Shape optimization of uncemented hip prostheses

A computational model to obtain optimized geometries for the femoral component of hip prosthesis is presented. Using structural optimization techniques, the objective is to determine the shape of uncemented stems that maximize initial stability and improve performance. To accomplish this, the optimization problem is formulated by the minimization of the contact stresses and relative displacement on bone–stem interface. Design variables are geometric parameters that characterize selected cross sections. These parameters are subject to a set of linear geometric constraints in order to obtain clinically admissible geometries. Furthermore, a multiple load formulation is used to incorporate different daily life activities. Optimization results are useful to design new stems or, if integrated in an appropriate computer-aided design (CAD) system, to design custom-made hip prostheses. In the later case, the model is able to include personalized information such as patient's femur geometry and therefore personalized geometric constraints and optimization parameters.     

Application of geometric programming to transformer design

This paper considers the transformer design optimization problem. In its most general form, the design problem requires minimizing the total mass (or cost) of the core and wire material while ensuring the satisfaction of the transformer ratings and a number of design constraints. The constraints include appropriate limits on efficiency, voltage regulation, temperature rise, no-load current, and winding fill factor. The design optimization seeks a constrained minimum mass (or cost) solution by optimally setting the transformer geometry parameters and the relevant electrical and magnetic quantities. In cases where the core dimensions are fixed, the optimization problem calls for a constrained maximum volt-ampere or minimum loss solution. This paper shows that the above design problems can be formulated in geometric programming (GP) format. The importance of the GP format stems from two main features. First, GP provides an efficient and reliable solution for the design optimization problem with several variables. Second, it guarantees that the obtained solution is the global optimum. The paper includes a demonstration of the application of the GP technique to transformer design. It also includes a comparative study to emphasize the advantage of including the transformer core dimensions as variables in the design problem.     

基于kano-QFD的印刷品个性化制作平台优化设计

目的为印刷品个性化制作平台提供一种提升客户满意度、高效优化的方法。方法采用kano和QFD模型的研究方法,以常用印刷品个性化制作平台为研究对象,通过调查问卷等形式,归纳总结出10个产品服务需求指标,对其分别进行kano分类,满意度和重要度标定,运用数学模型修正不同产品服务重要度,得到各产品服务属性最终重要度。结果在线设计服务和数据传播速度2个属性的斜率值分别为1.0091和2.6981,重要度为0.6025和0.5974,是平台优化首要考虑的2个属性,并根据kano类型、重要度等参数,得到了印刷个性化制作平台各属性的优化顺序。结论从客户需求的角度为印刷品个性化制作平台提供了设计和优化的重点。     

CFD-based optimization of hovering rotors using radial basis functions for shape parameterization and mesh deformation

Aerodynamic shape optimization of a helicopter rotor in hover is presented, using compressible CFD as the aerodynamic model. An efficient domain element shape parameterization method is used as the surface control and deformation method, and is linked to a radial basis function global interpolation, to provide direct transfer of domain element movements into deformations of the design surface and the CFD volume mesh, and so both the geometry control and volume mesh deformation problems are solved simultaneously. This method is independent of mesh type (structured or unstructured) or size, and optimization independence from the flow solver is achieved by obtaining sensitivity information for an advanced parallel gradient-based algorithm by finite-difference, resulting in a flexible method of ‘wrap-around’ optimization. This paper presents results of the method applied to hovering rotors using local and global design parameters, allowing a large geometric design space. Results are presented for two transonic tip Mach numbers, with minimum torque as the objective, and strict constraints applied on thrust, internal volume and root moments. This is believed to be the first free form design optimization of a rotor blade using compressible CFD as the aerodynamic model, and large geometric deformations are demonstrated, resulting in significant torque reductions, with off-design performance also improved.     

Multidisciplinary Design Optimization Procedure for Improved Design of a Cooled Gas Turbine Blade

A multidisciplinary optimization procedure for gas turbine blade design has been developed and demonstrated on a generic 3-D blade. The blade is cooled both internally and externally (film cooling). Aerodynamic and heat transfer design criteria are integrated along with various constraints on the blade geometry. The blade is divided into numerous spanwise sections and each section is represented by a Bezier-Bernstein polynomial. A comprehensive solver for 3-D Navier-Stokes equations is used for the viscous flow calculations. The finite element method is used to obtain the blade interior temperatures. The average blade temperature and maximum blade temperature at each spanwise section are minimized, with aerodynamic and geometric constraints on the blade geometry. The constrained multiobjective optimization problem is solved using the Kreisselmeier-Steinhauser function approach. The results for a generic turbine blade design problem show significant improvements after optimization.     

A Bidirectional Deep Neural Network for Accurate Silicon Color Design

Silicon nanostructure color has achieved unprecedented high printing resolution and larger color gamut than sRGB. The exact color is determined by localized magnetic and electric dipole resonance of nanostructures, which are sensitive to their geometric changes. Usually, the design of specific colors and iterative optimization of geometric parameters are computationally costly, and obtaining millions of different structural colors is challenging. Here, a deep neural network is trained, which can accurately predict the color generated by random silicon nanostructures in the forward modeling process and solve the nonuniqueness problem in the inverse design process that can accurately output the device geometries for at least one million different colors. The key results suggest deep learning is a powerful tool to minimize the computation cost and maximize the design efficiency for nanophotonics, which can guide silicon color manufacturing with high accuracy.     

基于几何因子的复合材料气动弹性剪裁设计

实现了基于几何因子的复合材料层合板建模,解决了几何因子与Natran的参数输入问题,并根据工艺约束中的最小铺层比例对几何因子可行空间进行了推导补充。在此基础上,提出了一种基于几何因子和Nastran的复合材料气动弹性剪裁优化设计方法。首先以总厚度和几何因子作为设计变量以及以Nastran作为求解器,以强度、刚度、颤振和发散速度以及几何因子相关性约束作为约束条件进行结构寻优,得到最优的铺层总厚度和几何因子。其次,以最优几何因子作为目标,进行铺层结构逆问题求解,约束条件为复合材料铺层工艺约束。因几何因子为铺层厚度和铺层顺序的表达式,与传统的多级优化相比,以几何因子作为设计变量可以避免铺层厚度和铺层顺序的解耦,进而获得更大的设计空间,且得到的铺层结构可以满足工艺约束。最后,对一矩形悬臂复合材料层合板进行剪裁设计,使得铺层结构满足气动弹性约束且质量最小。结果显示,运用该优化方法可以得到质量更小且满足工艺约束的铺层结构。     

OPTIMAL TOPOLOGIES OF FLEXURAL SYSTEMS

The main objects of this paper are:

a)To introduce some relationships between optimal topologies and the geometric parameters of flexural systems.b) To investigate the effect of compatibility conditions on the optimal topology.

Assuming the force method analysis, a linear programming formulation can be obtained under certain circumstances. In such cases where the active constraints can be determined a priori, a direct solution in the space of redundant forces might be possible.

It is shown that the optimal design might correspond to a singular point in the design space. Neglecting compatibility conditions, multiple optimal topologies might be obtained for certain geometries. In such cases some of the resulting solutions usually represent statically determinate structures, therefore compatibility conditions do not affect the optimum

Numerical examples illustrate these phenomena and how the optimal topology and its corresponding load path change with the geometric parameters.     

Tight packaging of erbium-doped waveguide amplifiers

A numerical model for erbium-doped waveguide amplifiers (EDWAs) containing bent waveguides was developed. The model uses rate-propagation equations and takes into account bend-induced losses in the waveguide with a varying radius of curvature. It is applied to the design of tightly packed erbium-doped waveguide amplifiers under two constraints: minimization of the area required to obtain a predetermined gain and maximization of the gain available from a given area. Numerical calculations based on realistic waveguide parameters demonstrate the possibility of fabricating high-gain, small-size EDWAs. Simple design rules, based on geometric formulas and consideration of bend losses, are given and compared with the results of numerical calculations.     

A unified parametric design approach to structural shape optimization

This paper presents a general parametric design approach for 2-D shape optimization problems. This approach has been achieved by integrating practical design methodologies into numerical procedures. It is characterized by three features: (i) automatic selection of a minimum number of shape design variables based on the CAD geometric model; (ii) integration of sequential convex programming algorithms to solve equality constrained optimization problems; (iii) efficient sensitivity analysis by means of the improved semi-analytical method. It is shown that shape design variables can be either manually or systematically identified with the help of equality constraints describing the relationship between geometric entities. Numerical solutions are performed to demonstrate the applicability of the proposed approach. A discussion of the results is also given:     

The effect of compatibility conditions on optimal design of flexural structures

In most structural optimization problems the time-consuming implicit analysis must be repeated many times during the solution process. To alleviate this difficulty, the implicit analysis equations are often neglected or replaced by explicit approximations. Assuming the force method analysis formulation, optimal solutions of two problems are studied and compared:

• (a) The equilibrium linear programme (ELP), where only explicit equilibrium conditions are considered in the analysis model
• (b) The non-linear programme (NLP), where the implicit compatibility conditions are included to obtain a complete formulation.

The effect of geometrical parameters on optimal solutions of both problems is investigated and geometries with particular properties are identified. The main observations that have been made are as follows:

• (a) Multiple optima of the ELP have been obtained for geometries where transitions in the set of active constraints at the ELP optimum occur. The NLP optimum for such a geometry might be included in the set of ELP optima.
• (b) Identical optimal solutions of the two problems have been found for geometries where transitions in the set of active constraints at the NLP optimum occur.

The explicit ELP can be solved instead of the implicit NLP for the two classes of transition geometries. The relationships between optimal force distributions and objective function values for the two problems are studied and examples where compatibility conditions can be neglected are illustrated.     

模糊参数平面连续体结构的拓扑优化设计

研究了具有模糊参数的连续体结构在模糊载荷作用下的拓扑优化设计问题。利用信息熵将模糊变量转换为随机变量,构建了随机载荷作用下的随机参数的连续体结构的拓扑优化设计数学模型,以结构的形状拓扑信息为设计变量,结构总质量均值极小化为目标函数,满足单元应力可靠性为约束条件,利用分布函数法对应力可靠性约束进行了等价显式化处理。基于随机因子法,利用代数综合法导出了应力响应的数字特征的计算表达式。采用双方向渐进结构优化(BESO)方法求解。通过两个算例验证了该文模型及求解方法的合理性和有效性。     

Rapid risk assessment using probability of fracture nomographs

Traditional risk-based design process involves designing the structure based on risk estimates obtained during several iterations of an optimization routine. This approach is computationally expensive for large-scale aircraft structural systems. Therefore, this paper introduces the concept of risk-based design plots that can be used for both structural sizing and risk assessment for fracture strength when maximum allowable crack length is available. In situations when crack length is defined as a probability distribution the presented approach can only be applied for various percentiles of crack lengths. These plots are obtained using normalized probability density models of load and material properties and are applicable for any arbitrary load and strength values. Risk-based design plots serve as a tool for failure probability assessment given geometry and applied load or they can determine geometric constraints to be used in sizing given allowable failure probability. This approach would transform a reliability-based optimization problem into a deterministic optimization problem with geometric constraints that implicitly incorporate risk into the design. In this paper, cracked flat plate and stiffened plate are used to demonstrate the methodology and its applicability.     

考虑结构稳定性的变密度拓扑优化方法

将稳定性问题引入传统变密度法中,可实现包含稳定性约束的平面模型结构拓扑优化。以单元相对密度为设计变量,结构柔度最小为目标函数,结构体积和失稳载荷因子为约束条件建立优化问题数学模型,提出了一种考虑结构稳定性的变密度拓扑优化方法。通过分析结构柔度、体积、失稳载荷因子对设计变量的灵敏度,并基于拉格朗日乘子法和Kuhn-Tucker条件,推导了优化问题的迭代准则。同时,利用基于约束条件的泰勒展开式求解优化准则中的拉格朗日乘子。通过推导平面四节点四边形单元几何刚度矩阵的显式表达式,得到了优化准则中的几何应变能。最后,通过算例对提出的方法进行了验证,并与不考虑稳定性的传统变密度拓扑优化方法进行对比,结果表明该方法能显著提高拓扑优化结果的稳定性。研究结果对细长受压结构的优化设计有重要指导意义,对结构的稳定性设计有一定参考价值。     

Sequential algorithms for structural design optimization under tolerance conditions

A deterministic optimization usually ignores the effects of uncertainties in design variables or design parameters on the constraints. In practical applications, it is required that the optimum solution can endure some tolerance so that the constraints are still satisfied when the solution undergoes variations within the tolerance range. An optimization problem under tolerance conditions is formulated in this article. It is a kind of robust design and a special case of a generalized semi-infinite programming (GSIP) problem. To overcome the deficiency of directly solving the double loop optimization, two sequential algorithms are then proposed for obtaining the solution, i.e. the double loop optimization is solved by a sequence of cycles. In each cycle a deterministic optimization and a worst case analysis are performed in succession. In sequential algorithm 1 (SA1), a shifting factor is introduced to adjust the feasible region in the next cycle, while in sequential algorithm 2 (SA2), the shifting factor is replaced by a shifting vector. Several examples are presented to demonstrate the efficiency of the proposed methods. An optimal design result based on the presented method can endure certain variation of design variables without violating the constraints. For GSIP, it is shown that SA1 can obtain a solution with equivalent accuracy and efficiency to a local reduction method (LRM). Nevertheless, the LRM is not applicable to the tolerance design problem studied in this article.     

Multiobjective robust optimization method for drawbead design in sheet metal forming

It is recognized that fracture and wrinkling in sheet metal forming can be eliminated via an appropriate drawbead design. Although deterministic multiobjective optimization algorithms and finite element analysis (FEA) have been applied in this respect to improve formability and shorten design cycle, the design could become less meaningful or even unacceptable when considering practical variation in design variables and noises of system parameters. To tackle this problem, we present a multiobjective robust optimization methodology to address the effects of parametric uncertainties on drawbead design, where the six sigma principle is adopted to measure the variations, a dual response surface method is used to construct surrogate model and a multiobjective particle swarm optimization is developed to generate robust Pareto solutions. In this paper, the procedure of drawbead design is divided into two stages: firstly, equivalent drawbead restraining forces (DBRF) are obtained by developing a multiobjective robust particle swarm optimization, and secondly the DBRF model is integrated into a single-objective particle swarm optimization (PSO) to optimize geometric parameters of drawbead. The optimal design showed a good agreement with the physical drawbead geometry and remarkably improve the formability and robust. Thus, the presented method provides an effective solution to geometric design of drawbead for improving product quality.     

Metamaterial topology optimization of nonpneumatic tires with stress and buckling constraints

This article presents the design of a metamaterial for the shear layer of a nonpneumatic tire using topology optimization, under stress and buckling constraints. These constraints are implemented for a smooth maximum function using global aggregation. A linear elastic finite element model is used, implementing solid isotropic material with penalization. Design sensitivities are determined by the adjoint method. The method of moving asymptotes is used to solve the numerical optimization problem. Two different optimization statements are used. Each requires a compliance limit and some aspect of continuation. The buckling analysis is linear, considering the generalized eigenvalue problem of the conventional and stress stiffness matrices. Various symmetries, base materials, and starting geometries are considered. This leads to novel topologies that all achieve the target effective shear modulus of 10 MPa, while staying within the stress constraint. The stress-only designs generally were susceptible to buckling failure. A family of designs (columnar, noninterconnected representative unit cells) that emerge in this study appears to exhibit favorable properties for this application.     

Geometric parametrization and constrained optimization techniquesin the design of salient pole synchronous machines

The shape optimization of magnetic devices is efficiently performed with field calculation and sensitivity analysis based on the finite element method. Several sequential unconstrained optimization techniques are discussed and evaluated with respect to their application in engineering design. The optimization of the geometry of a salient pole generator so as to achieve a desired field configuration in the airgap is used as an illustrative numerical example to demonstrate the geometric parametrization technique, emphasize the importance of constraints in engineering design, and highlight the advantageous features of the augmented Lagrangian multiplier method for nonlinear constrained optimization. For the required geometric parametrization a recent novel use of structural mapping is extended to incorporate constrained optimization. The associated equations of structural mapping are presented     

Towards causally cohesive genotype–phenotype modelling for characterization of the soft-tissue mechanics of the heart in normal and pathological geometries

A scientific understanding of individual variation is key to personalized medicine, integrating genotypic and phenotypic information via computational physiology. Genetic effects are often context-dependent, differing between genetic backgrounds or physiological states such as disease. Here, we analyse in silico genotype–phenotype maps (GP map) for a soft-tissue mechanics model of the passive inflation phase of the heartbeat, contrasting the effects of microstructural and other low-level parameters assumed to be genetically influenced, under normal, concentrically hypertrophic and eccentrically hypertrophic geometries. For a large number of parameter scenarios, representing mock genetic variation in low-level parameters, we computed phenotypes describing the deformation of the heart during inflation. The GP map was characterized by variance decompositions for each phenotype with respect to each parameter. As hypothesized, the concentric geometry allowed more low-level parameters to contribute to variation in shape phenotypes. In addition, the relative importance of overall stiffness and fibre stiffness differed between geometries. Otherwise, the GP map was largely similar for the different heart geometries, with little genetic interaction between the parameters included in this study. We argue that personalized medicine can benefit from a combination of causally cohesive genotype–phenotype modelling, and strategic phenotyping that captures effect modifiers not explicitly included in the mechanistic model.