Topology Optimization Algorithm Research Articles

Proportional Topology Optimization algorithm for two-scale concurrent design of lattice structures

In this paper, the Proportional Topology Optimization (PTO) algorithm is extended for the two-scale concurrent topology optimization, in which both the structure and material cellular micro-structure are subject to design. PTO was originally developed on the concept that the amount of material being distributed to an element would be proportional to the contribution of that element in the objective function. Sensitivity analysis is not required. In a two-scale concurrent topology optimization problem, two sets of design variables are defined, one for macro-structure and one for micro-structure. Here, the objective function is reformulated such that the contribution of each micro-scale design variable can be determined, facilitating the employment of PTO. The macroscopic effective elastic tensor is evaluated by the energy-based homogenization method (EBHM), providing a link between micro-structure and macro-structure. Feasibility and efficiency of the proposed PTO approach are demonstrated via several benchmark examples of both two and three dimensional structures.

Isogeometric gradient‐free proportional topology optimization (IGA‐PTO) for compliance problem

AbstractThis study presents the incorporation of the effective gradient‐free proportional topology optimization algorithm into the framework of isogeometric analysis. The minimization of the compliance is considered, and the solid isotropic material with penalization method is used. The geometry, displacements, and density are all described by non‐uniform rational B‐spline (NURBS) basis functions. The density at an integration point is determined proportionally to its compliance. Then, the NURBS description of the density is constructed elementwise by deriving a relation between densities assigned to integration points and control points. The global NURBS description of the density for the whole domain is a blend of those from elements. Furthermore, a multiresolution scheme is presented by means of ‐refinement technique to enable the efficient performance for large‐scale problems. The accuracy and efficiency of the proposed approach are assessed through six numerical examples, including two‐ and three‐dimensional structures, with several rigorous tests and comparisons with the gradient‐based optimality criteria algorithm.

ON THE TREATMENT OF REQUIREMENTS IN DFAM: THREE INDUSTRIAL USE CASES

AbstractOptimization-driven design offers advantages over traditional experience-based mechanical design. As an example, topology optimization can be a powerful tool to generate body shapes for Additive Manufacturing (AM). This is helpful, when (1) load paths are non-intuitive due to complex design domains or boundary conditions, or (2) the design process is to be automated to minimize effort associated with experience-based design. However, practically relevant boundary conditions are often difficult to put into a formal mathematical language to, for example, either feed it into a topology optimization algorithm, or provide precise quantitative criteria for CAE-supported manual design. This paper presents a survey of three industry use cases and identifies three types of requirements: the first can be directly cast into parts of an optimization problem statement (∼ 40%), the second is considered indirectly by adapting the optimization problem without explicit reference to the requirement (∼ 20%), and the third is only assessed after the design is finalized (∼ 40%). For categories 2 and 3 we propose directions of improvement to support formulating complex design tasks as unambiguous design problems.

An integrated method of topological optimization and path design for 3D concrete printing

As an advanced construction technology, 3D concrete printing (3DCP) has the advantage of high manufacturing freedom for various freeform structures. The digital design of 3D printing using topology optimization contributes to obtaining the maximum performance potential from manufactured structures. However, most digitally designed structures obtained by topology optimization cannot be directly manufactured using 3DCP owing to various manufacturing constraints that have not yet been considered in the design process. This paper presents an integrated design method for 3DCP by incorporating extrusion-based manufacturing characteristics into the topology optimization algorithm. Topological optimization is based on the solid isotropic material with penalization (SIMP) method owing to its ease of adaptation to multiple constraints. During the optimization iteration, the manufacturing characteristics of nozzle size and path continuity are considered as the design requirements of 3D printed structures to achieve high-quality manufacturing by using intermittent interruption of topology optimization to modify the design variables. Meanwhile, the anisotropic behaviors of material constraints and the volume and Tsai-Wu criterion of design constraints are introduced to obtain the desired mechanical performance with lightweight designs. Moreover, the number of closed regions and overhang angle controls are incorporated to ensure the global path continuity and stable stacking of optimized 3D structures. A concrete arch structure is 3D printed to validate the proposed integrated method, and the removal of breakpoints and short paths and complete filling rate are demonstrated. The integrated method facilitates the engineering application of 3DCP in a high-efficiency and high-quality manner.

Implicitly Represented Architected Materials for Multi‐Scale Design and High‐Resolution Additive Manufacturing

AbstractBio‐inspired structured materials have achieved unprecedented progress in realizing exceptional, effective properties. However, a rational design paradigm that enables both tailoring complex 3D architectures and manufacturing the engineered hierarchical structured materials is still missing. To bridge this gap, this study presents a holistic design‐through‐printing framework with implicitly represents cellular materials for high‐resolution structured materials design and manufacturing. Attributed to the parameterized implicit function‐based representation (FRep), the material's microstructures can be effectively controlled to tune the material properties (e.g., isotropic, orthotropic, and anisotropic) while enabling functional gradation in the multi‐scale hierarchical design. Given prescribed material properties in different applications, the proposed framework finds the optimal layout of microstructures with an adaptive cluster‐based topology optimization algorithm. The geometry frustration problem brought by the mixture of distinct microstructures is simultaneously addressed with a spatial gradation scheme in the optimization loop. Lastly, the FRep‐based architected material enables efficient geometry processing (e.g., slicing) for modern AM processes, thus facilitating the manufacturing of high‐resolution delicate designed materials. The proposed framework is scalable and adaptable to accomplish a broad spectrum of design demands in various applications.

Real-Time structure topology optimization using CNN driven Moving Morphable component method

Classical optimization methods require finite element analysis in iterations, which increase the computing time and decrease the algorithmic efficiency. The deep learning model can potentially realize real-time topology optimization design, but it normally requires large training set. This paper presents a real-time topology optimization algorithm based on the Moving Morphable Component (MMC) method using a Convolutional Neural Network (CNN). The optimization algorithm uses a new data pre-processing method, which can preserve the numerical characteristics and smoothness of the structure boundary, hence it can help CNN to capture data features with a limited sample set. The topology optimization boundary information of the optimized result is used as the sample set label to avoid the components dislocation phenomenon. The new algorithm effectiveness has been verified with several examples. The trained model can significantly improve the optimization efficiency of the MMC method and offer accurate results with a clear structure boundary.

Topology optimized design and validation of sandwich structures with pure-lattice/solid-lattice infill by additive manufacturing

Compared to standard structures with pure solid members, sandwich structures behave mechanical advantages in terms of strength-to-weight, stiffness-to-weight, energy absorption capabilities, yet lightweight potentials. Sandwich structures can be driven by both exterior layout and infill configuration design to improve structural performance while reduce the weight. In this paper, sandwich structures with pure-lattice / solid-lattice infill by additive manufacturing is systematically investigated in combination with topology optimized design and validation. The equivalent material properties of infill BCC and F2BCC lattices are determined though finite element simulation. The newly developed sandwich structural topology optimization algorithm based on two-step density filtering is employed to obtain the conceptual designs with pure or hybrid infill. The topology optimized structures are fabricated by additive manufacturing, which are validated through three-point bending experiments and numerical simulations.

A continuous field adaptive mesh refinement algorithm for isogeometric topology optimization using PHT-Splines

This study proposes a continuous density-field based isogeometric topology optimization (ITO) using Polynomial splines over Hierarchical T-meshes (PHT-Splines). Taking the benefit of isogeometric methods, the design density values for the mesh are defined using spline basis functions as a continuous density function (CDF) through the control points. The material density at the control points will then appear as a facade over the domain, which is further employed to generate a very smooth topology and also to propose a marking criterion for an adaptive mesh refinement (AMR) strategy during the optimization process. During this adaptive meshing, the isogeometric domain mesh is refined during each adaptive step, properly tracking the density variation over the elements and sharpening the boundaries of the optimized topologies. By utilizing the rationale of the Geometry Independent Field approximaTion (GIFT) framework, any complex multi-patch geometry constructed in an industry-standard CAD package using Non-Uniform Rational B-Splines (NURBS) may be imported and discretized using PHT-Splines, including higher dimensions. This helps to maintain the geometrical accuracy through an initial coarse mesh and computational accuracy of the optimization iterations through the local refinement feature of the PHT-Splines. An adaptive first-neighbourhood smoothening algorithm based on the Shepard function is also proposed to obtain manufacturable topologies and to circumvent post-processing stages. The proposed method was observed to provide remarkably smooth topologies with an initial coarse mesh, thereby obtaining a computationally efficient domain to be solved. Compared to existing element density based methods, the proposed method demonstrates a substantial minimization in Degree’s-of-Freedom (DoF) requirement to arrive at clear and realistic solutions. Also, when compared to globally refined solutions, a 50%–90% reduction in DoF is achieved using the adaptive refinement strategy.

Topology optimization for mass transfer enhancement in open thermochemical energy storage reactors

The mass transfer enhancement in open system thermochemical energy storage is achieved in this work through the optimal design of flow channel geometries. Such flow channel geometries aim to maximize how gas reactants are distributed to the reactive sites and are derived from the topology optimization algorithm. Two reactor configurations are analyzed, namely sieve reactors and cylindrical reactors, and the performance of the generated designs are compared with literature benchmarks. Tentacular flow channel geometries emerged, with the flow channels elongating in the reactive bed without directly connecting the inlet and outlet interfaces. In the instance of a fixed time, a +757.8 % increase in the amount of discharged energy is obtained compared to literature solutions. Besides, the optimal geometrical features differ depending on the targeted performance metric. In particular, thinner channels are found to be favourable to increasing the amount of discharged exergy compared to discharged energy. Overall, the emerging design trends define new enhancement pathways for the performance improvement of open system thermochemical energy storage reactors and significantly contribute to the technology advancement.

Experimental study of topology optimized, additively manufactured microchannel heat sinks designed using a homogenization approach

Topology optimization generates complex geometry heat sink designs having intricate features well-suited for fabrication by additive manufacturing. In particular, a homogenization approach to topology optimization creates microchannel heat sink designs wherein the material porosity distribution corresponds to microstructures of varying dimensions, thereby eliminating the need to penalize the porosities to achieve binarized solid/liquid designs. This approach is inherently able to take into consideration the capabilities and limitations of available additive manufacturing processes as the types of microstructures can be user-defined. The current study is the first to fabricate and experimentally test microchannel heat sink designs that are topology optimized using the homogenization approach. To this end, a multi-objective optimization is performed to generate a series of Pareto optimal designs that minimize pressure drop and thermal resistance. The effect of the grid resolution is investigated. The resulting topology optimized designs are found to have different geometries and performances with different grid cell sizes because this impacts the physical dimensions of the microstructures. A series of pin fin arrays with different grid cell sizes and fin thicknesses are fabricated using Direct Metal Laser Sintering of AlSi10Mg. The additively manufactured surfaces have high roughness which creates connections between pin fins with small gap sizes and creates tortuous flow paths. The smallest pin fin that consistently survived the fabrication process is ∼0.25 mm thick and hence series of topology optimized microchannel heat sinks with a 0.5 mm grid cell size are additively manufactured. The pressure drop and thermal resistance of the fabricated heat sinks are experimentally characterized, and the measured results lie on the Pareto optimality curve predicted by the topology optimization algorithm. This work demonstrates that the homogenization approach to topology optimization generates high-performance microchannel heat sink designs that can be achieved using available additive manufacturing processes.

Development of a prototype 6 degree of freedom robot arm

The study presents a design alternative, simulates the operation, and analyzes the new structure of the 6 DOF robot arm. The proposed robot model is based on reference shapes from AR3 robot arm, with modifications to details and structures to accommodate the actual and economic circumstances in Vietnam. Solidwork software was first utilized for the arm structure's design, strength testing, and optimization. The material is chosen with the goal of reducing production cost and ensuring the robot's operation properly. The study concludes by applying the topology optimization algorithm to a machine component to determine the optimal structure of the robot arm. To validating the design results, the prototype is manufacturers using CNC machine. The experimental results show the robot arm basic functions effectively. This research could be used as references for designing and manufacturing a 6 DOF robot arm with relative robot's structure.

Optimization of the offshore wind power grid-connected structure based on an improved genetic algorithm

Large-scale offshore wind power generation has become one of the research hotspots in the development of new energy in the world. However, the planning of far-reaching offshore wind power is faced with many technical difficulties, such as the need to consider the optimization of line transmission capacity caused by the truncation effect in combination with the wind power output probability, and solve the problem that traditional algorithms cannot solve the dynamic programming problem, and the greedy algorithm for solving the dynamic programming problem cannot solve the global optimal solution. Therefore, in order to solve the above problems, based on the full life cycle (FLC) investment calculation of the collecting and transmission system, the topology optimization model of the offshore wind power system is established. In addition, in order to solve the grid-connection problem of offshore wind farms, an improved topology optimization algorithm based on greedy idea is proposed. The optimization results show that the critical values of economic transmission distance of HVAC, FFTS and HVDC are usually 50 km and 170 km respectively. Finally, the collection scheme of the wind farm cluster including three far-reaching offshore wind farms are analyzed, and the results show that the total cost of the optimized point-to-point scheme is reduced by 5.6% and 10.2% respectively compared with the star topology and the circular collection topology, with significant economic benefits.

A shape optimization algorithm based on directional derivatives for three‐dimensional contact problems

AbstractThis work deals with shape optimization for contact mechanics. More specifically, the linear elasticity model is considered under the small deformations hypothesis, and the elastic body is assumed to be in contact (sliding or with Tresca friction) with a rigid foundation. The mathematical formulations studied are two regularized versions of the original variational inequality: the penalty formulation and the augmented Lagrangian formulation. In order to get the shape derivatives associated to those two non‐differentiable formulations, we follow an approach based on directional derivatives introduced in previous works. This allows us to develop a gradient‐based topology optimization algorithm, built on these derivatives and a level‐set representation of shapes. The algorithm also benefits from a mesh‐cutting technique, which gives an explicit representation of the shape at each iteration, and enables us to apply the boundary conditions strongly on the contact zone. The different steps of the method are detailed. Then, to validate the approach, some numerical results on two‐dimensional and three‐dimensional benchmarks are presented.

Development of a novel fast tool servo using topology optimization

Micro/nanostructured surfaces have wide applications in optics, electronics, and aerospace. However, the current fast tool servo (FTS) cannot satisfy the large demand for micro/nanostructured surfaces in the industry, because their low working frequency influences the machining efficiency. To solve this problem, this paper develops a novel FTS with the high working frequency. To improve the working frequency, a topology optimization algorithm is proposed to design its mechanical structure. Then, the numerical models of the FTS, including the input stiffness, amplification ratio, natural frequency, and maximum stress, are established to analyze its specifications. Performance tests show that the stroke and maximal working frequency of the developed FTS are 15 μm and 1250 Hz, demonstrating superior performance. Besides, to improve motion accuracy, a closed-loop control system is designed based on the proportional-integral controller and feed-forward compensation methods. Experimental results show that errors of motion trajectories in three cases are lower than ± 50 nm, demonstrating the ultrahigh motion accuracy of the developed FTS. Therefore, this research develops a new FTS, which not only has a high working frequency but also has an ultrahigh motion accuracy.

Topology optimization for additive manufacturing with strength constraints considering anisotropy

Abstract Combining topology optimization and additive manufacturing (AM) is a promising approach to breaking through the limitations of conventional design and developing innovative structures with high performance. However, the unique manufacturing constraints in AM should be considered when developing the topology optimization algorithms for AM. Material anisotropy is one of the common characteristics of AM materials due to the layer-by-layer manufacturing techniques. This work proposes a topology optimization approach for AM with strength constraints considering anisotropy. The Hoffman failure criterion is adopted to represent the anisotropic strength behaviors of AM materials. Based on the Hoffman failure criteria and the p-norm measure aggregation function, a global strength constraint formulation is established. Under the framework of solid isotropic material with penalization, we develop a topology optimization methodology to minimize the structural weight or volume fraction subject to structural stiffness and strength constraints. Several two-dimensional (2D) or 3D numerical test cases are performed to validate the effectiveness and performance of the developed method. The results indicated that the proposed method could make full use of material properties by considering anisotropic strength. Besides, the topological optimization considering strength anisotropy could be combined with build direction optimization to further reduce the structural weight.

A multi-material Proportional Topology Optimization approach for compliant mechanism problems

This paper presents an extension for the Proportional Topology Optimization (PTO) algorithm to solve multi-material topology optimization of compliant mechanism problems. The objective function is firstly transformed from maximization of output displacement into maximization of mutual strain energy. In this setting, the contribution of each element to the objective function can be evaluated, facilitating the application of the PTO algorithm. The objective function is further multiplied by minus one so that a familiar form of minimization can be obtained. When multiple materials are involved, the problem is decomposed into several two-phase sub-problems based on the alternating active phase algorithm (AAPA). Using the PTO algorithm, each material is distributed into elements proportionally to the contribution of that material in the mutual strain energy. Due to the fact that the mutual strain energy can be either negative or positive, a modification has been made in the PTO inner loop to update the pseudo-density (the design variables). The applicability and feasibility of the developed approach are illustrated through several numerical examples.

Experimental characterisation and data-driven modelling of unsteady wall pressure fields induced by a supersonic jet over a tangential flat plate

This work deals with the investigation and modelling of wall pressure fluctuations induced by a supersonic jet over a tangential flat plate. The analysis is performed at several nozzle pressure ratios around the nozzle design Mach number, including slightly over-expanded and under-expanded conditions, and for different radial positions of the rigid plate. Pitot measurements and flow visualizations through the background oriented schlieren technique provided a general overview of the aerodynamic interactions between the jet flow and the plate at the different regimes and configurations. Wall pressure fluctuations were measured using a couple of piezoelectric pressure transducers flush mounted over the plate surface. The spectral analysis has been carried out to clarify the effect of the plate position on the single and multivariate wall pressure statistics, including the screech tone amplitude. The experimental dataset is used to assess and validate a surrogate model based on artificial neural networks. Sound pressure levels and coherence functions are modelled by means of a single fully connected network, built on the basis of a recently implemented fully deterministic topology optimization algorithm. The metamodel uncertainty is also quantified using the spatial correlation function. It is shown that the flow behaviour as well as the screech and broadband noise signatures are significantly influenced by the presence of the plate, and the effects on spectral quantities are correctly reproduced by the proposed data-driven model that provides predictions in agreement with the available data.

Topological optimization of flow-shifting microchannel heat sinks

Efficient thermal management is required for electronic devices that generate multiple different spatially nonuniform thermal workloads during operation. Conventional heat sinks route coolant to all potential heat-generating regions of an electronic component which may result in unnecessarily broad dispersion of the coolant to regions that are sometimes inactive. To fully utilize flow for multiple potential thermal workloads, a “flow-shifting” design approach is proposed. A flow-shifting heat sink has multiple inlets, where the flow path from each inlet is optimized for cooling of a specific workload or heat map. Only the inlet corresponding to the active operating workload is open at a given time, while the rest of the inlets are kept closed until the operating workload changes, allowing a majority of the flow to be properly utilized for cooling the active heat map. This has the potential to allow many different optimal heat sinks to be simultaneously encoded into a single structure but brings forth a complex design problem to optimize the internal fluid flow pathways. A multi-objective topology optimization algorithm is implemented in this work for flow-shifting heat sink design generation. Microchannel heat sink designs are generated for a demonstration case involving two workloads. Designs optimized for flow-shifting between two inlets are compared to a benchmark that is optimized with only a single inlet. Pareto optimality curves, as well as the associated heat sink designs, are created that weigh between the thermal resistances of the two workloads. The flow-shifting designs are predicted to have lower thermal resistance under both workloads compared with every benchmark heat sink design generated along the Pareto optimality curve. Investigation of two designs selected from the Pareto curve showed that the flow-shifting heat sink achieved 10.7% and 6.8% lower thermal resistance at the two workloads relative to the benchmark. The flow-shifting approach is superior as it utilizes more flow rate for cooling the active heated region. The flow-shifting approach thereby allows for fixed heat sink structures that can be topologically optimized for many different possible heat maps and actively respond to changes in workload.

Process-Specific Topology Optimization Method Based on Laser-Based Additive Manufacturing of AlSi10Mg Components: Material Characterization and Evaluation

In the laser powder bed fusion process (PBF-LB), components are built up incrementally by locally melting metal powder with a laser beam. This process leads to inhomogeneous material properties of the manufactured components. By integrating these specific material properties into a topology optimization algorithm, product developers can be supported in the early phases of the product development process, such as design finding. For this purpose, a topology optimization method was developed, which takes the inhomogeneous material properties of components fabricated in the PBF-LB process into account. The complex pore architecture in PBF-LB components was studied with micro-computed tomography (µCT). Thereby, three characteristic regions of different porosity were identified and analyzed. The effective stiffness in each of these regions was determined by means of resonant ultrasonic spectroscopy (RUS) as well as finite element analysis. Afterward, the effective stiffness is iteratively considered in the developed topology optimization method. The resulting design proposals of two optimization cases were analyzed and compared to design proposals derived from a standard topology optimization. To evaluate the developed topology optimization method, the derived design proposals were additionally manufactured in the PBF-LB process, and the characteristic pore architecture was analyzed by means of µCT.

Topology optimization design of antennas with complex radiation characteristics

AbstractAntennas with complex radiation characteristics can enhance the adaptability of radiofrequency systems in complex electromagnetic environments. However, The realization of complex targets is extremely challenging for conventional antenna design methods. It is difficult to find a suitable initial topology of the antenna with complex radiation characteristics. Therefore, in this paper, topology optimization is used to explore the initial structure with complex radiation properties. A two‐dimensional lossy thin layer model based on the transitional boundary condition is constructed, and target field functions for complex radiation are proposed. To verify the effectiveness of the algorithm, a high gain antenna with 10.2 dBi is realized, which has the highest aperture efficiency compared with the literature in similar directions. Then, for more complex targets, the radiation patterns of arbitrary direction null, arbitrary direction beam, and equal‐amplitude dual beam are realized, respectively. The topology optimization algorithm provides a new approach for the design of complex multitarget antennas.