Topology Optimization Process Research Articles

Stress and Strain Analysis for a Topological Optimized Beam

This paper presents a study of a beam manufactured using fused deposition modeling (FDM) which was topologically optimized and subjected to 3-point bending. In this paper polylactic acid (PLA) was used as a material in order to obtain the beams. Topology optimization is a method widely used in the additive manufacturing (AM) field, that uses algorithmic models to optimize the material layout within some parametric restrictions, like conditions, constraints, or sets of loads and it maximizes the performance and capability of the design by extracting material from different zones that are insignificant in terms of carrying loads to reduce the weight of the model. In the first step, the stress and strain state of the simple beam was numerically and analytically calculated, likewise, the experimental test of the beam subjected to 3-point bending was achieved. After the calculus for the simple beam, the next phase aims at the topological optimization process of the beam subjected to 3-point bending. For all the numerical investigations a calibrated material determined experimentally was used. Following calculations and experimental tests, a final version of the beam topologically optimized was reached, with a minimization of the cost regarding the mass of the beam and the material required for its reproduction.

Optimizing Additive Manufacturable Structures with Computer Vision to Enhance Material Efficiency and Structural Stability

This study introduces an innovative technique that merges computer vision with topology optimization to advance additive manufacturing. Employing advanced photogrammetry software, we obtain high-resolution images of the design domain, which are then used to develop accurate 3D models through meticulous scanning procedures. These models are transformed into an STL file format and remeshed using an adaptive algorithm within COMSOL 5.3 Multiphysics, facilitated by a custom MATLAB 2023 application. This integration achieves the optimal mesh resolution and precision in analytical assessments. We applied this technique to the design of a concrete pillar for 3D printing, targeting a 75% reduction in volume to improve the material efficiency and structural stability—critical factors for extraterrestrial applications. The design, captured with a 360-degree camera array, guided the MATLAB-based topology optimization process. By combining MATLAB’s optimization algorithms with COMSOL’s meshing and finite element analysis tools, we investigated various material-efficient configurations. The findings reveal a substantial volume reduction, especially in the central region of the design, effectively optimizing material utilization while preserving structural integrity. The optimization algorithm exhibited a swift and stable convergence, reaching near-optimal solutions within approximately 20 iterations.

Stress-based topology optimization using maximum entropy basis functions-based meshless method

AbstractThis paper presents volume-constrained stress minimization-based, topology optimization. The maximum entropy (maxent) basis functions-based meshless method for two-dimensional linear elastic structures is explored. This work focuses to test the effectiveness of the meshless method in handling the stress singularities during the topology optimization process. The commonly used moving least square basis functions are replaced with maximum entropy basis functions, as the latter possess weak Kronecker delta property which leads to the finite element method (FEM) like displacement boundary conditions imposition. The maxent basis functions are calculated once at the beginning of the simulation and then used in optimization at every iteration. Young’s modulus for each background cell is interpolated using the modified solid isotropic material with penalization approach. An open source pre-processor CUBIT is used. A comparison of the proposed approach with the FEM is carried out using a diverse set of problems with simple and complex geometries of structured and unstructured discretization, to establish that maxent-based meshless methods perform better in tackling the stress singularities due to its smooth stress field.

Problem-independent machine learning-enhanced structural topology optimization of complex design domains based on isoparametric elements

Topology optimization requires dozens or even hundreds of iterations, each requiring a complete finite element analysis (FEA). Significant computation cost limits the application of topology optimization in engineering, especially for high-resolution problems containing complex design domains. To address the issue, a Problem-Independent Machine Learning (PIML) model based on isoparametric elements is proposed. Effectively reducing the computational time of FEA, the proposed model enables efficient topology optimization and extends the solvable problem range to complex design domains. The essential idea is leveraging the substructure method and establishing a mapping from element shapes and material distribution within the substructure to its numerical shape functions through machine learning models. Both sample generation and model training are conducted offline, allowing the trained machine learning model to be directly employed during the topology optimization process. Since the shape function of the substructure is problem-independent, it requires no sample regeneration or modification of the proposed machine learning model when changing the geometry or boundary conditions of the optimization problem. Numerical examples demonstrate that the proposed machine learning model boosts the efficiency of topology optimization by one order of magnitude without parallel techniques.

Design optimization of heat exchanger using deep reinforcement learning

A micronuclear reactor is currently being developed using 3D printing technology, with a focus on refining the design of its heat exchanger. The objective is to optimize the topology of heat exchangers to improve their performance. The initial thermofluidic topology design is a crucial factor influencing the efficiency of the final optimized heat exchanger. This paper presents a novel approach for the topology optimization of heat exchangers using initial designs generated via deep reinforcement learning (DRL). A printed circuit heat exchanger (PCHE) served as the target for this optimization. Extensive simulations demonstrated that the DRL-assisted optimization method enhanced the heat exchange efficiency by 14.8% compared with that of conventional topology-optimized PCHEs. The optimized heat exchanger was fabricated using 3D printing, and its feasibility was confirmed by comparison with simulation data. The integration of DRL into the topology optimization and production processes via 3D printing lays the groundwork for the development of more efficient thermal systems and demonstrates a viable method for complex engineering applications.

Current status of the application of additive-manufactured TPMS structure in bone tissue engineering

AbstractBone tissue engineering provided the innovative solution to regenerate bone tissue using scaffolds (porous) structures. This research investigates optimization, additive manufacturing methods and the application areas of triply periodic minimal surface-based (TPMS) porous structures in the broad field of tissue engineering through literature review. The properties of TPMS structures are compared with more classical strut-based structures. Also, information on how TPMS can be formulated and how they can be designed to obtain desired properties are presented. Attention is dedicated to the topological optimization process and how it can be applied to scaffolds to further increase their biomechanical properties and improve their design through density, heterogenization, and unit cell size grading. Common numerical algorithms as well as the difference between gradient-based and non-gradient-based algorithms are proposed. Efforts also include the description of the main additive manufacturing technologies that can be utilized to manufacture either stochastic or periodic scaffolds. The information present in this work should be able to introduce the reader to the use of TPMS structures in tissue engineering.

Analysis on the effect of novel topological optimization fin structures considering eccentricity on the heat storage and release characteristics of shell and tube phase change heat accumulator

Shell and tube phase change accumulator (STPCA), as a common type of heat accumulator, can effectively solve the mismatching of time and space in solar thermal power generation by using phase change storage technology. However, the low thermal conductivity of phase change materials (PCMs) reduces its heat storage and release rate. To achieve a rapid latent heat energy storage and release, it needs to carefully modify the structure of STPCA. In the existing literature, insufficient attention has been given to simultaneously addressing the heat storage and release processes, while there is a scarcity of topological optimization methods employed in fin design. On one hand, it is difficult to find the optimal structure. On the other hand, the optimized structure is suitable for melting process but may not be suitable for solidification process. In this contribution, we initially integrated topological optimization and eccentricity to derive fin structures suitable for respective melting and solidification processes. Then, we compared and analyzed the effects of eccentricity and objective function on melting and solidification processes. Finally, we summarized the topology optimization process, objective function and eccentricity suitable for fast heat storage and release. The findings indicated that as the eccentricity increases, the rate of heat storage and release initially rises before subsequently declining. In this work, it is found that an eccentricity of 5 mm is the best. From the whole heat storage and release cycle, when the eccentricity is 5 mm, the objective function is the minimum temperature difference and the topological optimization fin structure calculated during solidification process shows the best heat storage and release performance. Compared with the topology optimization structure without eccentricity, the heat storage speed is increased by 36.43 %, and the heat release speed is increased by 15.53 %. The design law of the STPCA based on combined with the eccentricity influence and topology optimization method is summarized to help improve its heat storage and release performance.

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.

Adaptive Variable Design Algorithm for Improving Topology Optimization in Additive Manufacturing Guided Design

CAD-CAE software companies have introduced numerous tools aimed at facilitating topology optimization through Finite Element Simulation, thereby enhancing accessibility for designers via user-friendly interfaces. However, the imposition of intricate constraint conditions or additional restrictions during calculations may introduce instability into the resultant outcomes. In this paper, an algorithm for updating the design variables called Adaptive Variable Design is proposed to keep the final design space volume of the optimized part consistently under the target value while giving the main algorithm multiple chances to update the optimization parameters and search for a valid design. This algorithm aims to produce results that are more conducive to manufacturability and potentially more straightforward in interpretation. A comparison between several commercial software packages and the proposed algorithm, implemented in MATLAB R2023a, is carried out to prove the robustness of the latter. By simulating identical parts under similar conditions, we seek to generate comparable results and underscore the advantages stemming from the adoption and comprehension of the proposed topology optimization methodology. Our findings reveal that the integrated enhancements within MATLAB pertaining to the topology optimization process yield favourable outcomes with respect to discretization and the manufacturability of the resultant geometries. Furthermore, we assert that the methodology evaluated within MATLAB holds promise for potential integration into commercial packages, thereby enhancing the efficiency of topology optimization processes.

Topology Optimization of Motorbike Footsteps Using Finite Element Method

Footsteps are a foothold for motorbike riders and passengers; they also play a role in maintaining stability when driving. Footsteps must have a solid and lightweight material to support the load from the feet and body of the rider and passengers. In this study, the footstep with the material made from the waste drum brake shoe varied by reducing mass through the static structural simulation process and topology optimization process using Ansys Workbench to get optimal mass, total deformation, equivalent stress, maximum principal stress, and safety factor from each variation. The footstep geometry will be subjected to a load of 1000N and provided with the necessary support. Based on the data obtained during this study, the initial footstep geometry produces data in the form of total deformation (1.383 mm), equivalent stress (21.013 MPa), and safety factor (1.227). The 10% variation produces data in the form of total deformation (1.4368 mm), equivalent stress (20,564 MPa), ,and safety factor ( 1.2538). The 20% variation yields data in the form of total deformation (0.98037 mm), equivalent stress (18.111 MPa), maximum principal stress (18.41 MPa), and safety factor (yield strength: 1.4236,. At the same time, the 25% variation produces data in the form of total deformation (1.3058 mm), equivalent stress (22.27 MPa), and safety factor (1.1577).

Design of the shell-infill structures using a phase field-based topology optimization method

The design of shell-infill structures has been a focal point in the topology optimization community due to their advantages in energy absorption characteristics, strength-to weight ratio and bucking resistance. This paper introduces a phase field-based topology optimization method for designing shell-infill structures. Interface-related issues can be easily addressed through the phase field function. A coupled topology optimization process is proposed to establish the connection between the shell and infill, facilitating the generation of optimized structures. The shell thickness, infill pattern and infill volume percentage, can be naturally controlled by different model parameters. Additionally, multiscale phase field topology optimization integrates the numerical homogenization method to evaluate the effective elasticity matrix of the microstructural infill. The approach is introduced for a uniform, periodical microstructure layout in the infill region, thereby achieving superior mechanical properties. Numerical results indicate the effectiveness of the proposed method in the design of both 2D and 3D shell-infill structures.

A two-step topology and layout wind farm optimization approach

A novel two-step approach is presented to optimize the placement of wind turbines within a wind farm. The goal is to maximize the annual energy production, while the topology and layout of the wind turbines are optimized in sequence with a two-step procedure using gradient-based algorithms. In particular, in the first step the topology of the wind farm is optimized. A grid of potential wind turbine locations is defined, and continuous density variables ranging from zero to one are assigned to each location. The variables indicate the presence or absence of a wind turbine. Throughout the topology optimization process, we penalize the intermediate values of these variables, implicitly pushing the algorithm towards crisp 0-1 final layouts. Constraints are imposed on the minimum and maximum number of wind turbines and the spacing between them. Subsequently, in the second step, we refine the wind farm layout by optimizing the coordinates (x, y) of the wind turbines, which are initialized based on the optimal topology obtained in the first step. Numerical findings demonstrate the capability of the proposed approach to identify non-intuitive optimized wind farm layouts, with reasonable computational resources and time.

Topology optimization of non-linear electromagnetic actuator based on Reluctance Network Analysis

Topology Optimization (TO) enables unrestricted exploration within a design domain and is typically based on a spatial discretization that is also used as the mesh for simulation. In this article, we propose to use for the simulation a mesh-based equivalent circuit method termed the Reluctance Network Analysis (RNA), with nonlinear magnetic properties of the material. The simulation tool is then used in a topology optimization process solved with generalized optimality criteria (GOC) method. During the optimization, the sensitivity matrix is needed, and we describe here how to derive the matrix in the case of a nonlinear RNA using Adjoint Variable Method (AVM). Finally, we implemented this topology optimization through a case study of an electromagnetic actuator.

Topological optimization of ballistic protective structures through genetic algorithms in a vulnerability-driven environment

Reducing the vulnerability of a platform, i.e., the risk of being affected by hostile objects, is of paramount importance in the design process of vehicles, especially aircraft. A simple and effective way to decrease vulnerability is to introduce protective structures to intercept and possibly stop threats. However, this type of solution can lead to a significant increase in weight, affecting the performance of the aircraft. For this reason, it is crucial to study possible solutions that allow reducing the vulnerability of the aircraft while containing the increase in structural weight. One possible strategy is to optimize the topology of protective solutions to find the optimal balance between vulnerability and the weight of the added structures. Among the many optimization techniques available in the literature for this purpose, multi-objective genetic algorithms stand out as promising tools. In this context, this work proposes the use of a in-house software for vulnerability calculation to guide the process of topology optimization through multi-objective genetic algorithms, aiming to simultaneously minimize the weight of protective structures and vulnerability. In addition to the use of the in-house software, which itself represents a novelty in the field of topology optimization of structures, the method incorporates a custom mutation function within the genetic algorithm, specifically developed using a graph-based approach to ensure the continuity of the generated structures. The tool developed for this work is capable of generating protections with optimized layouts considering two different types of impacting objects, namely bullets and fragments from detonating objects. The software outputs a set of non-dominated solutions describing different topologies that the user can choose from.

Multi-field coupling in designing embedded microchannels for three-dimensional integrated chip: A topology optimization approach

Topology optimization methods have shown promise in enhancing the heat transfer performance of microchannel structures. However, the thermal-electrical-force multi-field coupling effects in three-dimensional integrated chips present a complex heat generation scenario that necessitates their consideration in the design of embedded microchannel structures. Here, we perform topology optimization of embedded microchannels specifically tailored for three-dimensional integrated chip, with a specific focus on the multi-field coupling effects of through-silicon-via structures within the topology optimization process. A new and improved 2D microchannel structure that exhibits superior heat transfer performance was obtained by analyzing the effects of pressure drop constraints within the channel, as well as fixing the microfin diameter and local heat flux of through-silicon-via. Furthermore, the obtained topology optimization results were validated through rigorous three-dimensional numerical simulations. The findings demonstrate that the new microchannel structure, when compared to the original microfin model, yields a significant improvement in the comprehensive heat transfer performance coefficient, achieving a remarkable enhancement factor of 1.43. Furthermore, under identical flow conditions, the structural stress within the chip experiences a substantial reduction of 43.9%. These outcomes underscore the efficacy of the topology optimization approach in effectively addressing the thermal management challenges associated with three-dimensional integrated chip.

A limit analysis-based topology optimisation method for geostructure design

Geostructures, vital for the progress of civilisation, often face inefficiencies and suboptimal performance due to the lack of optimisation in current designs. Achieving cost-efficiency in geostructure design involves optimising material usage while considering practical construction aspects. While size and shape optimisations are common in geostructure design, the application of topology optimisation remains underexplored. This paper addresses this gap by introducing a novel topology optimisation method for three-dimensional geostructure design. The method integrates mixed limit analysis and density-based topology optimisation theories, allowing for two-material design focused on the ultimate bearing capacity of the geostructure. The innovation resides in aligning the applied external load in the topology optimisation process with the ultimate load that the designed geostructure can sustain. The robustness of the proposed method is exemplified through its application to the design of an embankment and soil foundation, showcasing its potential to enhance the efficiency and performance of geostructures. This research contributes to the advancement of geostructure design practices, ultimately promoting sustainable and resilient infrastructure development.

Functionally graded multi-morphology lattice structures as an optimized sandwich core via digital light processing additive manufacturing

This investigation aims to present a high-strength sandwich core with functionally graded multi-morphology lattice inner structures through vat photo-polymerization additive manufacturing (AM). The five better strut-based designs based on [1], are considered here. All printed specimens have been fabricated from photopolymer resin to ensure manufacturability in a digital light processing (DLP) 3D printer. Firstly, the resin and structural characteristics have been examined. Simultaneously, the lattice core is divided into three regions based on the von Mises stress distribution and tensile and compression responses in finite element analysis (FEA). Based on the mechanical responses of the beam-based structures, these topologies have been applied in each region in an optimal fixed relative density distribution, considering different steps and types. This proposed technique is numerically investigated and experimentally validated using a three-point bending test. As a result, the optimized core demonstrated a 96% increase in maximum fracture force and a 174% increase in stiffness compared to the homogeneous body. Additionally, it exhibited a different deformation mode than the single morphology under similar conditions. These significant findings indicate that this approach provides a new perspective on a high-strength design involving more than three morphologies, and it is faster than computational topology optimization processes.

A novel topology optimization of fin structure in shell-tube phase change accumulator considering the double objective functions and natural convection

Shell-tube phase change accumulator (STPCA) has been widely applied in renewable energy generation and energy-saving building field. However, due to the low thermal conductivity of phase change material (PCM), its structure needs to be carefully designed to obtain the best heat release and storage rate. Most of the traditional design schemes are trial and error method, which has long design cycle, low efficiency, and difficulty in obtaining the optimal structure. In this contribution, we firstly adopt the topology optimization methods to obtain novel fins in STPCA considering natural convection. Then, we compared the difference between different objective functions and demonstrated the superiority of topology optimization. In addition, we have further studied fin design under double objective functions with different weight ratios and analyzed the synergistic effects on the objective functions. The results have shown that after natural convection has been considered in the topological optimization process, it can help obtain a better structure, and the generated fins can better enhance the performance of STPCA. For the case of single objective function, the conclusions are as follows: the maximum average temperature can be used to obtain the faster melting speed, while the minimum temperature difference can be used to obtain the best temperature uniformity. The conclusions of using double objective function are as follows: when the weight ratio of the maximum average temperature and the minimum temperature difference is 0.6: 0.4, the field synergy angle is smallest, and the performance of STPCA is further improved. This contribution can provide a guidance for STPCA design and enhance its thermal storage performance.

A polygonal topology optimization method based on the alternating active-phase algorithm

<abstract> <p>We propose a polygonal topology optimization method combined with the alternating active-phase algorithm to address the multi-material problems. During the process of topology optimization, the polygonal elements generated by signed distance functions are utilized to discretize the structural design domain. The volume fraction of each material is considered as a design variable and mapped to its corresponding element variable through a filtering matrix. This method is used to solve a multi-material structural topology optimization problem of minimizing compliance, in which a descriptive model is established by using the alternating active-phase algorithm and the solid isotropic microstructure with penalty theory. This method can accomplish the topology optimization of multi-material structures with complex curve boundaries, eliminate the phenomena of checkerboard patterns and a one-node connection, and avoid sensitivity filtering. In addition, this method possesses fine numerical stability and high calculation accuracy compared to the topology optimization methods that use quadrilateral elements or triangle elements. The effectiveness and feasibility of this method are demonstrated through several commonly used and representative numerical examples.</p> </abstract>

Design of multi-material structures using material jetting technology: Topology optimisation, numerical analysis and experiments

This paper presents a thorough experimental/numerical validation of optimised multi-material structures fabricated by material jetting technology. The proposed methodology uses, on the one hand, non-uniform rational basis spline (NURBS) entities to represent the geometric descriptor associated with each material phase constituting the continuum and, on the other hand, a general multi-phase material interpolation scheme to penalise the stiffness tensor of the structure. Two design requirements are included in the problem formulation: the lightness and the minimum length scale of each material phase. The influence of the integer parameters intervening in the definition of the NURBS entity and the influence of different combinations of material phases on the optimised solutions are investigated. The proposed approach is applied to 2D and 3D benchmark structures subjected to prescribed displacements representative of a three-point bending test. Based on the result of the topology optimisation process one of the optimised solutions, balancing the requirements of structural stiffness, lightness, and manufacturing constraints, is selected, manufactured and tested. A comparison between experimental and numerical results (obtained by non-linear analyses) is carried out to show the effectiveness of the approach.