Topology Optimization Results Research Articles

Design of Lattice Structures Using Local Relative Density Mapping Method

In order to solve the problem of substantial computational resources of lattice structure during optimization, a local relative density mapping (LRDM) method is proposed. The proposed method uses solid isotropic microstructures with penalization to optimize a model at the macroscopic scale. The local relative density information is obtained from the topology optimization result. The contour lines of an optimized model are extracted using a density contour approach, and the triangular mesh is generated using a mesh generator. A local mapping relationship between the elements’ relative density and the struts’ relative cross-sectional area is established to automatically determine the diameter of each individual strut in the lattice structures. The proposed LRDM method can be applied to local finite element meshes and local density elements, but it is also suitable for global ones. In addition, some cases are considered in order to test the effectiveness of the LRDM method. The results show that the solution time of the LRDM is lower than the RDM method by approximately 50%. The proposed method provides instructions for the design of more complex lattice structures.

Study on Topology Optimization Method of Particle Moving Based on Element-Free Galerkin Method

A novel topology optimization method is proposed based on particle moving, in which the topological optimization results can be obtained by moving particle instead of “soft delete” or “hard delete”. The relation between particle coordination and its density is built. The moving of particles can be controlled according to its density value, that is, with the particle density values change in the optimal iteration, the particle will be moved from a location to the other one in accordance with given step. The density gradient is derived. As the compliance, the particle density is chosen as the objective function and the design variables, respectively, the topology optimization model of particle moving based on EFGM is built by using the SIMP material model, and calculating flow chart is given. Combined OC method, the two topology optimization examples are achieved. The results obtained verify that the presented optimal method is feasible.

Development of Foot Structure for Humanoid Robot Using Topology Optimization

This paper addresses the development of a foot structure for 22-Degree of Freedom (DoF) humanoid robot. The goal of this research is to reduce the weight of the foot and enable the robot to walk steadily. The proposed foot structure is based on the consideration of cases where the ground reaction forces are set up in different situations. The optimal foot structure is a combination of all the topology optimization results. Additionally, a gait pattern is generated by an approximated optimization method based on Response Surface Model (RSM) and Improved Self-Adaptive Differential Evolution Algorithm (ISADE). The result is validated through dynamic simulation by a commercially available software called Adams (MSC software, USA) with the humanoid robot named KHR-3HV belonging to Kondo Kagaku company.

Multimaterial multijoint topology optimization

SummaryIn this paper, a methodology that solves multimaterial topology optimization problems while also optimizing the quantity and type of joints between dissimilar materials is proposed. Multimaterial topology optimization has become a popular design optimization technique since the enhanced design freedom typically leads to superior solutions; however, the conventional assumption that all elements are perfectly fused together as a single piece limits the usefulness of the approach since the mutual dependency between optimal multimaterial geometry and optimal joint design is not properly accounted for. The proposed methodology uses an effective decomposition approach to both determine the optimal topology of a structure using multiple materials and the optimal joint design using multiple joint types. By decomposing the problem into two smaller subproblems, gradient‐based optimization techniques can be used and large models that cannot be solved with nongradient approaches can be solved. Moreover, since the joining interfaces are interpreted directly from multimaterial topology optimization results, the shape of the joining interfaces and the quantity of joints connecting dissimilar materials do not need to be defined a priori. Three numerical examples, which demonstrate how the methodology optimizes the geometry of a multimaterial structure for both compliance and cost of joining, are presented.

A Novel Design Method for Nonuniform Lattice Structures Based on Topology Optimization

Lattice structures are broadly used in lightweight structure designs and multifunctional applications. Especially, with the unprecedented capabilities of additive manufacturing (AM) technologies and computational optimization methods, design of nonuniform lattice structures has recently attracted great research interests. To eliminate constraints of the common “ground structure approaches” (GSAs), a novel topology optimization-based method is proposed in this paper. Particularly, the structural wall thickness in the proposed design method was set as uniform for better manufacturability. As a solution to carry out the optimized material distribution for the lattice structure, geometrical size of each unit cell was set as design variable. The relative density model, which can be obtained from the solid isotropic microstructure with penalization (SIMP)-based topology optimization method, was mapped into a nonuniform lattice structure with different size cells. Finite element analysis (FEA)-based homogenization method was applied to obtain the mechanical properties of these different size gradient unit cells. With similar mechanical properties, elements with different “relative density” were translated into unit cells with different size. Consequently, the common topology optimization result can be mapped into a nonuniform lattice structure. This proposed method was computationally and experimentally validated by two different load-support design cases. Taking advantage of the changeable surface-to-volume ratio through manipulating the cell size, this method was also applied to design a heat sink with optimum heat dissipation efficiency. Most importantly, this design method provides a new perspective to design nonuniform lattice structures with enhanced functionality and manufacturability.

Topology and parametric optimization based lightweight design of a space reflective mirror

For large space telescopes, the design of lightweight primary mirrors with an acceptable level of optical performance is a challenge. A parametric optimization method based on topology optimization of the basic configuration of the mirror is proposed. A finite-element model of the mirror is generated with linear shell elements, and the optimal distribution of the material is obtained using the continuum topology optimization technique. The lightweight ribs are grouped according to the results of topology optimization results. The design of experiment method is used to pick out the key factors for parametric optimization. The RMS value of the surface shape error of the mirror and the total mass of the mirror are treated as the objective merit functions, and the first-order natural frequency of the mirror is taken as a constraint for parametric optimization. Results show that the local stiffness of the mirror is significantly affected by the thicknesses of the ribs at the corresponding positions. The optimum mirror design obtained using our optimization method is compared with the initial design, and the comparison shows superior optical performance for the optimized mirror.

Optimizing Model of the Power Collection System of Offshore Wind Farm Based on Improved Single Parent Genetic Algorithm

Based on the detailed analysis of the power collection system of offshore wind farm, establishing a mathematical model to evaluate its economy and reliability, and proposing a topology optimization mode of the power collection system of offshore wind farm based on improving single parent’ genetic algorithms. Example analysis shows that the proposed model can consider the optimization of economy and reliability in overall rapidly and at the same time get the topology optimization results. Compared with the traditional genetic algorithm, the rate of convergence is faster and better optimization results. which can provide the design of large-scale photovoltaic power station of power collection system topology with the reference.

A Realization Method for Transforming a Topology Optimization Design into Additive Manufacturing Structures

Topology optimization is a powerful design approach that is used to determine the optimal topology in order to obtain the desired functional performance. It has been widely used to improve structural performance in engineering fields such as in the aerospace and automobile industries. However, some gaps still exist between topology optimization and engineering application, which significantly hinder the application of topology optimization. One of these gaps is how to interpret topology results, especially those obtained using the density framework, into parametric computer-aided design (CAD) models that are ready for subsequent shape optimization and manufacturing. In this paper, a new method for interpreting topology optimization results into stereolithography (STL) models and parametric CAD models is proposed. First, we extract the skeleton of the topology optimization result in order to ensure shape preservation and use a filtering method to ensure characteristics preservation. After this process, the distribution of the nodes in the boundary of the topology optimization result is denser, which will benefit the subsequent curve fitting. Using the curvature and the derivative of curvature of the uniform B-spline curve, an adaptive B-spline fitting method is proposed in order to obtain a parametric CAD model with the fewest control points meeting the requirement of the fitting error. A case study is presented to provide a detailed description of the proposed method, and two more examples are shown to demonstrate the validity and versatility of the proposed method.

Metamodeling approach for concurrent optimization considering structural topology and its circumstances of mechanical component

Conventional topology optimization method only optimizes a single machine component structure while its circumstances are fixed. Concurrent optimization of topology and circumstances widens the effective range of topology optimization in mechanical design. We have developed a method for the concurrent optimization, which includes problem decomposition and metamodeling. However, the method requires further verification, especially, for cases where a relationship between circumstance variables and results of topology optimization becomes complex. In this research, we examine whether the method can be successfully applied to complex case if a metamodeling approach is switched. Case studies of three kinds of metamodeling techniques are performed. In the case studies, we test following metamodeling approaches: polynomial approximation, radial basis function(RBF) interpolation, polynomial approximation with spatial reduction. It shows that the proposed method can be applied even for complex cases by appropriate selection of metamodeling.

Structural analysis and topology optimisation of an aftercooler cover for weight reduction in off-highway engine application

It is endeavoured to gain design direction by use of computational topology optimisation methods on off-highway engines to improve fuel economy and costs to the service provider via weight reductions. Most published studies are focused on key functional components of an on-highway vehicle that are required for the engine or vehicle to function. However, this study aims to use topology optimisation methods on the off-highway Cummins Inc. QSK78 aftercooler cover to achieve an improved design that at least maintain the current product performance, while the weight of the component is reduced. Such analysis has not hitherto reported in the context of off-highway vehicles. The method involves using topology optimisation techniques based on the given objectives relating to strain energy and natural frequencies. The topology optimisation results are used to provide an informed direction for the design of an optimised 3D CAD model. FEA is used to investigate the structural response of both the baseline and optimised covers. The final optimised design shows an improvement even at worst case of generated stress results while a weight reduction of 6.5% is achieved. It was concluded that further improvements could be made in the optimised design considering limitations due to customer constraints.

Topology and thickness optimization of an indenter under stress and stiffness constraints

Indenter is one of the core components of a waste compression station. In this paper, a new layout free from the existing structure for indenter with lighter weight and good performance is presented. The design procedure includes two steps: Topology optimization and thickness optimization. In topology optimization process, a creative layout of indenter is obtained using Solid isotropic microstructures with penalization (SIMP) method. In thickness optimization process, based on topology optimization results, a design review was conducted, and a revised model was created which addresses all structural and manufacturability concerns. Shape and size optimization was then performed in the detailed design stage to further minimize the mass while meeting the stiffness and stress targets. Finally, an optimized model for the indenter is obtained. From the finite element analysis, it can be seen that there is a 31.8 % reduction in total mass while the performance increased compared with the original model.

Structural analysis and topology optimisation of an aftercooler cover for weight reduction in off-highway engine application

It is endeavoured to gain design direction by use of computational topology optimisation methods on off-highway engines to improve fuel economy and costs to the service provider via weight reductions. Most published studies are focused on key functional components of an on-highway vehicle that are required for the engine or vehicle to function. However, this study aims to use topology optimisation methods on the off-highway Cummins Inc. QSK78 aftercooler cover to achieve an improved design that at least maintain the current product performance, while the weight of the component is reduced. Such analysis has not hitherto reported in the context of off-highway vehicles. The method involves using topology optimisation techniques based on the given objectives relating to strain energy and natural frequencies. The topology optimisation results are used to provide an informed direction for the design of an optimised 3D CAD model. FEA is used to investigate the structural response of both the baseline and optimised covers. The final optimised design shows an improvement even at worst case of generated stress results while a weight reduction of 6.5% is achieved. It was concluded that further improvements could be made in the optimised design considering limitations due to customer constraints.

A data mining method for mechanical interpretation of topology optimization results

A data mining method for mechanical interpretation of topology optimization results

An engineering constraint method for continuum structural topology optimization

Manufacturing and machining property are the most important features of structures. The product with good processing property is not only to decrease its costs but also to increase its efficiency. It is very difficult to design and machine because of the complicated results of topology optimization. This study introduces a heuristic approach using an engineering constraint in topology optimization sensitivity process. With this special method, the result of topology optimization can meet the structural design requirement. Several numerical examples were provided to show that the positive influence of new engineering constraint method on the reasonable results of topology optimization was significant. It was a good way to control the material distribution of continuum structural topology optimization using this method.

Topology optimization of fluid flow channel in cold plate for active phased array antenna

This article presents a topology optimization method for the design of the fluid flow channel of cold plate, aiming to solve the problem of heat dissipation for power devices in active phased array antenna (APAA). The density-based topology optimization method is used in the topology optimization design of flow path, in which the conjugate heat transfer analysis is performed. In the numerical experiment, we use the central plane of the cold plate to make a two-dimensional topology optimization, and then the result of two-dimensional topology optimization was used to build the three-dimensional flow channel of cold plate. The results of simulation show that the optimized flow channel has a better ability of heat dissipation compared with the traditional S style flow channel, which provides important reference for engineering application.

The Topology Optimization Design Research for Aluminum Inner Panel of Automobile Engine Hood

This article discusses the topology optimization methods for automobile engine hood design. The aluminum inner panel of engine hood and mucilage glue regions are set as design areas, and the static performances of engine hood included modal frequency, lateral stiffness, torsional stiffness and indentation stiffness are set as the optimization objectives. The topology optimization results about different objective functions are contrasted for analysis. And based on the reasonable topology optimization result, a suited automobile engine hood designs are raised to further study. Finally, an automobile engine hood that good at all of static performances is designed, and a favorable topology optimization method is put forward for discussion.

An Open Source Framework for Integrated Additive Manufacturing and Level-Set-Based Topology Optimization

Topology optimization has been considered as a promising tool for conceptual design due to its capability of generating innovative design candidates without depending on the designer's intuition and experience. Various optimization methods have been developed through the years, and one of the promising options is the level-set-based topology optimization method. The benefit of this alternative method is that the design is characterized by its clear boundaries. This advantage can avoid postprocessing work in conventional topology optimization process to a large extent and realize direct integration between topology optimization and additive manufacturing (AM). In this paper, practical algorithms and a matlab-based open source framework are developed to seamlessly integrate the level-set-based topology optimization procedure with AM process by converting the design to STereoLithography (STL) files, which is the de facto standard format for three-dimensional (3D) printing. The proposed algorithm and code are evaluated by a proof-of-concept demonstration with 3D printing of both single and multimaterial topology optimization results. The algorithm and the open source framework proposed in this paper will be beneficial to the areas of computational design and AM.

Homogenization‐based topology optimization for high‐resolution manufacturable microstructures

SummaryThis paper presents a projection method to obtain high‐resolution, manufacturable structures from efficient and coarse‐scale homogenization‐based topology optimization results. The presented approach bridges coarse and fine scale, such that the complex periodic microstructures can be represented by a smooth and continuous lattice on the fine mesh. A heuristic methodology allows control of the projected topology, such that a minimum length scale on both solid and void features is ensured in the final result. Numerical examples show excellent behavior of the method, where performances of the projected designs are almost equal to the homogenization‐based solutions. A significant reduction in computational cost is observed compared to conventional topology optimization approaches.

Quick pseudo-random topology optimization design based on triangle element

This paper focuses on the fast highly approximate modal analysis and its applications in topology optimization design based on the triangle finite element. The proposed modal analysis methods are based on the initialized pseudo-random number vectors with the Rayleigh-Ritz analysis, which is very simple to implement and can easily be extended for structural dynamic topology optimization design. The numerical examples show that the proposed method is very effective with small computational cost and high efficiency which can effectively reduce huge computational cost without affecting the outcome of the optimization process. Meanwhile, the introduction of pseudo-random approximate modal analysis leads to the randomness and sub-optimal multiplicity of topology optimization results. Numerical examples show that the approximate pseudo-random modal analysis could also enlarge the search ability of the Optimality Criterion Method (OCM).

Automatic reconstruction of beam structures from 3D topology optimization results

This paper presents a fully-automated reconstruction of beam-like CAD solid structures from 3D topology optimization (TO) results. Raw TO results are first processed to generate a triangulation that represents boundaries of the optimal shape derived. This triangulation is then smoothed and a curve skeletonization procedure is carried out to recover meaningful characteristics of this smoothed triangulation. The resulting skeleton, made with curvilinear geometry, is transformed into straight lines through a normalization process. These straight lines are used to generate a 3D beam structure. Thus, following these steps, a 3D beam structure is automatically derived from TO results. This 3D beam structure is meshed with beam finite elements and since TO non-design material is represented by 3D solid geometry, which is meshed using tetrahedron, the FEA beam structure needs to be rigidly connected with these tetrahedrons. Rigid connections between beam elements and 3D solid elements are ensured using specific FEA beam elements referred to as mini-beams. This results in a mixed-dimensional FEA model with beam and solid finite elements. Results obtained with this mixed-dimensional FEA model allow validating the beam structure obtained from TO results. Performance of the approach is demonstrated on several TO examples.