.

Design of a Stiffened Space Membrane Structure Using Explicit Topology Optimization

Abstract In this work, a hybrid topology optimization scheme based on the moving morphable component (MMC) method is presented for the design of stiffened membrane structure. The stiffened membrane structure is composed of a base membrane, reinforcing stiffeners, and functional cells. For an accurate and effective simulation of the structure, a hybrid structure model with multiple element types is constructed. In this study, MMC components used as the basic elements for the topology description will include several different types: bar elements for the stiffeners and continuum elements for the base membrane and functional cells. The base membrane is modeled using bi-modulus material. With this approach, the distribution of element types in different parts can be changed as the components are moved around during the optimization process. Some numerical examples are presented to validate the effectiveness of the proposed scheme.

Topology optimization of heat source distribution for volume-to-point heat conduction

Optimizing the heat source distribution is an effective strategy to enhance the heat dissipation in electronic devices. In this paper, a topology optimization (TO) scheme with a penalty factor between 0 and 1 is developed to solve the volume-to-point heat source distribution. The topology-optimized heat source always lies around the heat sink with continuous design, and the isotherms show semicircular arcs with the semicircle center located at the heat sink. Compared with other optimization methods, the current TO method obtains better designs approximate to the theoretical optimal solution with higher cooling performance and lower computational cost. Moreover, an equivalent distance function reflecting the distance between the heat source and the heat sink is introduced to evaluate the performance of different heat source distributions. Topology-optimized designs and mathematical analyses show that reducing the equivalent distance between the heat source and the heat sink is an effective way to enhance heat transport. This work extends the application of the TO method and deepens the understanding of the optimization of heat source distribution.

Development of a joint distance constraint for optimized topology and optimized connection for multiple components

This article develops a new topology optimization scheme for finding optimized joints for multiple components. As the optimized topologies for each component are determined by several structural conditions, simultaneously optimizing the joint location as well as the optimized topology is regarded as one of the difficult problems. Because joint connections are normally defined at nodes, inevitably the optimized locations of joints are mesh dependent. To contribute to these research topics, this research presents a new method for controlling the optimized location of joints. In particular, a joint dispersal constraint is developed in order to control the number and optimized locations of optimized joints. With the developed scheme, it is possible to find optimized joints as well as optimized topology while maintaining a minimum distance between all joints. To show the effectiveness of the present optimization scheme, several numerical optimization problems are solved.

Solid isotropic material with thickness penalization – A 2.5D method for structural topology optimization

SIMP is the most common topology optimization scheme to minimize the material utilization of a structural component using element densities as a design variable. This paper presents a new methodology, SIMTP, Solid Isotropic Material with Thickness Penalization, introducing a nodal thickness variable to the plane stress element. SIMTP uses a 2.5D element, and it is developed considering the varying thickness as a 3D problem and planar transformation as a 2D problem. The developed 2.5D element is used for projecting the 2D strain energy onto a 3D space. Classical optimization problems like Cantilever, MBB, and L-, beams are solved using 2.5D SIMTP, and results are compared with SIMP. The implementation is simple, directly representing the thickness, and nodal design variables enhance the resolution. Checkerboarding or other topology-related issues are not noticed during the process. Also, 2.5D SIMTP can yield desired results with fewer elements, thereby reducing the computational efforts. Besides, a 211-line MATLAB implementation of 2.5D SIMTP with examples is provided at the end of this paper.

A topology optimization of open acoustic waveguides based on a scattering matrix method

This study presents a topology optimization scheme for realizing a bound state in the continuum along an open acoustic waveguide comprising a periodic array of elastic materials. First, we formulate the periodic problem as a system of linear algebraic equations using a scattering matrix associated with a single unit structure of the waveguide. The scattering matrix is numerically constructed using the boundary element method. Subsequently, we employ the Sakurai–Sugiura method to determine resonant frequencies and the Floquet wavenumbers by solving a nonlinear eigenvalue problem for the linear system. We design the shape and topology of the unit elastic material such that the periodic structure has a real resonant wavenumber at a given frequency by minimizing the imaginary part of the resonant wavenumber. The proposed topology optimization scheme is based on a level-set method with a novel topological derivative. We demonstrate a numerical example of the proposed topology optimization and show that it realizes a bound state in the continuum through some numerical experiments.