Structural Optimization Techniques Research Articles

Review on structural optimization techniques for additively manufactured implantable medical devices

Recent developments in additive manufacturing (AM) have led to significant opportunities in the design and fabrication of implantable medical devices due to the advantages that AM offers compared to conventional manufacturing, such as high customizability, the ability to fabricate highly complex shapes, good dimensional accuracy, a clean build environment, and reduced material usage. The study of structural design optimization (SDO) involves techniques such as Topology Optimization (TO), Shape Optimization (SHO), and Size Optimization (SO) that determine specific parameters to achieve the best measurable performance in a defined design space under a given set of loads and constraints. Integration of SDO techniques with AM leads to utmost benefits in designing and fabricating optimized implantable medical devices with enhanced functional performance. Research and development of various lattice structures represents a powerful method for unleashing the full potential of additive manufacturing (AM) technologies in creating medical implants with improved surface roughness, biocompatibility, and mechanical properties. Furthermore, the integration of artificial intelligence (AI) and machine learning (ML) in structural optimization has expanded opportunities to improve device performance, adaptability, and durability. The review is meticulously divided into two main sections, reflecting the predictability of the implant’s internal structure: (a) unpredictable interior topology, which explores topology-based optimization techniques, and (b) predictable inner topology, concentrating on lattice structures. The analysis of the reviewed literature highlights a common focus on addressing issues such as stress shielding, osseointegration enhancement, customization to individual needs, programmable functionalities, and weight reduction in implant designs. It emphasizes significant advances in reducing stress shielding effects, promoting osseointegration, and facilitating personalized implant creation. The review provides a detailed classification of optimization methods, with each approach scrutinized for its unique contribution to overcoming specific challenges in medical implant design, thus leading to more advanced, effective, and patient-oriented implantable devices.

Topology Optimization using Nonlinear Finite Element Analysis

Topology optimization is a structural-mechanical investigation that structures optimization function values in an optimization iteration. Topology optimization with nonlinear static behavior is difficult due to several design considerations. Due of significant integrate distortion, low-density finite elements provide significant numerical challenges in the prevailing element density focused topology planning taking nonlinear dynamics under factor. Iterative procedures are used in the Bi-directional Evolutionary Structural Optimization (BESO) technique for reducing waste from a structure while concurrently adding efficient material using a finite element-based topology optimization strategy. Integrating the fully-connected Deep Neural Network (DNN) with the norm-level-set techniques yields a powerful method for optimizing structural topology. Hence, BESO-DNN has been designed spatial optimization of material distribution inside a specified area is the focus of topology optimization is a mathematical approach for minimizing a certain cost function while meeting a set of predefined restrictions. Topology optimization of geometrically non-linear systems is advantageous because of the solutions' lack of intermediate-density components and their great processing efficiency of high-resolution barrier representation can be effective. As a result, topology optimization is ensuring effective and providing fresh and efficient designs, understanding that outcomes needs an integration of credible decision-making, domain knowledge, and numerical analytic skills. The outcome of finite element analysis has to understand and anticipate an object's performance under various physical conditions using mathematical models, and testing.

Ultimate Strength Behaviour and Optimization of Laser-Welded Web-Core Sandwich Panels under In-Plane Compression

In pursuit of more efficient load-bearing solutions for ship deck panels of Very Large Crude Carriers exposed to vertical hull girder bending forces, laser-welded web-core sandwich panels are considered as an alternative to conventional stiffened panels. The primary goal is to identify a lighter steel sandwich structure capable of matching the ultimate strength of conventional counterparts. Utilizing non-linear finite element analysis, the ultimate strength of conventional decks subjected to uniaxial compression is assessed. Attention is then shifted to laser-welded sandwich panels, with a detailed examination of how various design parameters influence their performance. Specifically, four key design aspects of unidirectional vertical webs, including face thickness, web thickness, web height, and web spacing, are optimized to strike a balance between weight and strength through structural optimization techniques combined with the response surface method. Ultimately, a comparison is drawn between the ultimate strength of these innovative steel sandwich panels and their conventional, stiffened counterparts. The findings reveal that web-core sandwich panels, when employed as an alternative, result in a notable reduction in hull weight, thereby showcasing the potential for a more efficient and sustainable approach in the maritime industry.

Design and Optimization of Heat Sinks for the Liquid Cooling of Electronics with Multiple Heat Sources: A Literature Review

This paper presents a detailed literature review on the thermal management issue faced by electronic devices, particularly concerning uneven heating and overheating problems. Special focus is given to the design and structural optimization of heat sinks for efficient single-phase liquid cooling. Firstly, the paper highlights the common presence and detrimental consequences of electronics overheating resulting from multiple heat sources, supported by various illustrative examples. Subsequently, the emphasis is placed on single-phase liquid cooling as one of the effective thermal management technologies for power electronics, as well as on the enhancement of heat transfer in micro/mini channel heat sinks. Various studies on the design and structural optimization of heat sinks are then analyzed and categorized into five main areas: (1) optimization of channel cross-section shape, (2) optimization of channel flow passage, (3) flow distribution optimization for parallel straight channel heat sinks, (4) optimization of pin-fin shape and arrangement, and (5) topology optimization of global flow configuration. After presenting a broad and complete overview of the state of the art, the paper concludes with a critical analysis of the methods and results from the literature and highlights the research perspectives and challenges in the field. It is shown that the issue of uneven and overheating caused by multiple heat sources, which is commonly observed in modern electronics, has received less attention in the literature compared to uniform or single-peak heating. While several design and structural optimization techniques have been implemented to enhance the cooling performance of heat sinks, topology optimization has experienced significant advancements in recent years and appears to be the most promising technology due to its highest degree of freedom to treat the uneven heating problem. This paper can serve as an essential reference contributing to the development of liquid-cooling heat sinks for efficient thermal management of electronics.

A standard benchmarking suite for structural optimization algorithms: ISCSO 2016–2022

Benchmarking is an essential part of developing efficient structural optimization techniques. Despite the advent of numerous metaheuristic techniques for solving truss optimization problems, benchmarking new algorithms is often carried out using a selection of classic test examples which are indeed unchallenging for contemporary sophisticated optimization algorithms. Furthermore, the limited optimization results available in the literature on new test examples are usually not accurately comparable. This is typically due to the lack of infromation about the performance of the investigated algorithms and the inconsistencies between the studies in terms of adopted test examples for benchmarking, optimization problem formulation, maximum number of objective function evaluations and other similar issues. Accordingly, there exists a need for developing new standard test suites composed of easily reproducible challenging test examples with rigorous and comparable performance evaluation results of algorithms on these test suites. To this end, the present work aims to propose a new baseline for benchmarking structural optimization algorithms, using a set of challenging sizing and shape optimization problems of truss structures selected from the international student competition in structural optimization (ISCSO) instances. The most recent six structural optimization examples from the ISCSO are tackled using a representative metaheuristic structural optimization algorithm. The statistical results of all the optimization runs using the proposed benchmarking suite are provided to pave the way for more rigorous benchmarking of structural optimization algorithms.

Topological optimization design on constrained layer damping treatment for vibration suppression of thin-walled structures via improved BESO method

In this paper, an improved bi-directional evolutionary structural optimization (BESO) technique is proposed, to investigate topological optimization design on constrained layer damping (CLD) treatment for vibration suppression of experiment rack backplane. First, the optimization model for vibration reduction of CLD treated backplane is established, with volume fraction of CLD material as constraint condition, and the maximization of weighted value of the first four order modal loss factors of the structure as objective function. An improved evolutionary rate considering the CLD element sensitivity coefficient of variation of each iteration is presented to increase optimization efficiency. Then, the BESO with improved evolutionary rate is utilized to search the optimal CLD layout of the experiment rack backplane. CLD layouts of three optimization schemes with different volume fraction of CLD material are obtained, and are highly consistent with the stress distribution of the backplane viscoelastic layer, which verifies the rationality of the optimization results. Visualization of iterative optimization process, including elements removal/addition and dynamic change of CLD elements sensitivity in each iteration, is demonstrated, respectively. Further, the effect of improved evolutionary rate on optimization process is discussed. Compared with the conventional BESO method, the improved BESO technique can not only obtain a more reasonable optimized CLD layout, but also improve the optimization efficiency and accuracy. Finally, the validity of the optimized CLD layout is analyzed from three following aspects: natural frequency, modal loss factor and vibration response under order excitation. Numerical and experimental results show that the proposed BESO technique is effective and efficient in the application of CLD material, and the small amount of CLD material can be retained under the premise of ensuring damping.

Synthesis of Compliant Parallel Mechanisms Using an Improved Beam-Based Method with the Optimization of Multiple Resonant Modes

This paper proposes an improved beam-based method to synthesize a compliant parallel mechanism (CPM) with multiple degrees of freedom (DoFs). The proposed method utilizes a structural optimization technique to synthesize a three-legged CPM with a single-beam structure constructed by two perpendicular segments in each leg to achieve the desired DoFs and fully decoupled motion. In addition, an objective function is proposed to optimize the primary resonant frequencies in actuating directions to targeted values to achieve the desired dynamic behaviors. A 4-DoF CPM, with one translation and three rotations, is synthesized using the improved beam-based method and all of the primary resonant frequencies are optimized to the targeted values. The 4-DoF CPM prototype is fabricated monolithically and evaluated experimentally in terms of its mechanical characteristics, workspace, and resonant modes. The obtained results show that the experimental stiffness and dynamic properties agree with the predictions. In particular, the prototype has good motion decoupling capability, as reflected by the high stiffness ratios of more than 500 between the non-actuating and actuating directions; the large workspaces of up to 4.0 mm and 7.2° for the translation and rotations, respectively; and the resonant frequencies being close to the targeted ones. In addition, the highest deviations between the predicted and experimental results are 9.49% and 9.13% for the stiffness and dynamic behaviors, respectively, demonstrating the correctness and effectiveness of the proposed method.

Sensitivity-enhanced Fabry-Perot interferometric fiber-optic microphone using hollow cantilever.

Transducer components are crucial in optimizing the sensitivity of microphones. Cantilever structure is commonly used as a structural optimization technique. Here, we present a novel Fabry-Perot (F-P) interferometric fiber-optic microphone (FOM) using a hollow cantilever structure. The proposed hollow cantilever aims to reduce the effective mass and spring constant of the cantilever, thereby enhancing the sensitivity of the FOM. Experimental results demonstrate that the proposed structure outperforms the original cantilever design in terms of sensitivity. The sensitivity and minimum detectable acoustic pressure level (MDP) can reach 91.40 mV/Pa and 6.20 µPa/Hz at 1.7 kHz, respectively. Notably, the hollow cantilever provides an optimization framework for highly sensitive FOMs.

Multidisciplinary topology and material optimization approach for developing patient-specific limb orthosis using 3D printing

PurposeThis study aims to explore the potential benefits favoring the adaptation of structural optimization techniques in the additive manufacturing (AM) of medical utilities to meet the repetitive demand for functionally precise customized orthoses. Irregularities encountered during the conventional treatment of tendon injuries can be eschewed using advanced structural simulation in design and innovative splint fabrication using 3D printing.Design/methodology/approachA customized mallet finger splint designed from 3D scans was subjected to ANSYS topological simulation comprising multi-level weight reduction to retain optimal mass (100%, 90%, 80%, 70% and 60%). A batch of the four typical 3D printing materials was chosen to conduct a comparative mechanical and thermal stress analysis, facilitating the selection of the optimal one for fabricating functionally adaptive splints. Assurance of structural safety was accomplished through the experimental validation of simulation results against the testing data set of ASTM D695 and ASTM D638 Type-1 specimens over a universal testing machine (UTM). Fused deposition modeling (FDM) 3D printing processed the optimized splint fabrication to assist evaluation of weight reduction percentage, fitting aesthetics, appearance, comfort, practicality and ventilation ease at the user end.FindingsAM efficacy can efficiently execute the design complexity involved in the topology optimization (TO) results and introduces rehabilitation practicality into the application. Topologically optimized splint provided with favorable comfort, stiffness and strengthening features, offers ventilation ease and structural stability for customized appliances, with 30.52% lighter weight and 121.37% faster heat dissipation than unoptimized one.Originality/valueThe state of art multidisciplinary optimization featured with structural and material optimization attributes can deliberately meet medical necessity for performance-oriented orthotic devices.

Design and optimization of multi-MW offshore direct-drive wind turbine electrical generator structures using generative design techniques

The use of generative design as an alternative to typical structural optimization techniques opens the door to new methods of manufacturing. In this study, generative design techniques were used as an automated iterative process with an extensive set of control variables and initial models to explore and optimise the stiffness and weight of different configurations for a 3 MW offshore wind turbine electrical generator structure. With this new approach of adding generative design techniques to a structural optimization process, a 4% reduction in structural mass was achieved. The modification in the structural geometry also help to enlarge the machine's operational range with the consequent growth in energy gathering.

Interactive Structural Topology Optimization with Subjective Scoring and Drawing Systems

Topology optimization techniques can create efficient and innovative structural designs by redistributing underutilized materials to the most-needed locations. These techniques are typically performed based purely on structural performance without considering factors like aesthetics and other design requirements. Hence, the obtained structural designs may not be suitable for specific practical applications. This study presents a new topology optimization method, SP-BESO, by considering the subjective preferences (SP) of the designer. Here, subjective scoring and drawing systems are introduced into the popular bi-directional evolutionary structural optimization (BESO) technique. The proposed SP-BESO method allows users to iteratively and interactively create topologically different and structurally efficient solutions by explicitly scoring and drawing their subjective preferences. Hence, users do not need to passively accept the optimization results. A user-friendly digital design tool, iBESO, is developed, which contains four optimizers to simultaneously perform the proposed SP-BESO method to assist in the design exploration task. A variety of 2D examples are tested using the iBESO software to demonstrate the effectiveness of the proposed SP-BESO method. It is found that the combination of parameters used in the scoring and drawing systems controls the formation of final structural topologies toward performance-driven or preference-driven designs. The utilization of the proposed SP-BESO method in potential practical applications is also demonstrated.

A Quantum Monte Carlo Study of the Structural, Energetic, and Magnetic Properties of Two-Dimensional H and T Phase VSe2.

Previous works have controversially claimed near-room-temperature ferromagnetism in two-dimensional (2D) VSe2, with conflicting results throughout the literature. These discrepancies in magnetic properties between both phases (T and H) of 2D VSe2 are most likely due to the structural parameters being coupled to the magnetic properties. Specifically, both phases have a close lattice match and similar total energies, which makes it difficult to determine which phase is being observed experimentally. In this study, we used a combination of density functional theory, highly accurate diffusion Monte Carlo (DMC), and a surrogate Hessian line-search optimization technique to resolve the previously reported discrepancy in structural parameters and relative phase stability. With DMC accuracy, we determined the free-standing geometry of both phases and constructed a phase diagram. Our findings demonstrate the successes of the DMC method coupled with the surrogate Hessian structural optimization technique when applied to a 2D magnetic system.

Topology optimization of large ultrasonic tools for uniform vibration using density model

The uniform vibration of vibrating tools for ultrasonic welding is important for industrial applications but the design requires considerable know-how due to the nature of the wave phenomena. Topology optimization is a structural optimization technique that achieves the desired objective by controlling the material distribution in the design region including voids. In this study, we propose an objective function that maximizes the amplitude of a specific target point in phase with the input. A uniform vibration is obtained by maximizing the point with the smallest amplitude among multiple target points. Optimization is performed using a commonly used density model, resulting in a vibration distribution with an aligned phase on the output surface. In addition, we perform an eigenvalue analysis of the structure by isosurface extraction to study the frequency error and the deterioration in the uniformity of the assumed vibration mode.

Development of fuel filter cap of comet diesel engine using structural optimization technique and additive manufacturing

As market competition and computational technologies grow, engineering design and development process heavily relies on the computer modelling, simulation and prototype manufacturing to accelerate the development cycles and to save the cost. This article intends to use finite element method as a structural optimization tool and 3D additive manufacturing for manufacturing of prototype to optimize the weight and strength of fuel filter cap of 5HP, 1500 rpm water cooled comet diesel engine within the lesser time cycle. The developed fuel filter cap is manufactured through the stages of pattern making using 3D printing machine, casting of cap by sand casting process, finishing operations and subsequently tested on the comet diesel engine testing set up. The development work has resulted in 48.67% stress reduction and 17.87% reduction in the weight of the fuel filter cap.

The effect of joint stiffness on optimization design strategies for gridshells: The role of rigid, semi-rigid and hinged joints

Structural optimization techniques are becoming popular and effective approaches for the design of constructions, able to support architects and structural designers in the complex process of searching competitive solutions, usually in terms of structural weight, cost and accounting for specific structural/functional requirements. In case of gridshells, the structural weight is strictly related to the susceptibility of the structure to global buckling, which is often the governing design criterion. The susceptibility to global buckling is mainly due to the global stiffness of the structures, primarily related to the stiffness of the joints, to the boundary conditions, and to the presence of imperfections. In this context, the paper presents design strategies based on optimization techniques that specifically take into accounts the presence of semi-rigid, rigid and hinged joints in order to guarantee light solutions safe from global buckling phenomena. In particular, two approaches are proposed: the joint stiffness approach, which considers the gridshell composed by semi-rigid joints, all characterized by the same rotational stiffness, and the rigid/hinged approach, which considers the gridshell composed by most hinged joints, and by a low number of rigid joints arranged in optimal positions. The approaches have been applied to a case study characterized by different boundary conditions, different rise-to-span ratios and also considering both perfect and imperfect shapes. The results of the proposed optimization processes highlight the beneficial effect of a finite value of the rotational stiffness of the joints in the susceptibility of the gridshell to global buckling phenomena, leading to light structural solutions.

OPTIMUM DESIGN OF THERMO-PLUNGER SUPPORT IN COMMERCIAL VEHICLES BY USING STRUCTURAL DESIGN AND FINITE ELEMENT METHODS

This paper focuses on creating an optimum design and development of thermo-plunger parts for commercial vehicles in order to save material, reduce mass and make more sustainable automobiles. In this paper, natural frequency analysis, topology, and topography optimization methods have been used to create a new design for the thermo-plunger part. Thermo-plunger means an electric heater that is used for heating the inside of automobiles effectively and quickly and providing customer thermal comfort. It is positioned in the vehicle body, and its support parts have been developed by structural optimization techniques because there is not enough space in the engine compartment for automatic transmission commercial vehicles. The aim of this study is to make a lightweight and reinforced thermo-plunger support part design. Initially, a draft design was created in 3D model software. After that, topology and topography optimizations were applied on this draft design. At the end of studies, a final optimum support design has been obtained. The final design is 41.1% lighter than the initial design. At the same time, above 50 Hz natural frequency value has been obtained on the final design to avoid resonance problems.

FFT-based Inverse Homogenization for Cellular Material Design

• An FFT-based inverse homogenization approach is proposed for efficiently designing cellular materials. • Rotating architected materials with negative Poisson's ratio are generated. • Architected cellular materials with maximum stiffness and isotropy are sought out. • The inverse homogenization method for scaffold design with specified mechanical performance is validated. Besides constituting components, the properties of composites are highly relevant to their microstructures. The work proposed a fast Fourier transform (FFT)-based inverse homogenization method implemented by the bi-directional evolutionary structural optimization (BESO) technique to explore the vast potential of cellular materials. The periodic boundary condition of self-repeated representative volume elements can be naturally satisfied in the FFT-based homogenization scheme. The objective function of the optimization problem is the specific moduli or the quadratic difference between the effective value and the target, which are obtained in terms of mutual strain energies. Its sensitivity to the design variable, namely the elemental density, is derived from the adjoint variable method and used as the criterion to remove or add material in local elements. Numerical examples show that the proposed method generates a series of architected cellular materials with maximum modulus, negative Poisson's ratio, and specific elasticity tensor. FFT-based homogenization in the method demands less memory usage but has high efficiency. Thus, it can achieve topology optimization of unit cell with one million hexahedral elements. This approach contributes to the extended application of FFT-based homogenization and can guide the microstructure design of mechanical metamaterials. :

Smoothing topology optimization results using pre-built lookup tables

Topology optimization techniques are typically performed on a design domain discretized with finite element meshes to generate efficient and innovative structural designs. The optimized structural topologies usually exhibit zig-zag boundaries formed from straight element edges. Existing techniques to obtain smooth structural topologies are limited. Most methods are computationally expensive, as they are performed iteratively with topology optimization. Other methods, such as post-processing methods, are applied after topology optimization, but they cannot guarantee to obtain equivalent structural designs, as the volume and geometric features may be changed. This study presents a new method that uses pre-built lookup tables to transform the shape of boundary elements obtained from topology optimization to create smoothed structural topologies. The new method is developed based on the combination of the bi-directional evolutionary structural optimization (BESO) technique and marching geometries to determine structural topologies and lookup tables, respectively. An additional step is used to ensure that the generated result meets a target volume. A variety of 2D and 3D examples are presented to demonstrate the effectiveness of the new method. This research shows that the new method is highly efficient, as it can be directly added to the last step of topology optimization with a low computational cost, and the volume and geometric features can be preserved in smoothed topologies. Finite element models are also created for original and smoothed structural topologies to show that the structural stiffness can be significantly enhanced after smoothing.

Strength-based concurrent shape and fiber path optimization of continuous fiber composites

This paper introduces a novel strength-based structural optimization technique capable of concurrent design of shape and fiber path in continuous fiber-reinforced composites. To this end, a higher order function, i.e., the level-set function, is employed to update both shape and fiber placement. The shape evolution relies on a shape sensitivity analysis based on the Tsai–Wu failure criterion. The fiber path evolution depends on the level-set function determined from the shape boundary. A scheme combining the classical level-set method using fixed mesh and a level-set-based mesh evolution method is developed to ensure the efficiency and accuracy of the process. A revision step over fiber orientations along the ridge of the level-set function is introduced to alleviate the local failure index singularity. Manufacturability of the design is further ensured by incorporating a thickness control term, avoiding the appearance of ultra-thin members in the optimized design. The developed scheme is applied to three benchmark examples, showing that the failure index concentration is largely reduced compared with the initial shape, the compliance-based optimized design, and the design with optimized shape but unidirectional fibers.

The parametrized superelement approach for lattice joint modelling and simulation

From large scale structures such as bridges and cranes to small-scale structures such as lattices, mechanical structures today increasingly consist of “tuneable parts”: parts with a simple geometry described by a small set of strongly varying parameters. For example, although a bridge is a macroscale structure with a complex geometry, it is made from simple beams, bolts and plates, all of which depend on spatially varying, geometrical parameters such as their length-to-width ratio. Accelerating this trend is the concurrent improvement of, on one hand, Additive Manufacturing techniques that allow for increasingly complex parts to be manufactured and, on the other, structural optimization techniques that exploit this expanded design space. However, this trend also poses a challenge to current simulation techniques, as for example the Finite Element Method requires large amounts of elements to represent such structures. We propose to exploit the large conformity between parts inside the mechanical structure through construction of semi-analytic “Parametrized Superelements”, built by meshing with solid elements, reduction to a fixed interface and approximation of the reduced stiffness matrices. These new elements can be employed next to standard elements, enabling the simulation of more complex geometries. The technique we propose is applied to lattice structures and provides a flexible, differentiable, more accurate but still efficient way to simulate their elastic response. A net gain in total computation time occurs after simulating more than twenty lattices. As such, the proposed method enables large-scale parameter exploration and optimization of lattice structures for improved energy absorption, mass and/or stiffness.