Combined Topology Optimization Research Articles

Topology optimization of periodic cellular materials employing the finite-volume theory

Topology optimization is a technique used in engineering to determine the optimal distribution of material within a defined design domain. This technique has been applied to the design of cellular materials to create an efficient microstructural arrangement that meets the necessary performance criteria and minimizes the weight of the material. This article presents an innovative approach that combines topology optimization, a homogenization method based on the unit cell concept and finite-volume theory to design highly efficient periodic cellular materials with optimized macroscopic elastic properties. To determine the optimal microstructural topology, specific linear combinations of components of the homogenized elastic matrix are considered to obtain optimized elastic properties, such as maximum shear/bulk moduli, considering a prescribed volume fraction constraint of solid material. Numerical examples are analysed, and the results demonstrate the exceptional performance of this approach in achieving optimal designs of cellular materials characterized by chequerboard-free patterns without filtering techniques.

Generative design framework for RC deep beams using topology optimization and generative tie method: Experimental and numerical investigation

This research paper proposes a generative design framework that combines topology optimization and the Generative Tie Method (GTM). The study explores the design and performance evaluation of structural concrete deep beams using this framework. A comprehensive investigation involving computational simulations and rigorous large-scale experimental testing provides insights into the optimization strategies of structural concrete deep beams. Specimens designed in accordance with the proposed framework, with an allowable value of compressive strength reduction in concrete (ηadm) set to 0.7, exhibited lower ductility ratios compared to specimens designed with ηadm equal to 0.5. Ductility ratio losses varied significantly, ranging from 28.2 % to 66.2 % among specimens subject to the same optimization level. The topology optimization process significantly influenced stress distribution, cracking behavior, and overall ductility. The Global Warming Potential factor is employed to assess the environmental impact of the optimized structural members. Comparative analyses between the proposed design methodology and a traditional method demonstrate several advantages, including greater material efficiency, higher ductility, and reduced environmental impact. However, the framework demands advanced tools, expertise, and additional training for practical application.

Towards advanced piezoelectric metamaterial design via combined topology and shape optimization

Metamaterials open up a spectrum of artificially engineered properties otherwise unreachable in conventional bulk materials. For electromechanical energy conversion systems, lightweight materials with high hydrostatic piezoelectric coupling coefficients and negative Poisson’s ratio can be obtained. Thus, in this contribution, we explore the possibilities of piezoelectric metamaterials design by employing structural optimization. More specifically, we apply a sequential framework of topology and shape optimization to design piezoelectric metamaterials with negative Poisson’s ratio for electromechanical energy conversion under uniform pressure. Topology optimization is employed to generate the initial layout, whereas shape optimization fine tunes the design and improves durability and manufacturability of the structures with the help of a curvature constraint. An embedding domain discretization (EDD) method with adaptive domain and shape refinement is utilized for an efficient and accurate computation of the state problem in the shape optimization stage. Multiple case studies are conducted to determine the importance of desired stiffness characteristics, symmetry conditions and objective formulations on the design of piezoelectric metamaterials. Results show that the obtained designs are highly dependent on the desired stiffness characteristics. Moreover, the addition of the EDD-based shape optimization step introduces significant changes to the designs, confirming the usability of the sequential framework.

Performance-Based Analysis of Mesh Smoothing Methods Combining Topology Optimization and Additive Manufacturing

Most design-to-manufacturing frameworks combining topology optimization (TO) and additive manufacturing (AM) integrate mesh smoothing methods as post-processing techniques to remove discrete irregularities of optimized topologies. Notably, a design framework is proposed incorporating all the CAD development stages within the design phase providing smooth and ready-to-print topologies. The Laplacian-based smoothing algorithms have demonstrated a high capacity in removing surface noise. This study focuses on investigating the smoothing capacity of both HC Laplacian and Taubin methods using mesh quality metrics to assess on their performance in terms of geometric preservation and volume shrinkage. Taubin method was found to produce high-quality smooth meshes with less volume shrinkage compared to HC Laplacian. The Taubin model exhibited an increase of 15.06% in mesh volume whereas the HC Laplacian model had a volume shrinkage of 28.14%. Additionally, finite element analyses of the three-point bending test using ANSYS is set to measure the flexural stiffness of an optimized MBB beam under both HC Laplacian and Taubin smoothing methods. Overall, the flexural stiffness of Taubin is nearly two times the original model with a surplus of 46.91% whereas HC Laplacian exhibited a flexural stiffness that is less with 72.07% than the original model.

A topology-based in-plane filtering technique for the combined topology and discrete fiber orientation optimization

This work proposes a filtering technique for the concurrent and sequential finite element-based topology and discrete fiber orientation optimization of composite structures. The proposed filter is designed to couple the morphology with the topology of the structural domain throughout the optimization process in a way such that it suppresses the impact of the close-to-void finite elements’ morphology on the overall morphology of the structure while steering at the same time the local fiber orientation towards the neighboring topologically dense areas of the geometry. The functionality of the filter becomes crucial at the boundaries of the optimized structure, where the fiber orientation is forced to conform to the morphology of the local boundaries. The developed filtering technique is incorporated into both the concurrent and sequential finite element-based topology and discrete fiber orientation optimization problem, and the respective optimization problems are formulated for the compliance minimization of the composite structure. To assess the efficacy of the filter, it is demonstrated in the benchmark academic case studies of the 2D Messerschmitt-Bölkow-Blohm and cantilever beams when different state-of-art interpolation techniques are employed for modeling the discrete fiber orientation optimization problem.

Experimental investigations of optimized 3D Printing Planar X-joints manufactured by stainless steel and high-strength steel

Welded joints are often employed in high-rise buildings and grid-shell structural systems but on-site welding of cut steel tubes for spatially complex frame systems is problematic, time consuming and difficult to ensure quality. Innovative prefabrication combining topology optimization (TO) using the Solid Isotropic Material Penalization Method (SIMP) and additive manufacturing (AM) provides an innovative solution for materially efficient mass production of repetitive joints. Optimized AM joints can be bolted to other members on-site, which promotes construction efficiency, and overcomes the barriers of on-site welding. In this paper, tensile tests are conducted to assess the material properties of mild and stainless steel materials used in different manufacturing processes. Welded and 3D printed joints using different materials are then investigated to maximize the mechanical properties by taking full advantage of AM and TO. A customized non-contact 3D-DIC (Digital Image Correlation) technique based on an open source tool (MultiDic) is applied to analyze and visualize the strain distribution in planar tubular and topologically optimized joints. AM joint exhibits a uniform stress distribution which avoids stress concentrations and the innovative configuration of the optimized joint has good energy absorption resulting in the protection of the central core region of the joint.

Digital design and manufacturing of spherical joint base on multi-objective topology optimization and 3D printing

Topology optimization techniques have been widely applied for the generation of highly efficient material structures in various fields. In addition, 3D printing has the ability to fabricate geometrically complex optimized results which are difficult to realize for conventional means. The research presented in here aims to implement a digital design and manufacture high-performance joints in space truss by combining topology optimization and 3D printing. Two multi-condition optimization models, i.e., minimum volume model and minimum compliance model, are employed to optimize the spherical joints under multiple conditions. The conditions are three most dangerous load conditions of joints in the space truss. Since single-objective topology optimizations only seek the optimal solution for a single objective, the mechanical properties of the optimized result may be limited. As a result, the compromise programming model, a multi-objective topology optimization model, is designed with the goals of minimum volume and compliance under each condition. In addition, multi-condition and multi-objective topology optimization design of the spherical joints are carried out based on density approach. The advantages of the multi-objective topology optimization are verified by comparing the mechanical performance of the optimized results obtained by the minimum volume model, the minimum compliance model and the compromise programming model. Finally, the additive manufacturing of the optimized results is completed by using 3D printing technology, which verifies the feasibility of digital design and manufacturing of joints.

Ant-Inspired Bionic Design Method for the Support Structure of the Fengyun-3 Satellite Payload Infilled with Lattice Structure.

Owing to their high design freedom and excellent performance, lattice structures have shown outstanding capabilities and great potential in aeronautics and astronautics fields. In this paper, we propose a method to construct lattice structures by parameterizing biological features. An ant-leg configuration is used as the bionic object to generate a bionic lightweight design with a gradient lattice structure. To achieve the above goal, an innovative optimization method combining topology optimization, size optimization, and a bionic lattice structure is proposed in this paper. Taking the support structure of the Fengyun-3 satellite payload as the research object, this optimization method is applied to optimize the design. Further, the reconstructed optimization model and the original model are simulated to evaluate and compare the structural performance. The simulation results show that when combined with bionic lattice structure and structural optimization, the method can achieve the lightweight design goal while ensuring the stiffness and strength of the structure. The results demonstrate that the application of a bionic lattice design in a lightweight design has feasibility and expectable potential.

Exhibit supports for sandstone artifacts designed through topology optimization and additive manufacturing techniques

In the Cultural Heritage field, the choice of materials and exhibit structures is essential to properly house and support artifacts without causing damage or deterioration. This problem is even more evident in the case of finds made of stone for which, due to their weight, a proper selection and dimensioning of the relative supports is required. In fact, without adequate support, this can result in stress concentrations that could compromise the artifact's state of conservation. As a consequence, more often such exhibition supports are customized items, that are designed and manufactured to meet specific functional and artistic setup needs. In this context, the paper presents a design approach that combines topology optimization and additive manufacturing techniques to develop customized support structures which undertake the twofold purpose of preserving the artifact and making it available for the exhibition in the museum. The proposed approach has been assessed through the case study of a sandstone Ionic capital hosted in the Brettii & Enotri Museum in Cosenza (Italy). The proposed approach is therefore meant as a guideline for the design of customized exhibit supports especially in the case of sandstone artifacts with a complex shape or a conservation condition that requires specific attention.

Topology Optimization Combined with a Parametric Algorithm for Industrial Synchronous Reluctance Motor Design

In this paper, we propose combining topology optimization with a parametric algorithm (TOCPA) to design an industrial synchronous reluctance motor (SynRM) that satisfies super-premium efficiency (IE4). TOCPA consists of two main processes. An improved niching algorithm is proposed as an existing parametric algorithm, and multiple optimal points were identified quickly and effectively within the design range specified by the user. Existing parametric algorithms lack the ability to find unpredictable new optimal shapes; therefore, topology optimization has been added. TOCPA converges the two optimization methods to compensate for the shortcomings of each and maximizes the advantages. In addition, the boundary surface ON–OFF method is applied to accelerate the topology optimization process. Subsequent ratio-based smoothing techniques smooth out discontinuous interfaces and remove clusters to improve the torque characteristics and reduce the manufacturing difficulty. Finally, the torque ripple was reduced using the skew technique, and mechanical stability was confirmed using a stress analysis. An IE4 industrial SynRM was successfully designed using TOCPA.

Structure Optimization and Verification of Portable Intelligent Gauge Calibrator

Portable intelligent gauge calibrator is a new type of gauge calibrator to replace the traditional gauge calibrator. It can effectively solve the problems of traditional gauge calibrator, such as unable to carry out on-site measurement, too large volume, low degree of intelligence and so on. In view of the problem that the maximum stress of the connector of the horizontal measuring platform is too large in the trial operation of the portable intelligent gauge calibrator, this paper puts forward a solution combining topology optimization with practical experience. The test shows that the method is effective and feasible.

A Novel Digital Design Approach for Metal Additive Manufacturing to Address Local Thermal Effects

The reliability and performance qualification of additively manufactured metal parts is critical for their successful and safe use in engineering applications. In current powder-bed fusion type metal additive manufacturing processes, local thermal accumulations affect material microstructure features, overall part quality and integrity, as well as bulk mechanical behavior. To address such challenges, the investigation presented in this manuscript describes a novel digital design approach combining topology optimization, process simulations, and lattice size optimization to address local thermal effects caused during manufacturing. Specifically, lattices are introduced in regions of topology optimized geometries where local thermal accumulations are predicted using the process simulations with the overall goal to mitigate high thermal gradients. The results presented demonstrate that the proposed digital design approach reduces local thermal accumulations while achieving target mechanical performance metrics. A discussion on how post-manufacturing heat treatment effects could be also considered, as well as comments on the computational implementation of the proposed approach are provided.

An Enhanced Topology Optimization Approach Based on the Combined MMC and NURBS-Curve Boundaries

An efficient topology optimization method is developed newly in this study by combining the Non-uniform rational B-spline (NURBS) curves and moving morphable components (MMC). The MMC-based topology optimization is an explicit and geometrical method that utilizes a set of morphable components to create basic blocks for optimization. Optimum topologies may be obtained by optimizing shapes, lengths, thicknesses, orientations and layout of these components. The combined method adopts a different way in the creation of morphable components that consist of NURBS curves. Various kinds of complicated curved components can be built with NURBS curves or surfaces. Here, the NURBS curve is applied for shaping the geometries of structural basic components, and the coordinates of control points become design variables for topology optimization. A MATLAB optimization code has been developed. Four numerical examples of a short cantilever, a MBB beam, a simply supported beam with two point loadings, and a vehicle lower chassis structure subjected to crash loadings are provided to prove that the combined topology optimization approach coupled with NURBS curves and basic morphable components can get optimum topologies with clear topological boundaries successfully. As results of comparison study with other approaches, we can obtain the same topologies and faster convergence rates for the three separate cases. The combined approach can improve the smoothness of the topological boundaries that are similar to the shape optimization results obtained by post-optimization after the density-based topology optimization.

A discrete-continuous parameterization (DCP) for concurrent optimization of structural topologies and continuous material orientations

Combining topology optimization and continuous orientation design of fiber-reinforced composites is a promising way to pursue lighter and stronger structures. However, the concurrent design problem of structural topologies and continuous orientations is a tough topic due to the issue of local optimum solutions. This paper presents a new parameterization of orthotropic materials with continuous orientations, which is labeled as discrete-continuous parameterization (DCP), to handle this difficulty. The starting point of DCP is that the risk of falling into local optima will be much smaller if the search range of orientation variables can be greatly reduced. To do so, the searching interval of orientation is averagely divided into several subintervals. Then, the original continuous orientation optimization problem is changed to a discrete subinterval selection problem and a continuous orientation optimization problem in a subinterval. Based on this, the new DCP is proposed to model orthotropic materials with continuously varying orientations by combining both discrete and continuous variables. Finally, a new and general concurrent topology optimization method is built based on the proposed DCP and a three-field topology optimization scheme. Verification studies with several benchmark examples are provided to validate the effectiveness of the proposed approach.

DzAIℕ: Deep learning based generative design

Generative Design is the methodology for automatic creation of a large number of designs via an iterative algorithmic framework while respecting user-defined criteria and limitations. It is mainly used as a designer assistive tool for the creation of prototypes in sectors like product manufacturing, automotive and aerospace industry while there are also references of use of Generative Design in architecture [1]. The algorithms used are mainly originating from nature-mimicking procedures [2]. Generative Design differentiates from shape optimization due to the fact that it does not focus on finding the optimal design but on being able to propose a large variety of designs that satisfy all designer-defined constraints in an automated procedure. Thus, it can be said that it focuses on proposing initial designs for inspiring the designer. In this work, a methodology for Generative Design called DzAIℕ is proposed. DzAIℕ is based on an algorithmic architecture that combines topology optimization and deep learning methods. Deep learning and specifically Deep Belief Networks (DBN) [3] are used for diversifying through stochasticity, designs generated by topology optimization method Solid Isotropic Material with Penalization (SIMP) [4]. SIMP is used for guiding the design procedure towards a local optimum. The response time for DzAIℕ to propose a series of shapes is minimal as only a small population of SIMP iterations is needed while the time needed for application of a series of DBNs is insignificant. In the current work, a series of examples of computer-generated designs with the use of DzAIℕ are presented in order to validate the proposed methodology.

Topology optimization of oilstone components considering carbon emissions associated with honing processes

Incorporating carbon emissions consideration into topology optimization can improve the environmental sustainability of machine tools. However, existing studies on combining topology optimization methods with low-carbon technologies for honing machines are limited. The study aims at minimizing compliance (i.e., the maximum stiffness) while considering the carbon emissions associated with honing processes by changing the shape and distribution of abrasive grains on oilstone components, which are the key parts causing carbon emissions in the use stage of honing machines. Considering the hierarchical characteristics of the problem, a one-to-many Stackelberg cooperative game model is proposed to describe the decision behavior in each level. The model has two subgames, i.e., a dynamic Stackelberg sub-game to obtain a benefit equilibrium between the upper-level compliance optimization problem and the lower-level carbon emissions optimization problem, and a static cooperative sub-game in the lower level to minimize carbon emissions. A bilevel game theoretic solution method is developed to solve the model. A case study is presented to demonstrate the feasibility of the proposed method. The results indicate that the proposed method can reduce compliance and carbon emissions of the oilstone component by 39.2% and 29.3% compared with a non-optimized oilstone component.

Optimizing Topology and Gradient Orthotropic Material Properties Under Multiple Loads

The goal of this research is to optimize an object's macroscopic topology and localized gradient material properties (GMPs) subject to multiple loading conditions simultaneously. The gradient material of each macroscopic cell is modeled as an orthotropic material where the elastic moduli in two local orthogonal directions we call x and y can change. Furthermore, the direction of the local coordinate system can be rotated to align with the loading conditions on each cell. This orthotropic material is similar to a fiber-reinforced material where the number of fibers in the local x and y-directions can change for each cell, and the directions can as well be rotated. Repeating cellular unit cells, which form a mesostructure, can also achieve these customized orthotropic material properties. Homogenization theory allows calculating the macroscopic averaged bulk properties of these cellular materials. By combining topology optimization with gradient material optimization and fiber orientation optimization, the proposed algorithm significantly decreases the objective, which is to minimize the strain energy of the object subject to multiple loading conditions. Additive manufacturing (AM) techniques enable the fabrication of these designs by selectively placing reinforcing fibers or by printing different mesostructures in each region of the design. This work shows a comparison of simple topology optimization, topology optimization with isotropic gradient materials, and topology optimization with orthotropic gradient materials. Finally, a trade-off experiment shows how different optimization parameters, which affect the range of gradient materials used in the design, have an impact on the final objective value of the design. The algorithm presented in this paper offers new insight into how to best take advantage of new AM capabilities to print objects with gradient customizable material properties.

Detailed design of a lattice composite fuselage structure by a mixed optimization method

In this article, a procedure for designing a lattice fuselage barrel is developed. It comprises three stages: first, topology optimization of an aircraft fuselage barrel is performed with respect to weight and structural performance to obtain the conceptual design. The interpretation of the optimal result is given to demonstrate the development of this new lattice airframe concept for the fuselage barrel. Subsequently, parametric optimization of the lattice aircraft fuselage barrel is carried out using genetic algorithms on metamodels generated with genetic programming from a 101-point optimal Latin hypercube design of experiments. The optimal design is achieved in terms of weight savings subject to stability, global stiffness and strain requirements, and then verified by the fine mesh finite element simulation of the lattice fuselage barrel. Finally, a practical design of the composite skin complying with the aircraft industry lay-up rules is presented. It is concluded that the mixed optimization method, combining topology optimization with the global metamodel-based approach, allows the problem to be solved with sufficient accuracy and provides the designers with a wealth of information on the structural behaviour of the novel anisogrid composite fuselage design.

On the balancing of structural and acoustic performance of a sandwich panel based on topology, property, and size optimization

Balancing structural and acoustic performance of a multi-layered sandwich panel is a formidable undertaking. Frequently the gains achieved in terms of reduced weight, still meeting the structural design requirements, are lost by the changes necessary to regain acceptable acoustic performance. To alleviate this, a design method for a multifunctional load bearing vehicle body panel is proposed which attempts to achieve a balance between structural and acoustic performance. The approach is based on numerical modelling of the structural and acoustic behaviour in a combined topology, size, and property optimization in order to achieve a three dimensional optimal distribution of structural and acoustic foam materials within the bounding surfaces of a sandwich panel. In particular the effects of the coupling between one of the bounding surface face sheets and acoustic foam are examined for its impact on both the structural and acoustic overall performance of the panel. The results suggest a potential in introducing an air gap between the acoustic foam parts and one of the face sheets, provided that the structural design constraints are met without prejudicing the layout of the different foam types. • A two stage optimization of a multi-functional sandwich panel. • Topology optimization decides the structural foam placement. • Structural and acoustic optimization designs the acoustic foam layers. • The resulting designs fulfill the requirements at low weight penalty.

Topology Optimization for the Base of Parallel Loading Device

The base of Parallel loading device withstand the pressure of hundreds of tons, Limited by the conditions of use, All components of the device must be manual handling, so Its weight becomes very sensitive. The initial design weight of base are about 170 kg, By handling environmental constraints, four men lift is also very convenient, Therefore it's urgent to reduce weight. In this paper, a powerful modeling capabilities of UG combined ANSYS topology optimization module on the base for a topology optimization, We refer to the shape of topology optimization design of the final design of the structure. Through finite element analysis, the structural stiffness and strength to meet the design requirements, And weight decreased from about 170 kg to 120 kg, reduced by nearly 30%.