Integrated Topology Optimization Research Articles

Comparative Analysis of Topology Optimization Platforms for Additive Manufacturing of Robot Arms

Recently, CAD environments have integrated topology optimization (TO) tools, enabling rapid development and manufacturing of parts with optimized mechanical properties. However, different CAD platforms incorporate TO differently, making a comparative analysis necessary. This study aims to systematically compare the efficiency, material usage, and design quality of five commonly used CAD/TO platforms when applied to the topology optimization of a six degrees of freedom robotic arm. The objective is to identify the key differences in how these platforms influence the final design and manufacturing outcomes. Practical validation of results is provided by printing and assembling optimized components into a fully functional robotic arm. Our findings indicate differences in optimization efficiency, material usage, and print time between analyzed platforms. Strengths and weaknesses of each platform are indicated and recommendations for optimization parameters are provided.

An isogeometric approach to dynamic structures for integrating topology optimization and optimal control at macro and micro scales

In the context of active vibration suppression, an integrated topology optimization framework is proposed for the optimal control of dynamic structures. This article formulates a new composite objective function by considering the external harmonic excitations with different excitation frequencies and the complex-valued displacement field. Within the proposed optimal control performance function, the symmetric weighting matrix, the magnitudes of which are related to the importance of the control forces, is integrated into dynamic compliance to serve the state displacement. Utilizing the non-uniform rational B-splines (NURBS) basis functions, the material interpolation model defined at control points is described by the NURBS surface, which is incorporated into the optimization formulation for optimal structural and vibration control design. The sensitivity results are deduced in terms of the pseudo-densities and the corresponding weights at control points from both macro and micro perspectives of structural dynamics. To demonstrate the effectiveness of the integrated topology optimization of dynamic structures at macro and micro scales, several numerical examples, including the topology optimization of solid beams in plane stress and Mindlin plates with 3D microstructures, are provided and discussed in terms of structural shape and topology, frequency response curve, and modal displacement.

Heat spreading effect on the optimal geometries of cooling structures in a manifold heat sink

Embedded cooling is a promising solution to address thermal challenges of power electronics. The present work investigates heat spreading effect on the optimal geometries of cooling structures within a single-phase manifold heat sink in laminar regime by integration of topology optimization (TO) and Bayesian optimization (BO). Such integration is for the manual parameter tuning issue in the density-based TO of conjugate heat transfer, and the TO process is accelerated by using a dual-level simulator and the optimality criteria optimizer combined with the stochastic gradient descent method. The heat spreading effect significantly alters the optimal geometries, due to the change of thermal resistance constitutions. Physical analyses on the BO-TO-generated geometries give two guidelines for improving the cooling structures here: (a) Heat source-coolant distance should increase properly for narrow heating area and small Biot number; (b) Highly-thermal-conductivity solid can be filled into low-velocity regions directly connecting to hot area. As an example, a fabrication-friendly cooling structure is devised in the case of concentrating heating following these guidelines, avoiding the computationally-expensive optimization process and the over-complicated geometries. The CFD simulations show this design can significantly reduce the thermal resistance with minor increase of pressure loss as the Reynold number from 50 to 300.

A hybrid CAD/CAE/CAM project‐based laboratory framework integrating topology optimization and laser powder bed fusion for engineering education

AbstractIn the era of Industry 4.0, laser‐based additive manufacturing (LBAM) has gained substantial momentum in the production of complex lightweight structures in several domains such as aerospace, civil, and biomedical engineering. The increasing demand for consistent and precise manufacturing processes has urged the manufacturing industry to consider the coupling of topology optimization (TO) and laser powder bed fusion (LPBF) in the design of sophisticatedly novel topologies that are unattainable through traditional processes. Notably, this union has demonstrated a highly efficient and productive capability toward the manufacturing industry. In line with this accelerated pace, engineering programs within universities exert significant effort to revise and update their engineering curriculum design to incorporate emerging manufacturing technologies providing students with skills that are aligned with the actual industrial context. In this article, a computer‐aided design (CAD)/computer‐aided engineering (CAE)/computer‐aided manufacturing (CAM) project‐based laboratory framework is proposed combining TO and LPBF exploiting a simulation‐based environment integrating CAD, CAE, and CAM. The structure of the proposed CAD/CAE/CAM design methodology is revisited to discern the added value of the newly developed framework and its particularity in assisting aerospace engineering students to meet industrial expectations. A new CAD/CAE/CAM project‐based laboratory framework has been developed integrating TO and LPBF using advanced engineering tools within the aerospace engineering education.

Topology Optimization of an Aerospace Bracket: Numerical and Experimental Investigation

The integration of topology optimization into additive manufacturing provides unmatched possibilities for the sustainable manufacturing of lightweight, intricate, custom parts with less material at a lower production time and cost. This study aims to apply and benchmark topology optimization methods, in conjunction with additive manufacturing, to enhance the design of functional components used in aerospace applications, while simultaneously providing an experimental verification and comparative analysis of such optimization techniques. This approach was applied to an industrial bracket used in aerospace applications, which was optimized with the aim of weight reduction without sacrificing its original mechanical stiffness. A density-based technique and a level-set method were used to perform the analysis and optimization, whereas fabrication was performed using fused deposition modeling. Finally, a compression and tensile testing machine was employed for the testing, verification, and comparison of the exhibited mechanical strength for the whole range of printed parts, under the same load conditions. The optimized designs achieved a 20% weight reduction while maintaining the compression displacement of the initial components at the given load. The achieved results demonstrate that topologically optimized components can significantly enhance the design of real-life components, such as those used in the weight-sensitive industrial applications considered in this work.

An integrated topology optimization method including manufacturing constraints for 3D printed fiber-reinforced concrete structures

The difficulty of achieving overall optimization design of concrete materials, structures, and performances has always been a bottleneck restricting the safety and comprehensive performance improvement of civil engineering structures throughout their life cycle. Driven by digital design, 3D concrete printing (3DCP) with a high degree of freedom and flexibility can achieve accurate distribution of materials and flexible construction, which is a favorable guarantee for the high-quality construction of high-performance structures. In this paper, an integrated design method of material-process-performance is developed by introducing both concrete material properties and printing process parameters into the optimization design. The nodal volume fraction and material orientation are selected as design variables to obtain lightweight structures, meanwhile the tensile capacity enhanced through fiber alignment is fully utilized. The minimum size control combined with the central axis algorithm is introduced to achieve integer multiple of nozzle size and also to improve the manufacturing quality. Structural compliance and stress are adopted as the objective function and constraint to improve structural stiffness and strength, respectively. Test results show that the strength-to-weight ratio of the optimized beam is 42 % higher than that of the cast-in-place one, and therefore the effectiveness of the proposed method is validated.

Topology optimized novel additively manufactured heat sink: Experiments and numerical simulations

Topology optimization is an effective method for designing high-performance heat sinks with reduced weight and size. The integration of topology optimization with additive manufacturing technology can effectively leverage the benefits of topology optimization to enhance the design process. In this study, nine types of heat sinks are designed by density-based topology optimization and fabricated via the laser powder bed fusion technology. Three different optimization goals including the minimization of temperature variance, thermal compliance and the temperature difference between the heat source surface and side surfaces are considered in design configurations. We develop a high-fidelity computational fluid dynamics model to investigate the velocity and temperature distributions of the cooling fluid around various fins, and conduct the corresponding experiments to test the thermal performance of the developed heat sinks. The results show that topology optimized fins can significantly enhance heat transfer capability of the heat sink. As the cooling fluid velocity increases from 0.3 m/s to 1.9 m/s, topology optimized heat sinks exhibit superior thermal performance with the highest heat transfer coefficient of 305 W·m−2·K−1 and the highest Nusselt number of 202. This research proves the powerful capability of laser powder bed fusion technology on manufacturing novel peculiar fins and provides a theoretical and experimental guidance for novel compact heat sink in the future designs.

Fixture Layout Optimization of Sheet Metals by Integrating Topology Optimization into Genetic Algorithm

Manufacturing process accuracy is obtained by proper arrangement of fixture elements known as fixture layout. A N-3-2-1 method is used for sheet metals which requires (N + 3) fixture elements to constrain deformation normal to surface. Genetic Algorithm (GA) is used for fixture layout optimization, but it requires high computational effort due to large number of populations. A new method for fixture layout optimization is proposed by integrating topology optimization into GA. In this method, topology optimization reduces the population for GA. The objective function is to reduce the population for GA and minimize total deformation normal to the plane of workpiece. The proposed approach comprised three stages. In the first stage, the initial number of clamps are determined. In the second stage, the population is reduced for GA and the feasible area of clamps are identified using the topology optimization technique. In the third stage, the number and position of clamps, earlier identified in stage one, are optimized using GA. Two different case studies are solved by varying applied load position and magnitude. The proposed method results 47.5% and 65% decreases in the population for subcase 1 and subcase 2, respectively. However, in subcase 3 and subcase 4 the population reduced was 90% and 80%, respectively. The 25% of reduced population is used as the convergence criteria. Similarly, total deformation normal to the plane is reduced in each subcase, with the highest reduction of 86.31% in subcase 1 and lowest of 59.85% in subcase 4. The experiment is performed on the first case study to validate results. This concludes that the proposed method is valid and that optimal results are found.

Topology optimization methods for additive manufacturing: a review

Topology optimization is widely recognized for its ability to determine the best distribution of material in a structure to optimize its stiffness. This process often leads to creative configurations that produce complicated geometries challenging to construct using traditional techniques. Additive manufacturing has recently received a lot of interest from academics as well as industry. When compared to traditional methods, additive manufacturing or 3D printing offers considerable benefits (direct manufacture, time savings, fabrication of complex geometries, etc.). Recently, additive manufacturing techniques are increasingly being employed in industry to create complex components that cannot be produced using standard methods. The primary benefit of these techniques is the amount of creative flexibility they give designers. Additive manufacturing technology with higher resolution output capabilities has created a wealth of options for bridging the topology optimization and product application gap. This paper is a preliminary attempt to determine the key aspects of research on the integration of topology optimization and additive manufacturing, to outline topology optimization methods for these aspects with a review of various scientific and industry applications during the last years.

Development of the Customized Asymmetric Fixation Plate to Resist Postoperative Relapse of Hemifacial Microsomia Following BSSO: Topology Optimization and Biomechanical Testing.

Hemifacial microsomia (HFM), one of the most common congenital facial anomalies, was usually treated with the bilateral sagittal split osteotomy (BSSO) procedure to correct the asymmetric appearance and malocclusion of the mandible. However, the frequent post-operative relapse incidents would lead to the restoration of the mandibular segment to its preoperative position and failure of the BSSO procedure. In this study, a customized asymmetric fixed plate (CAF plate) was developed to resist relapse due to hemifacial microsomia occlusal forces and the different muscular traction forces on both sides of the mandible. For the actual HFM case in this study, the reconstructed mandibular segmental bone model was fixed using BSSO with a rectangular plate (the original CAF plate appearance) in the topology optimization analysis. With the topology optimization technique, the CAF plate was designed with a lightweight profile and excellent structural strength in consideration of the HFM asymmetrical muscle traction and occlusal force. Using biomechanical simulations, the von-Mises stress and CAF plate mandibular segment displacement and the miniplate were compared to evaluate which had superior relapse resistance. In the in-vitro biomechanical test, a fatigue force of 250,000 cycles and a constant muscle traction force were applied to the HFM mandibular model, which was fixed with the CAF plate fabricated using metal 3D printing (selective laser melting, SLM) to obtain the mandibular segment displacement as a relapse assessment. The topology optimization analysis showed that the CAF plate has the best characteristics, light weight and structural strength with 30% volume retention. The biomechanical analysis showed that the maximum von Mises stress of the mini-plate was 2.71 times higher than that of the CAF plate. The relapse displacement of the mandibular segment fixed with the mini-plate was 1.62 times higher than that fixed with the CAF plate. The CAF plate ability to resist relapse was confirmed by the biomechanical testing results so that only 0.29mm of recurrence displacement was observed in the mandibular segment. The results indicated that the CAF plate structural strength and resistance to relapse was significantly better than that of the mini-plate. This study developed a customized asymmetric fixation plate for hemifacial microsomia, integrating topology optimization, metal 3D printing, and in vitro biomechanical testing to resist occlusal forces and differential muscle traction on both sides of the mandible to reduce relapse and improve fixation stability.

Loosely coupled reflective impedance metasurfaces: Precise manipulation of waterborne sound by topology optimization

Waterborne acoustic metasurfaces (WAMs), unlike airborne acoustic metasurfaces, generally suffer from nonlocal interaction induced by the strong fluid–solid coupling. Unpredictable parasitic scattering is usually caused by nonlocal vibration coupling between solid units, thereby interfering with the prescribed sound control. In this work, we propose a loosely coupled reflective impedance WAM to realize precise manipulation of waterborne sound. A function–structure integrated topology optimization framework involving surface impedance model and vibration coupling restriction is systematically established to inversely design WAMs. Successful individual design of lossy units with multiple inclusions is realized by weakening vibration coupling of solids through local resonance. Various customized waterborne sound fields, including extraordinary beam steering with steep deflection, propagating-to-evanescent mode conversion and super-resolution near-field focusing, have been successfully implemented and demonstrated. Good agreements between the theoretical and simulated results are observed, thereby validating the feasibility and effectiveness of the design strategy. In addition, inverse-design WAMs show very good robustness to the operating frequency, incident angle and geometrical shape. Deep-subwavelength precise manipulation of waterborne sound is further achieved by the WAM with the thickness of λ/40. The excellent performances of WAMs result from the precisely customized surface impedance distribution. The proposed strategy opens the door to practical applications of metasurfaces in the delicate and complex waterborne sound control.

Topology optimization of vapor chamber internal structures consisting of evaporator and condenser

This paper studies the integrated topology optimization of vapor chambers consisting of evaporator and condenser. Firstly, the patterning is regarded as a fundamental access-maximization problem and classified into two general categories: (1) “area to point” (AP) flow problem for condenser wick design and (2) “area to line” (AL) flow problem for evaporator wick design. Then, the branch-patterned disc with first order assembly of flow channels is deduced, where the design domain is divided into 18 identical sectors for both condenser and evaporator. A fluid dynamic model is established to analyze the flow characteristics of the working fluid driven by capillary force. Based on this, a generative topology optimization model with a bifurcation rule is developed to produce the hierarchical capillary flow channels that minimize the global resistance for AP flow problem and AL flow problem, respectively. Unlike the commonly used Eulerian framework for topology optimization, the generative topology optimization used in this paper is carried out essentially in a Lagrangian framework, where capillary flow channels undergoing changes of volume, of positions, of inclined angles and of shapes are described by a set of parameterized level-set surfaces which can move, deform, overlap and merge freely upon the underlying FEM grids. The generated constructal wick structures exhibit dichotomous, hierarchical and branching characteristics. Numerical comparisons show that the new wick structures can contribute to the vapor chambers with better thermal performance.

A review on additive manufacturing and topology optimization process for weight reduction studies in various industrial applications

Topology optimization is evolution of generating optimized components in the view of various design parameters. Creating optimal designs during the design process reduces the cost and eliminates design failures. Additive manufacturing is the assuredly severance manufacturing technology when compared with the conventional machining processes, where the product is built layer by layer by using the complex CAD models. The integration of topology optimization with additive manufacturing technologies develops lightweight parts by reducing assembling of number of parts which in return reduces cost and saves material. This review article mainly focuses on expeditious developments in additive manufacturing using topology optimization techniques. For using topology optimization in AM technologies different software’s are used by using different AM constraints. Challenges in this type of integration depend on design approach, material structure and different process parameters. The article reviews about the different considerations of constraints in topology and topography optimizations in various applications of automotive, aerospace& aircraft applications. The optimization algorithm is based on gradient based using optistruct software which uses solid tetrahedron meshing element. The resulting topology under different considerations are developed using optistruct software for 3D printing.

Topology Optimization of Self-Supporting Structures for Additive Manufacturing with Adaptive Explicit Continuous Constraint

The integration of topology optimization (TO) and additive manufacturing (AM) technologies can create significant synergy benefits, while the lack of AM-friendly TO algorithms is a serious bottleneck for the application of TO in AM. In this paper, a TO method is proposed to design self-supporting structures with an explicit continuous self-supporting constraint, which can be adaptively activated and tightened during the optimization procedure. The TO procedure is suitable for various critical overhang angles (COA), which is integrated with build direction assignment to reduce performance loss. Besides, a triangular directional self-supporting constraint sensitivity filter is devised to promote the downward evolution of structures and maintain stability. Two numerical examples are presented; all the test cases have successfully converged and the optimized solutions demonstrate good manufacturability. In the meanwhile, a fully self-supporting design can be obtained with a slight cost in performance through combination with build direction assignment.

From Topology Optimization to Complex Digital Architecture: A New Methodology for Architectural Morphology Generation

Owing to the capacities of generating structural configuration with both reasonable mechanical properties and high material utilization, topology optimization has been widely adopted in engineering design. Although numerous architects have tried to apply topology optimization tools to assist architectural morphology design in practical projects, topology optimization, like other quantitative analysis techniques, has not been systematically incorporated into the architectural morphology design. In this study, by integrating topology optimization toolsets and parametric design theory, combined with multiattribute decision-making analysis, a design method is proposed that could efficiently obtain several architectural structural architectural morphologies with both structural rationality and aesthetic rules and complete the evaluation and performance ranking of alternatives. In this study, the essential architectural application scenarios are divided into surface application scenarios and volumetric application scenarios, and the possible variation range of topology optimization parameters of architectural application scenarios is defined. By iteratively adjusting the influence parameters, diverse results of structural morphology are obtained. It is found that small changes in optimization parameters will bring great differences in topological results. Such a sensitive relationship can be utilized to generate a set of rational topological structures, and these topological results can be regarded as alternatives for architectural morphology design. For the performance evaluation and ranking analysis of alternatives, the application of FANP-TOPSIS multiattribute decision-making model is put forward in this study. The case study shows that this decision-making analysis model is efficient, convenient, and applicable in the architectural morphology design. The results of this study can provide new ideas and key references for scholars and architects in the field of architecture to explore the process and method of architectural morphology design and other related issues.

A Systems Approach of Topology Optimization for Bioinspired Material Structures Design Using Additive Manufacturing

Bioinspired design has been applied in sustainable design (e.g., lightweight structures) to learn from nature and support material structure functionalities. Natural structures usually require modification in practice because they were evolved in natural environmental conditions that can be different from industrial applications. Topology optimization is a method to find the optimal design solution by considering the material external physical environment. Therefore, integrating topology optimization into bioinspired design can benefit sustainable material structure designers in meeting the purpose of using bioinspired concepts to find the optimal solution in the material functional environment. Current research in both sustainable design and materials science, however, has not led to a method to assist material structure designers to design structures with bioinspired concepts and use topology optimization to find the optimal solution. Systems thinking can seamlessly fill this gap and provide a systemic methodology to achieve this goal. The objective of this research is to develop a systems approach that incorporates topology optimization into bioinspired design, and simultaneously takes into consideration additive manufacturing processing conditions to ensure the material structure functionality. The method is demonstrated with three lightweight material structure designs: spiderweb, turtle shell, and maze. Environmental impact assessment and finite element analysis were conducted to evaluate the functionality and emissions of the designs. This research contributes to the sustainable design knowledge by providing an innovative systems thinking-based bioinspired design of material structures. In addition, the research results enhance materials knowledge with an understanding of mechanical properties of three material structures: turtle shell, spiderweb, and maze. This research systemically connects four disciplines, including bioinspired design, manufacturing, systems thinking, and lightweight structure materials.

TopADD: a 2D/3D integrated topology optimization parallel-computing framework for arbitrary design domains

TopADD: a 2D/3D integrated topology optimization parallel-computing framework for arbitrary design domains

Evaluating Post Machining Process of 3D Printing Topology Optimization

There is significant interest today in additive manufacturing which is automatically producing 3D objects by adding layer-upon-layer of material. Additive manufacturing offers a revolutionary way of creating parts despite their geometric complexity compared to conventional manufacturing methods. Today, both the number of additive manufacturing processes and the materials available has developed rapidly which leads to the easy integration of topology optimization with it to improve structural performance in engineering fields such as in an automobile, aerospace, medical and biomechanical industries. The principal aim of this paper is to study the post-machining process of topology optimized parts. Topology optimization is an intelligent approach to get the best reduce weight design and achieve optimal performance at the same time in many fields. Yet unfortunately, it still faces some post-machining issues.

Topology optimization for additive manufacturing with self-supporting constraint

Topology optimization can devise structures with superior performance, while the results produced by topology optimization are often very complex and difficult to be manufactured directly. The additive manufacturing is a free-form manufacturing technique in which the component is built in a layer-by-layer manner. The integration of topology optimization and additive manufacturing technologies has the potential to bring significant synergy benefits. However, typical topology optimization algorithms have not considered the unique manufacturing limitations of additive manufacturing. This article focuses on the topology optimization for additive manufacturing considering self-supporting constraint based on the Solid Isotropic Material with Penalization (SIMP) framework. An explicit self-supporting constraint model is constructed, and the proposed method realizes self-supported by gradual evolution of supporting structures. The corresponding sensitivity analysis is investigated, which requires less computational cost and can be solved in parallel. Besides, a directional sensitivity filter is specifically proposed to promote the evolution of supporting structures. The performance and functionality of the proposed method is illustrated with three compliance minimization problems. All cases achieve self-supported successfully, and the solutions own good manufacturability.

Homogenization-based topology optimization integrated with elastically isotropic lattices for additive manufacturing of ultralight and ultrastiff structures

The integration of topology optimization with lattice structures has shown great potential for the additive manufacturing (AM) of lightweight structures with superior mechanical properties and multifunctional characteristics. To further improve the design manufacturability, structural efficiency, structural isotropy and computational efficiency, the homogenization-based topology optimization (HMTO) method was proposed to integrate with plate–lattices exhibiting superior mechanical properties and excellent elastic isotropy. The validity of the proposed method was demonstrated by comparing the optimized models with conventional models composed of truss–lattices and solid materials. Results show that the proposed method highly improves stiffness and energy absorption capability.