Simultaneous topology and build orientation optimization for minimization of additive manufacturing cost and time

The ever-present demand for increased performance in mechanical systems, and reduced cost and manufacturing time, has led to the adoption of computational design tools and innovative manufacturing methods. One such tool is topology optimization (TO), which often produces designs that are impracticable to manufacture. However, recent developments in additive manufacturing (AM) have made production of such complex designs feasible. Therefore, integration of these technologies has the potential to innovate the design and manufacture of mechanical components. This work presents a novel mathematical methodology for multiobjective minimization of structural compliance and AM cost and time, in simultaneous build orientation and density-based TO. Component surface area and support volume were implemented in this method as the physical factors influencing AM cost and time. A new methodology was produced to approximate support volume throughout TO with variable build orientation, enabling direct minimization of support volume in the proposed optimization. The methodology allows derivation of sensitivity expressions, thereby permitting the use of efficient gradient-based optimization solvers. Three numerical examples demonstrated that the proposed methodology can efficiently produce optimum build orientations and topologies, which significantly reduce structural compliance and AM cost and time.     

A multiobjective topology optimization approach for cost and time minimization in additive manufacturing

The ever-present drive for increasingly high-performance designs realized on shorter timelines has fostered the need for computational design generation tools such as topology optimization. However, topology optimization has always posed the challenge of generating difficult, if not impossible to manufacture designs. The recent proliferation of additive manufacturing technologies provides a solution to this challenge. The integration of these technologies undoubtedly has the potential for significant impact in the world of mechanical design and engineering. This work presents a new methodology which mathematically considers additive manufacturing cost and build time alongside the structural performance of a component during the topology optimization procedure. Two geometric factors, namely, the surface area and support volume required for the design, are found to correlate to cost and build time and are controlled through the topology optimization procedure. A novel methodology to consider each of these factors dynamically during the topology optimization procedure is presented. The methodology, based largely on the use of the spatial gradient of the density field, is developed in such a way that it does not leverage the finite element discretization scheme. This work investigates a problem that has not yet been explored in the literature: direct minimization of support material volume in density-based topology optimization. The entire methodology is formulated in a smooth and differentiable manner, and the sensitivity expressions required by gradient based optimization solvers are presented. A series of example problems are provided to demonstrate the efficacy of the proposed methodology.     

Optimal design approach for eco-efficient machine tool bed

An optimal design approach of machine tool bed with the aim of obtaining an eco-efficient machine structure is studied. The suggested method includes three phases. The first is the layout design optimization of stiffener plates inside bed. In order to improve the design efficiency, a simplified design model called fiber model is suggested, and the layout of the stiffener plates inside bed is optimized by changing a 3-dimensional topology design optimization problem to a 2-dimensional problem. The second is the detailed sizing optimization of stiffener plates and supporting blocks under the structure based on the initial optimal model resulted from phase one. Finally, a topology design optimization process is implemented to obtain a reasonable distribution of manufacturing holes in bed structure. By considering the manufacturing requirement, an optimal bed structure is obtained. The validity of the suggested method is confirmed by a typical cylindrical grinding machine tool bed, and the result shows that the suggested method is effective, and the optimal structure has much better mechanical and economical performance by comparing with the original structures.     

基于制造工艺约束的数控插齿机中床身拓扑优化设计

为解决立式数控插齿机中床身的拓扑优化结果在工程上加工制造困难的问题,建立了带有制造工艺约束的拓扑优化模型,采用OptiStruct对中床身进行拓扑优化设计,得到了约束条件含有体积分数及同时含有体积分数和制造工艺的2种拓扑优化结果.对比分析了2种拓扑优化结果,表明基于制造工艺约束的拓扑优化设计的中床身结构有更好的铸造性能...     

Simultaneous single-loop multimaterial and multijoint topology optimization

As the aerospace and automotive industries continue to strive for efficient lightweight structures, topology optimization (TO) has become an important tool in this design process. However, one ever-present criticism of TO, and especially of multimaterial (MM) optimization, is that neither method can produce structures that are practical to manufacture. Optimal joint design is one of the main requirements for manufacturability. This article proposes a new density-based methodology for performing simultaneous MMTO and multijoint TO. This algorithm can simultaneously determine the optimum selection and placement of structural materials, as well as the optimum selection and placement of joints at material interfaces. In order to achieve this, a new solid isotropic material with penalization-based interpolation scheme is proposed. A process for identifying dissimilar material interfaces based on spatial gradients is also discussed. The capabilities of the algorithm are demonstrated using four case studies. Through these case studies, the coupling between the optimal structural material design and the optimal joint design is investigated. Total joint cost is considered as both an objective and a constraint in the optimization problem statement. Using the biobjective problem statement, the tradeoff between total joint cost and structural compliance is explored. Finally, a method for enforcing tooling accessibility constraints in joint design is presented.     

A novel reliability-based topology optimization framework for the concurrent design of solid and truss-like material structures with unknown-but-bounded uncertainties

A new nonprobabilistic reliability-based topology optimization method for continuum structures with displacement constraints is proposed in this paper, in which the optimal layout consists of solid material and truss-like microstructure material simultaneously. The unknown-but-bounded uncertainties that exist in material properties, external loads, and safety displacements are considered. By utilizing the representative volume element analysis, rules of macro-micro stiffness performance equivalence can be confirmed. A solid material and truss-like microstructure material structure integrated design interpolation model is firstly constructed, in which design domain elements can be conducted to select solid material or truss-like microstructure material by a combination of the finite element method in the topology optimization process. Moreover, a new nonprobabilistic reliability measuring index, namely, the optimization feature distance is defined by making use of the area-ratio ideas. Furthermore, the adjoint vector method is employed to obtain the sensitivity information between the reliability measure and design variables. By utilizing the method of moving asymptotes, the investigated optimization problem can be iteratively solved. The effectiveness of the developed methodology is eventually demonstrated by two examples.     

Density and level set-XFEM schemes for topology optimization of 3-D structures

As the capabilities of additive manufacturing techniques increase, topology optimization provides a promising approach to design geometrically sophisticated structures. Traditional topology optimization methods aim at finding conceptual designs, but they often do not resolve sufficiently the geometry and the structural response such that the optimized designs can be directly used for manufacturing. To overcome these limitations, this paper studies the viability of the extended finite element method (XFEM) in combination with the level-set method (LSM) for topology optimization of three dimensional structures. The LSM describes the geometry by defining the nodal level set values via explicit functions of the optimization variables. The structural response is predicted by a generalized version of the XFEM. The LSM–XFEM approach is compared against results from a traditional Solid Isotropic Material with Penalization method for two-phase “solid–void” and “solid–solid” problems. The numerical results demonstrate that the LSM–XFEM approach describes crisply the geometry and predicts the structural response with acceptable accuracy even on coarse meshes.     

Robust shape and topology optimization considering geometric uncertainties with stochastic level set perturbation

When geometric uncertainties arising from manufacturing errors are comparable with the characteristic length or the product responses are sensitive to such uncertainties, the products of deterministic design cannot perform robustly. This paper presents a new level set‐based framework for robust shape and topology optimization against geometric uncertainties. We first propose a stochastic level set perturbation model of uncertain topology/shape to characterize manufacturing errors in conjunction with Karhunen–Loève (K–L) expansion. We then utilize polynomial chaos expansion to implement the stochastic response analysis. In this context, the mathematical formulation of the considered robust shape and topology optimization problem is developed, and the adjoint‐variable shape sensitivity scheme is derived. An advantage of this method is that relatively large shape variations and even topological changes can be accounted for with desired accuracy and efficiency. Numerical examples are given to demonstrate the validity of the present formulation and numerical techniques. In particular, this method is justified by the observations in minimum compliance problems, where slender bars vanish when the manufacturing errors become comparable with the characteristic length of the structures. Copyright © 2016 John Wiley & Sons, Ltd.     

Classical Fatigue Design Techniques as a Failure Analysis Tool

The classical method for designing against high-cycle fatigue fracture is based primarily on statistical models derived from laboratory experimental data. This paper considers a number of actual fatigue failures where the analyses of the failures, in part, made use of classical high-cycle fatigue resistance design methodology as an analytical tool. This paper uses failure analyses to demonstrate that the long-taught classical methodology is useful and accurate as both a design and an analysis tool. The usefulness and accuracy of the method is verified in that it is shown to have predicted actual failures, given known materials, manufacturing histories, and service operating conditions. Example analyses include: a fatigue-cracked roll from a paper-making machine, a fractured anvil on a steam powered forge, and a fractured shaft on a helical ribbon dryer.     

A mixed integer programming approach to designing periodic frame structures with negative Poisson’s ratio

Materials and microstructures with specific configurations are able to have negative Poisson’s ratio. This paper proposes a topology optimization methodology of frame structures to design a planar periodic structure that exhibits negative Poisson’s ratio. Provided that beam section of each existing member is chosen from a set of some given candidates, we can reduce the topology optimization problem to a mixed-integer linear programming problem. Since the proposed approach treats frame structures and stress constraints are rigorously addressed, the optimal solution contains no hinge region. A heuristic method with local search is used to solve large-scale problems. Numerical examples and fabrication test demonstrate that planar periodic frame structures exhibiting negative Poisson’s ratio can be successfully obtained by the proposed method.     

Design of Electrical Rotating Machines by Associating Deterministic Global Optimization Algorithm With Combinatorial Analytical and Numerical Models

This paper presents a new methodology of design of electrical rotating machines. The methodology is an extension of previous works of the second author. Indeed, associating combinatorial analytical models with exact global optimization algorithms leads to rational solutions of predesign. These solutions need to be validated by a numerical tool (using a finite-element method) before the expansive phase of hand-making a prototype. Such an automatic numerical tool for computing some characteristic values, such as the torque, was previously developed. The idea of this paper is to extend the exact global optimization algorithm by inserting the direct use of this automatic numerical tool. This new methodology makes it possible to solve design problems more rationally. Some numerical examples validate the usefulness of this new approach.     

Multi-material topology optimization of laminated composite beam cross sections

This paper presents a novel framework for simultaneous optimization of topology and laminate properties in structural design of laminated composite beam cross sections. The structural response of the beam is evaluated using a beam finite element model comprising a cross section analysis tool which is suitable for the analysis of anisotropic and inhomogeneous sections of arbitrary geometry. The optimization framework is based on a multi-material topology optimization model in which the design variables represent the amount of the given materials in the cross section. Existing material interpolation, penalization, and filtering schemes have been extended to accommodate any number of anisotropic materials. The methodology is applied to the optimal design of several laminated composite beams with different cross sections. Solutions are presented for a minimum compliance (maximum stiffness) problem with constraints on the weight, and the shear and mass center positions. The practical applicability of the method is illustrated by performing optimal design of an idealized wind turbine blade subjected to static loading of aerodynamic nature. The numerical results suggest that the proposed framework is suitable for simultaneous optimization of cross section topology and identification of optimal laminate properties in structural design of laminated composite beams.     

Multilevel assessment method for reliable design of composite structures

This work aims at demonstrating the interest of a new methodology for the design and optimization of composite materials and structures. Coupling reliability methods and homogenization techniques allow the consideration of probabilistic design variables at different scales. The main advantage of such an original micromechanics-based approach is to extend the scope of solutions for engineering composite materials to reach or to respect a given reliability level. This approach is illustrated on a civil engineering case including reinforced fiber composites. Modifications of microstructural components properties, manufacturing process, and geometry are investigated to provide new alternatives for design and guidelines for quality control.     

Additive Manufacturing of Porous Structures for Unmanned Aerial Vehicles Applications

Unmanned aerial vehicles (UAVs) have shown promising benefits in many applications. This has been enabled by the emergence of additive manufacturing (AM), which give the designers a large amount of geometrical freedom. In this paper, a novel design process of fused deposition modeling (FDM) combining both topology and infill optimization is introduced for AM of high performance porous structures. Tensile testing of FDM printed samples is first carried out to study the effect of the build orientation on the mechanical properties of acrylonitrile butadiene styrene (ABS) samples. It is found that samples built perpendicular to the load axis are the weakest with a tensile strength of 29 MPa and Young's modulus of 1960 MPa. The materials properties are fed to the finite elements analysis (FEA) for geometrical topology optimization, aiming to maximize stiffness and reduce weight of those parts. Afterwards, an infill optimization is carried out on the topology optimized parts using different mesostructures such as honeycomb, triangular, and rectangular to achieve high structural performance. The results showed that triangular pattern with 50% infill density had the lowest developed stresses, less mass, and strain energy when compared to other structures. Optimum UAVs parts of a quadcopter are successfully manufactured, assembled, and tested.

     

Structural topology optimization of vibrating structures with specified eigenfrequencies and eigenmode shapes

In vibration optimization problems, eigenfrequencies are usually maximized in the optimization since resonance phenomena in a mechanical structure must be avoided, and maximizing eigenfrequencies can provide a high probability of dynamic stability. However, vibrating mechanical structures can provide additional useful dynamic functions or performance if desired eigenfrequencies and eigenmode shapes in the structures can be implemented. In this research, we propose a new topology optimization method for designing vibrating structures that targets desired eigenfrequencies and eigenmode shapes. Several numerical examples are presented to confirm that the method presented here can provide optimized vibrating structures applicable to the design of mechanical resonators and actuators. Copyright © 2006 John Wiley & Sons, Ltd.     

Linear and nonlinear topology optimization design with projection-based ground structure method (P-GSM)

A new topology optimization scheme called the projection-based ground structure method (P-GSM) is proposed for linear and nonlinear topology optimization designs. For linear design, compared to traditional GSM which are limited to designing slender members, the P-GSM can effectively resolve this limitation and generate functionally graded lattice structures. For additive manufacturing-oriented design, the manufacturing abilities are the key factors to constrain the feasible design space, for example, minimum length and geometry complexity. Conventional density-based method, where each element works as a variable, always results in complex geometry with large number of small intricate features, while these small features are often not manufacturable even by 3D printing and lose its geometric accuracy after postprocessing. The proposed P-GSM is an effective method for controlling geometric complexity and minimum length for optimal design, while it is capable of designing self-supporting structures naturally. In optimization progress, some bars may be disconnected from each other (floating in the air). For buckling-induced design, this issue becomes critical due to severe mesh distortion in the void space caused by disconnection between members, while P-GSM has ability to overcome this issue. To demonstrate the effectiveness of proposed method, three different design problems ranging from compliance optimization to buckling-induced mechanism design are presented and discussed in details.     

基于ICM法的高层建筑大型支撑体系拓扑优化

提出应用连续体结构拓扑优化ICM法对高层建筑大型支撑体系进行拓扑优化。针对高层建筑规范对结构刚度限值是以层间相对位移差形式给出、并结合结构拓扑优化特点,推导了相对位移差敏度分析的伴随法公式,有效提高了计算效率。应用ICM法建立位移约束下结构重量极小化的优化模型,与高层建筑规范对结构刚度限值要求的提法更符合,得到的最优拓扑完全满足规范要求。所提方法应用在概念设计阶段,提供了一种自动化的分析计算及优化设计工具,可以有效地弥补基于经验设计的不足。     

城轨列车车辆空气传播噪声预测模型

为缩短城轨列车车辆这样大型复杂结构早期的声学结构设计周期,建立了城轨列车车辆室内噪声和车外噪声通用的理论计算模型;提出了室外声源声功率级转换到室内声源声功率级的等效计算方法;针对城轨列车车体常用的中空铝型材双层结构的隔声量进行了理论推导,并分析了表面粘附辅助材料后组合隔声结构的隔声量;根据计算模型对某城轨列车的噪声进行了预测,计算结果与测试结果虽存在一定的偏差,但仍在可接受范围之内。预测模型能为新车型研发和老车型的声学结构改进快速提供设计依据。     

Partial least square-based model predictive control for large-scale manufacturing processes

The Model Predictive Control (MPC) method has been widely adopted as a useful tool to keep quality on target in manufacturing processes. However, the conventional MPC methods are inadequate for large-scale manufacturing processes particularly in the presence of disturbances. The goal of this paper is to propose a Partial Least Square (PLS)-based MPC methodology to accommodate the characteristics of a large-scale manufacturing process. The detailed objectives are: (i) to identify a reliable prediction model that handles the large-scale "short and fat" data; (ii) to design an effective control model that both maximizes the required quality and minimizes the labor costs associated with changing the process parameters; and (iii) to develop an efficient optimization algorithm that reduces the computational burden of the large-scale optimization. The case study and experimental results demonstrate that the presented MPC methodology provides the set of optimal process parameters for quality improvement. In particular, the quality deviations are reduced by 99.4%, the labor costs by 84.2%, and the computational time by 98.8%. As a result, the proposed MPC method will save on both costs and time in achieving the desired quality for a large-scale manufacturing process.     

Simultaneous partial topology and size optimization of a wing structure using ant colony and gradient based methods

This article presents a methodology and process for a combined wing configuration partial topology and structure size optimization. It is aimed at achieving a minimum structural weight by optimizing the structure layout and structural component size simultaneously. This design optimization process contains two types of design variables and hence was divided into two sub-problems. One is structure layout topology to obtain an optimal number and location of spars with discrete integer design variables. Another is component size optimization with continuous design variables in the structure FE model. A multi city-layer ant colony optimization (MCLACO) method is proposed and applied to the topology sub-problem. A gradient based optimization method (GBOM) built in the MSC.NASTRAN SOL-200 module was employed in the component size optimization sub-problem. For each selected layout of the wing structure, a size optimization process is performed to obtain the optimum result and feedback to the layout topology process. The numerical example shows that the proposed MCLACO method and a combination with the GBOM are effective for solving such a wing structure optimization problem. The results also indicate that significant structural weight saving can be achieved.