Application Of Topology Optimization Research Articles

Research and application of topology optimization on air-cooled heat sinks

Research and application of topology optimization on air-cooled heat sinks

Applications of topology optimization considering physical nonlinearity

Topology optimization is a powerful computational tool that assists designers in determining efficient structural configurations. In civil engineering, most applications are still limited to the field of theoretical/computational analysis. This limitation restricts the scope and applications of topology optimization concepts for practical problems. Extensive research has focused on topology optimization using isotropic material with linear elastic behavior. However, there is a paucity of studies comparing linear and nonlinear material behaviors, highlighting a research gap in result analysis and structural application fields. For concrete structures, in particular, there is generally a deeply nonlinear behavior, including effects such as cracking, creep, and shrinkage. Therefore, it becomes a challenge to realistically optimize this type of material. This study investigates the applications of topology optimization for evaluating the structural behavior of beams considering the physical nonlinearity of the material. Using the ABAQUS® software and the SIMP method, a finite element numerical analysis is conducted to determine the density distribution in a design domain. The obtained results of the optimized models are compared, and it is observed that the presence of plastic deformations influences relevant aspects of structural behavior. This study contributes to the dissemination of the use of nonlinear constitutive models, highlighting the potential of the concept of optimization-assisted design.

Sustainability in bridge design—investigation of the potential of topology optimization and additive manufacturing on a model scale

AbstractBridge design represents a typical challenge in civil engineering. The high material usage in combination with the considerable construction effort makes their longevity a strongly desirable property. A mechanically efficient design contributes to optimum load distribution within the structure. Numerical topology optimization represents a valuable tool that can be applied for form finding of load‐appropriate structural layouts within a predefined design‐space. This study takes application of topology optimization to bridge design into focus. Different bridge types are designed using topology optimization considering self‐weight based on a routine that was presented in a previous work. The bridge designs are examined in detail and compared to already existing bridges with regard to the requirements of modern structures. In order to demonstrate manufacturability of the designs, they are realized on a model scale using an additive manufacturing (am) technique in the powder bed. The knowledge gained from this small scale consideration is transferred to the context of civil engineering to highlight the potential of AM in realization of resource efficient construction.

A NOVEL FRAMEWORK FOR THE APPLICATION OF TOPOLOGY OPTIMIZATION IN LIGHTWEIGHT STRUCTURES

Introduction: Topology optimization has been widely used in the fields of mechanical and structural engineering. In the field of architecture, especially in the context of lightweight structures, a strong understanding of programming is essential for meaningful involvement. The purpose of the study was to establish a fundamental framework that facilitates the seamless implementation of topology optimization in the design of lightweight structures by architects. Methods: This work employed a deductive approach to analyze six case studies that involve the application of topology optimization in various lightweight constructions. The analysis was conducted based on a predefined set of criteria. Additionally, the deductive technique was used to establish a framework for implementing topology optimization in the design of lightweight structures. Finally, the framework was used to create an optimized lightweight structure (a pentagonal Roman vault). Findings: An analysis of all case studies was conducted using two distinct processes: the form-finding process and the fabrication process. This inquiry aimed to determine the procedural framework involved in the design and fabrication process of each case study. The underlying framework was derived through an analytical comparison of these six case studies. This framework enables the production of an optimized lightweight structure. Novelty: This study presents significant findings on topology optimization and its use in lightweight structures, offering essential insights for architects seeking to create aesthetically pleasing and distinctive architectural forms that prioritize high stiffness and low mass.

Topology Optimization of Finite Periodic Structures with Compliance and Frequency Criteria

Periodic structures effectively address challenges in manufacturing, transportation, and installation of large-scale systems by streamlining processes and enhancing transport, replacement, and assembly efficiency. This paper introduces a topology optimization method specifically for cantilever beam structures, to minimize structural flexibility and optimize frequency by determining the optimal material distribution under given loads and constraints. The study explores continuum periodic structures, examining the effects of material properties, optimization parameters, and boundary conditions on the outcomes. Various aspects of periodic optimization design, such as structural configuration, connections, and layout, are also investigated. Through the application of topology optimization using SolidWorks and Ansys, the experimental results validate the method’s effectiveness in enhancing structural performance and material utilization. This research presents a systematic approach and highlights the practical potential of designing periodic structures.

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 and optimization of a novel patient-specific subperiosteal implant additively manufactured in yttria-stabilized zirconia

ObjectiveTo design a patient-specific subperiosteal implant for a severely atrophic maxillary ridge using yttria-stabilized additively manufactured zirconia (3YSZ) and evaluate its material properties by applying topology optimization (TO) to replace bulk material with a lattice structure. MaterialsA contrast-based segmented skull model from anonymized computed tomography data of a patient was used for the initial anatomical design of the implant for the atrophic maxillary ridge. The implant underwent finite element analysis (FEA) and TO under different occlusal load-bearing conditions. The resulting implant designs, in bulk material and lattice, were evaluated via in-silico tensile tests and 3D printed. ResultsThe workflow produced two patient-specific subperiosteal designs: a) an anatomically precise bulk implant, b) a TO lattice implant. In-silico tensile tests revealed that the Young’s modulus of yttria-stabilized zirconia is 205 GPa for the bulk material and 83.3 GPa for the lattice. Maximum principal stresses in the implant were 61.14 MPa in bulk material and 278.63 MPa in lattice, both tolerable, indicating the redesigned implant can withstand occlusal forces of 125–250 N per abutment. Furthermore, TO achieved a 13.10 % mass reduction and 208.71 % increased surface area, suggesting improved osteointegration potential. SignificanceThe study demonstrates the planning and optimization of ceramic implant topology. A further iteration of the implant was successfully implanted in a patient-named use case, employing the same fabrication process and parameters.

Finite elements for Matérn-type random fields: Uncertainty in computational mechanics and design optimization

This work highlights an approach for incorporating realistic uncertainties into scientific computing workflows based on finite elements, focusing on prevalent applications in computational mechanics and design optimization. We leverage Matérn-type Gaussian random fields (GRFs) generated using the SPDE method to model aleatoric uncertainties, including environmental influences, variating material properties, and geometric ambiguities. Our focus lies on delivering practical GRF realizations that accurately capture imperfections and variations and understanding how they impact the predictions of computational models as well as the shape and topology of optimized designs. We describe a numerical algorithm based on solving a generalized SPDE to sample GRFs on arbitrary meshed domains. The algorithm leverages established techniques and integrates seamlessly with the open-source finite element library MFEM and associated scientific computing workflows, like those found in industrial and national laboratory settings. Our solver scales efficiently for large-scale problems and supports various domain types, including surfaces and embedded manifolds. We showcase its versatility through biomechanics and topology optimization applications, emphasizing the potential to influence these domains. The flexibility and efficiency of SPDE-based GRF generation empowers us to run large-scale optimization problems on 2D and 3D domains, including finding optimized designs on embedded surfaces, and to generate design features and topologies beyond the reach of conventional techniques. Moreover, these capabilities allow us to model and quantify geometric uncertainties on reconstructed submanifolds, such as the interpolated surfaces of cerebral aneurysms provided by postprocessing CT scans. In addition to offering benefits in these specific domains, the proposed techniques transcend specific applications and generalize to arbitrary forward and backward problems in uncertainty quantification involving finite elements.

Topology Optimization of Structural Drive-Train Component of an Electric Driven Vehicle for Additive Manufacturing

Additive Manufacturing (AM) is an emerging technology and an important alternative to conventional manufacturing methods as it enables the production of lighter parts that are potentially more durable. In this context, the design for additive manufacturing (DFAM) has been drawing a considerable amount of attention mainly in the aerospace, and automotive industries as well as in academia. On the other hand, the ability of additive manufacturing to manufacture complex topology is often the outcome of topology optimization, which makes topology optimization a good design tool for additive manufacturing. The main objective of the present work is to redesign a structural component of the drivetrain of the Shell Eco-Marathon vehicle, with the use of Altair Inspire™, an industrial generative design tool, by application of Topology Optimization for Additive Manufacturing aiming mass reduction and does not cover the print process.

Dynamically configured physics-informed neural network in topology optimization applications

The integration of physics-informed neural network (PINN) and topology optimization (TO) is an attractive issue because PINN can avoid the prohibitive data acquisition of solving forward problems compared to traditional machine learning. To enhance the efficiency of this integrated optimization framework, a dynamically configured PINN-based topology optimization (DCPINN-TO) method is proposed in conjunction with an active sampling strategy. The DCPINN comprises two sub-networks with distinct training costs, capable of dynamically adjusting the trainable parameters based on the optimization state of TO. Moreover, the active sampling strategy selectively samples collocations based on the pseudo-densities, which can significantly reduce training costs by decreasing the number of input collocations. Additionally, the Gaussian integral is used to calculate the strain energy of elements to decouple the mapping of the material at the collocations. The proposed method is extended to various scenarios, including those with high resolution, multiple loads, and displacement constraints. Its efficiency and generalization are validated by several illustrative examples. Furthermore, the accuracy of DCPINN versus finite element analysis-based TO (FEA-TO) was also investigated.

A novel quasi-smooth tetrahedral numerical manifold method and its application in topology optimization based on parameterized level-set method

In this paper, a novel quasi-smooth tetrahedral numerical manifold method (NMM) and its two-dimensional (2D) counterpart are proposed. A new topology optimization method is established by combining the quasi-smooth manifold element (QSME) with the parameterized level set method (PLSM). The QSME introduces an innovative displacement function characterized by high accuracy and high-order continuity, effectively addressing the “linear dependence” (LD) issue inherent in traditional high-order NMM. To integrate QSME and PLSM, the corresponding optimization formulations and sensitivity analyses are provided. In order to fully utilize advantages of this novel quasi-smooth NMM and the PLSM, an element subdivision technique based on model recognition is proposed to accurately capture the physical boundaries. Additionally, a volume fraction update method based on element refinement is proposed. Taking advantage of the characteristics of the PLSM, a structure visualization method based on the sign distance function is developed to accurately describe curve boundary. This method allows for precise visualization of optimized structures. This study verifies high efficiency of the QSME-based PLSM for minimum compliance topology optimization problems in both 2D and 3D structures. Some representative structural optimization examples are tested to demonstrate effectiveness of the proposed method in both 2D and 3D problems, especially in complex design domain.

Finite Elements Analysis and Topology Optimization of Parking Brake Lever and Ratchet

Topology optimization is known as one of the basic categories of structural optimization. Topology optimization is received increasing attention in many engineering disciplines. Topology optimization contributes to minimizing emissions and environmental effects by increasing material utilization efficiency and manufacturing sustainability. The mechanical parking brake is still used in many vehicles. This study aims to contribute to the reduction in vehicle weight by applying topology optimization. In addition, it also purposes to promote sustainability in manufacturing by reducing material usage and energy consumption. A CAD model was created by considering the existing mechanism element dimensions. The parking brake lever mechanism component was evaluated using topology optimization and finite element analysis methods. Static analyses were performed using a finite element analysis program. The results of this analysis were used as input data for topology optimization. In the topology optimization, the response constraint mass was increased by 5 increments from 50% to 95%. As a result, the maximum equivalent (von Mises) stress for the parking brake lever is 230,29 MPa, and for the ratchet is 11,559 MPa. The maximum total deformation value for the brake lever is 0,95853 mm and for the ratchet is 0,0079482 mm. The parking brake lever mass decreased by 18,48% from 0.27751 kg to 0.22622 kg. The ratchet mass decreased from 0.095042 kg to 0.061911 kg by 34.85%.

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.

Topology optimization for rigid and compliant hybrid mechanisms

This paper proposes a topology optimization method integrating the variable trajectory constraints to design rigid and compliant hybrid mechanisms. The variable trajectory constraints are distributed in the design domain and are uniformly modeled by nonlinear spring model. Each of the variable trajectory constraints has an active or inactive state and different states map various mechanical properties of the nonlinear springs. The nonlinear relation between force and displacement of the spring is formulated. A new group of design variables denoting the states of the springs is introduced into the traditional density-based topology optimization model. The design variables representing the element density of the continuum structure and the states of the variable trajectory constraints are uniformly penalized to avoid intermediate values in order to obtain a physically realizable mechanism. Sensitivity analysis is performed by the adjoint equation method. To demonstrate the versatility and the generality of the proposed method, the typical numerical examples including linear, spline and circular trajectory constraints were implemented. The numerical comparisons between the nonlinear spring model and the actual trajectory constraints verify the accuracy. The proposed method expands the application of topology optimization and can be extensively employed to design the mechanisms integrating both the compliant members and rigid parts.

Application of Topology Optimization as a Form-Finding Method in Architectural Design, A Case Study: Pardisan Urban Footbridge

This paper proposes a framework to integrate Topology Optimization (TO) techniques into the architectural design by presenting a case study for the design of an urban footbridge. TO methods have gained popularity in several industrial sectors thanks to manufacturing and computational technology advancements. However, their applicability in architectural design could be improved by the indeterminacy of the final shapes produced by TO and their correlation with the initial design parameters. The unique form of the footbridge and its structural elements make it a suitable candidate for this study. The paper further outlines the design and implementation of the framework, including the application of TO and the subsequent refinement of the resulting form to meet the project’s functional and aesthetic requirements.

Topology optimization of modular structures with multiple assemblies and applications to airborne shelves

This work is devoted to the aeronautical application of topology optimization for modular structures with multiple assemblies that consist of repeated standard modules and optional reinforcements. These kinds of structures are widely used owing to their transportability, reconfigurability, low manufacturing and service costs. In this work, the design of airborne shelves with modular structures characterized by the standard module configuration is formulated for the first time as a topology optimization problem of multiple assemblies and multiple load cases subjected to the volume constraint. It is shown that the weighted compliance design of multiple assemblies is a compromising solution compared to the optimization result of each individual assembly of standard modules. Meanwhile, the performance of optimized airborne shelves with the modular structures can effectively be ameliorated with the help of reinforcements.

Blended structural optimization of steel joints for Wire-and-Arc Additive Manufacturing

Metal Additive Manufacturing, and in particular Wire-and-Arc Additive Manufacturing (WAAM) has proved to be a great and efficient alternative to the common subtractive manufacturing processes to realize complex-shape members and connections for construction. With reference to complex spatial structures such as gridshells, the connections play a crucial role both in the design and the construction processes. Novel computational design tools allow designers to conceive optimized joint solutions while minimizing the material use, resulting in difficult geometries to be fabricated with conventional methods. The present work aims at providing an innovative integrated design and fabrication framework to efficiently apply topology optimization algorithms to improve the efficiency of steel joints in complex spatial structures. The framework is based on the so-called “blended” structural optimization approach aimed at incorporating manufacturing constraints, basic principles of conceptual structural design and structural requirements into topology optimization to design ready-to-fabricate complex steel joints. The designs are suitable for fabrication with the WAAM process. The approach is applied to a case study to re-design the joint connections of the world’s renowned British Museum gridshell rooftop structure. From a catalogue of various designs for each unique joint, one selected design is optimized and then checked for structural requirements in terms of strengths and stiffness. Then the optimized joint is validated for fabrication with WAAM process.

Topology optimization and numerical analysis of cold plates for concentrating photovoltaic thermal management

Continuous advances in concentrating photovoltaic (CPV) panel efficiency are increasingly affected by cell temperature. Improving PV panel cooling performance is critical. This application optimizes the internal flow channel structure of PV panel cooling systems using topology optimization techniques like multi-objective and multi-stage optimization with penalty factors. Three-dimensional CFD simulation is used to compare the heat transfer performance of topology optimized channel cooling configuration and traditional straight channel cooling configuration for photovoltaic panel systems. Effects of inlet flow rates, concentration ratios, and other parameters on cooling performance are investigated. Results show the topology optimized flow channel configuration has better cooling than the straight channel. At different concentration ratios, the solar cell temperature reduces 13.85%–23.45%. The optimized application also has lower inlet and outlet pressure drops for the same operating conditions, requiring less external power. Compared to the straight channel, the topology optimized flow channel increases net PV system output power 3.00%–19.37% at different concentration ratios. Applying topology optimization provides new ideas for optimizing PV cooling system designs.

Lightweight design of Knee-Ankle-Foot Orthotic Devices using Voronoi patterns for Additive Manufacturing

Traditionally fabricated knee-ankle-foot orthosis (KAFO) device that is used to aid in the mobility user is uncomfortable. Problems such as weight and enclosure in almost all the part of the leg make it strenuous and humid for the user to wear for a long time. Furthermore, in the traditional production method, it can take up to a week to fabricate. The aim of this study is to redesign the knee-ankle-foot-orthosis by using the application of topology optimization in order to reduce the material used on the product and to make it lightweight. The parameters of the KAFO were determined by using indirect method; similar to traditional method. The modelling and analysis of the KAFO is completed by using CAD and CAE software. Optimization of the product is performed by redesigning the shape and applying topology optimization function. It is able to reduce the maximum stress of the product by 22.56% and the volume by 4.33%. Application of the Voronoi pattern further reduces the mass of the KAFO and produces more organic looks to the product. SLS Lisa Pro 3D printer is used to produce the KAFO in a period of less than a week. This prove to be a viable alternative for producing customized KAFO.

Topology optimization of Superhydrophobic Surfaces to delay spatially developing modal laminar–turbulent transition

Super-Hydrophobic Surfaces (SHSs) have been shown to reduce skin friction of an overlying fluid as a consequence of gas pockets trapped within the surface’s microstructure. More recently, they have also been shown capable of delaying laminar–turbulent transition. This article investigates the applicability of topology optimization in designing the macroscopic layout of SHSs in a channel that are able to further delay K-type transition in a spatial setting. Unsteady direct numerical simulations are performed to simulate the transition scenario. This is coupled with adjoint–based sensitivity analysis and gradient based optimization. The optimized designs found through this procedure are capable of moving the transition location further downstream compared to a homogeneous counterpart by inhibiting the growth of secondary instability modes. This article provides the first application of topology optimization to a spatially developing transition scenario.