评定直线度误差的新算法——缩小约束域的有效特征点法

 提出了最小区域法评定直线度误差的新算法——缩小约束域的有效特征点法。建立了算法的数学模型, 阐明了算法基本原理; 新算法应用相间准则和特征点搜索包容直线斜率, 自动建立最小区域包容直线斜率的约束域并使之快速缩小, 能快速、准确地搜索出最小区域包容直线的斜率并获得直线度误差的最小值。大量算例证实新算法首轮搜索成功率高, 计算速度快, 迭代次数小, 算法可推广应用于其他形状误差的最小区域法评定, 亦可用于实时计算机辅助测量系统。     

A review of fracture toughness transferability with constraint and stress gradient

In this review paper, only constraint and stress gradient approaches to transferability of fracture toughness are examined. The different constraint parameters are defined and discussed, and one example is given in each case. Factors that influence the constraint are studied. Special attention is given to the actual trends to use the plastic constraint in the material failure master curve and the material transition temperature master curve. The paper also deals on the influence of T stress on the crack path and out‐of‐plane constraint and on the influence of thickness on fracture toughness. The uses of plasticity with gradient and the relative stress gradient in local fracture approaches are also examined.     

A basis change strategy for the reduced gradient method and the optimum design of large structures

This paper proposes a basis change strategy within the reduced gradient method for optimization under linear constraints. It ensures a non-singular basis matrix at every iteration. The same strategy can reliably be used within the generalized reduced gradient method for optimization under non-linear constraints. This method is applied to the minimum weight design of large structures under displacement and stress constraints, exploiting the sparsity of the constraint Jacobian matrix.     

Further discrete variable results for a panel flutter optimization problem

Numerical solutions are presented for the problem of minimum weight design of a thin one-dimensiona simply-supported, solid panel in compression with one side exposed to a parallel high supersonic air flow. The flutter speed is held fixed, and a minimum thickness constraint is imposed. In addition, a multiplier technique is incorporated into the discrete variable minimization process to improve the convergence speed.     

基于齿轮动态激励和弹流润滑的多目标优化

依据齿轮啮合动态激励基本原理和弹性流体动力润滑理论,建立同时追求齿轮啮合时变刚度激励最小、齿间最小油膜厚度最大(倒数最小)及齿轮传动总体积最小的约束多目标优化设计数学模型.对现有的用于两目标优化设计的粒子群优化方法加以改进,给出了约束3目标优化设计方法.利用Matlab编制优化程序,并对范例进行分析计算.优化过程及结果表明,采用较多的齿数,在小于1的范围内采用较大的正变位系数,适度采用较大的压力角可以增大轮齿啮合综合刚度谱图中基频谐波的幅值,有效地提高齿轮传动系统抵抗内部激励振动的能力及性价比.     

Optimization of clamped columns under distributed axial load and subject to stress constraints

The optimum designs are given for clamped-clamped columns under concentrated and distributed axial loads. The design objective is the maximization of the buckling load subject to volume and maximum stress constraints. The results for a minimum area constraint are also obtained for comparison. In the case of a stress constraint, the minimum thickness of an optimal column is not known a priori, since it depends on the maximum buckling load, which in turn depends on the minimum thickness necessitating an iterative solution. An iterative solution method is developed based on finite elements, and the results are obtained for n=1, 2, 3 defined as I=α _n A ⁿ , with I being the moment of inertia, and A the cross-sectional area. The iterations start using the unimodal optimality condition and continue with the bimodal optimality condition if the second buckling load becomes less than or equal to the first one. Numerical results show that the optimal columns become larger in the direction of the distributed load due to the increase in the stress in this direction. Even though the optimal columns are symmetrical with respect to their mid-points when the compressive load is concentrated at the end-points, in the case of the columns subject to distributed axial loads the optimal shapes are unsymmetrical.     

Shape and cross-section optimization of plane trusses subjected to earthquake excitation using gradient and Hessian matrix calculations

This article describes a second-order shape and cross-section optimization method of plane truss subjected to earthquake excitation. The method is based on gradient and Hessian matrix calculation. First, the first and second derivatives of dynamic response with respect to design variables are calculated based on the Newmark method. Second, the inequality time-dependent constraint problem is converted into a sequence of appropriately formed unconstrained problems using the integral interior penalty function method. Then, the gradient and Hessian matrix of the integral interior penalty function are computed. Third, Marquardt's method is employed to solve the unconstrained problems. Finally, the new approach is validated through several case studies. The results show that the new optimization method is an efficient and effective approach for minimum weight design of truss structures.     

Eigenfrequency optimization of stiffened plate using Kriging estimation

This paper describes the optimization of the beam stiffeners attached to plates in an eigenfrequency problem. The solution space is estimated using the Kriging method. A finite element analysis is carried out to evaluate the objective function at the sample points used for the estimation. The gradient method is used as a local optimizer. The Kriging estimation incurs relatively low cost, and is easy to combine with the gradient method. In this paper, we solve eigenfrequency optimization problems for a fully supported plate to maximize the minimum eigenfrequency and the difference between the 1st- and 2nd-order eigenfrequency. An optimization problem for an L-shaped plate with an eigenfrequency constraint is also solved. Good solutions are obtained for each example, and all the optimizations for these problems can be done at a lower computational cost. The results highlight the effectiveness of the method to solve the eigenfrequency optimization problems for the stiffened plate.     

Continuum structural topological optimizations with stress constraints based on an active constraint technique

Stress‐related problems have not been given the same attention as the minimum compliance topological optimization problem in the literature. Continuum structural topological optimization with stress constraints is of wide engineering application prospect, in which there still are many problems to solve, such as the stress concentration, an equivalent approximate optimization model and etc. A new and effective topological optimization method of continuum structures with the stress constraints and the objective function being the structural volume has been presented in this paper. To solve the stress concentration issue, an approximate stress gradient evaluation for any element is introduced, and a total aggregation normalized stress gradient constraint is constructed for the optimized structure under the r?th load case. To obtain stable convergent series solutions and enhance the control on the stress level, two p‐norm global stress constraint functions with different indexes are adopted, and some weighting p‐norm global stress constraint functions are introduced for any load case. And an equivalent topological optimization model with reduced stress constraints is constructed,being incorporated with the rational approximation for material properties, an active constraint technique, a trust region scheme, and an effective local stress approach like the qp approach to resolve the stress singularity phenomenon. Hence, a set of stress quadratic explicit approximations are constructed, based on stress sensitivities and the method of moving asymptotes. A set of algorithm for the one level optimization problem with artificial variables and many possible non‐active design variables is proposed by adopting an inequality constrained nonlinear programming method with simple trust regions, based on the primal‐dual theory, in which the non‐smooth expressions of the design variable solutions are reformulated as smoothing functions of the Lagrange multipliers by using a novel smoothing function. Finally, a two‐level optimization design scheme with active constraint technique, i.e. varied constraint limits, is proposed to deal with the aggregation constraints that always are of loose constraint (non active constraint) features in the conventional structural optimization method. A novel structural topological optimization method with stress constraints and its algorithm are formed, and examples are provided to demonstrate that the proposed method is feasible and very effective. © 2016 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.     

A computer program for filter design having arbitrary magnitude specifications in the frequency domain

A general procedure is presented for the design of analogue or digital filters having arbitrary specifications in the frequency domain. The algorithm developed uses a simple technique for constraining the pole zero locations, for stability and minimum phase considerations, which is far more elegant than methods used by previous workers.¹ This constraint procedure yields a unified approach to the design of both digital and analogue filters. The method employed is that of minimizing a square-error criterion using the Fletcher–Powell² conjugate gradient minimization routine. The programme is written in FORTRAN IV double precision complex arithmetic.     

腹板屈曲约束钢连梁抗震性能研究

腹板屈曲约束钢连梁通过在钢连梁腹板两侧设置约束板,保证钢连梁在往复剪切荷载作用下腹板剪切屈服后承载力能够持续强化,相比在腹板上设置加劲肋的传统方式,腹板屈曲约束钢连梁的腹板在接近钢材极限剪应变前不会发生面外屈曲,具有优越的耗能能力。通过5个腹板屈曲约束钢连梁的拟静力试验,研究了不同约束方式对钢连梁抗震性能的影响。试验结果表明：所有试件均实现了剪切屈服及承载力强化,破坏模式主要为翼缘、端板焊缝断裂和约束板弯曲破坏。钢连梁的超强系数平均值为1.38,大于《建筑抗震设计规范》GB 50011-2010的最低要求1.1,其中采用50 mm厚的钢筋混凝土约束板和25 mm厚的木板约束板的试件的超强系数超过了1.5。通过建立有限元分析模型进行试验对比验证和参数分析,提出了约束板最小厚度的建议取值,可为实际工程设计提供参考。     

Stationary shoulder tool in friction stir processing: a novel low heat input tooling system for magnesium alloy

Present work aims to propose a new and novel low heat input stationary shoulder friction stir processing (SSFSP) for grain refinement. It uses stationary shoulder and rotating probe tool, which generates low heat input and small temperature gradient across thickness of material. In this study, SSFSP was performed in 6.35 mm thick AZ31B magnesium alloy without use of external cooling. The homogenous grain refinement occurred throughout the thickness (top, middle, and bottom). Enhancement in hardness and ductility exhibited minimum anisotropy across the processing thickness. Furthermore, fractography confirmed the similar fracture modes with dimples and tear ridges in all tensile specimens across the thickness.     

Rapid forming of superplastic aluminium alloy 5083

Abstract

Decreasing the cycle time significantly for forming the commercially available superplastic aluminium alloy 5083 has been achieved. Forming results and conditions are compared with previous relevant works which are actually scarce. A circular cup having a depthdiameter ratio of 1:2 can be formed in 70 s. This ratio requires flat sheet to be stretched in area by up to three times, which should be large enough when dealing with actual industrial sheet forming. On average, the thickness is decreased by two-thirds; in fact, the thickness distribution is not uniform and the gradient is concentrated at the wall of the cup. The location of minimum thickness in rapid forming is different from that in conventional forming. Disregarding the traditional approach, the pressure-time profile employed in this work was not restricted to yield the so called optimum strain rate, which is usually low. Following the same processing profile, but proceeding in stages of partial forming, a series of progressive forming configurations was obtained in order to analyse the strain rate path leading to the successful rapid forming. For a specimen processed at 500C, the maximum volume fraction of cavities is 4 existing at the location of minimum thickness.     

航空复合材料翼面结构气动伺服弹性剪裁

本文对航空复合材料翼面结构进行了带主动控制系统、满足颤振速度及工艺尺寸要求的最小重量设计.采用亚音速偶极子格网法计算非定常气动力,用状态空间法计算翼面颤振速度,利用最佳控制理论进行最优控制设计,结构固有振动用谱变换Lanczos方法求得.机翼结构用有限元进行模拟,共采用金属及复合材料的杆元、受剪板元、正应力四边形及三角板元等,设计变量取为腹板板厚、杆元截面积及复合材料各定向铺层的厚度,目标函数取为结构重量,约束函数取为闭环颤振速度及工艺尺寸要求,优化问题用可行方向法求解,其中约束函数对设计变量的导数用差分法进行计算.文中对一个实验用机翼进行了颤振主动控制设计,对一个复合材料机翼进行了气动伺服弹性剪裁,证明本方法能充分考虑结构与控制系统的作用,具有很好的收敛性.     

丝束变角度层合板屈曲性能的有限元分析

连续丝束剪切（CTS）作为一种新的丝束变角度（VAT）铺放技术,能克服传统的自动铺丝技术（AFP）的诸多缺陷。鉴于此,分别采用CTS和AFP这2种技术铺设而成的VAF层合板为研究对象,对其屈曲性能进行了有限元分析;在施加相同端部轴向位移的条件下,以铺层顺序[90±<0|75>]_4s为例,对比分析了2种层合板的内力分布;最后,讨论了丝束最小转弯半径对2种铺放技术的影响。结果表明：CTS层合板因其变厚度的特性,其屈曲性能优于AFP层合板;与AFP技术受制于最小转弯半径,导致其在小尺寸结构中的应用受到限制相比,CTS技术适用于各种尺寸的层合板。     

In‐plane and out‐of‐plane constraint for single edge notched bending specimen and cruciform specimen under uniaxial and biaxial loading

Considering fracture constraint is an efficient way to describe stress–strain field and fracture toughness more accurately, so it is necessary to realise the relationship with in‐plane and out‐of‐plane constraint for different standard specimens. In this paper, three‐dimensional finite element method is applied to study the in‐plane and out‐of‐plane constraint for both cruciform specimen and single edge notched bending specimen made from commercial pure titanium. Crack length and in‐plane loading as the factors affecting in‐plane constraint, and thickness as the factor affecting the out‐of‐plane constraint are used to study the effect on both in‐plane and out‐of‐plane constraint in this paper. From the results, in‐plane and out‐of‐plane constraint are both related to specimen geometries and loading styles. And there exist relationships with in‐plane and out‐of‐plane constraint because of factors for different specimens. Depending on crack length, out‐of‐plane constraint increases with in‐plane constraint. While depending on transverse loading, out‐of‐plane constraint decreases with in‐plane constraint. In addition, when the in‐plane constraint of a specimen is higher, in‐plane constraint increases with out‐of‐plane constraint (thickness). When the in‐plane constraint is lower, in‐plane constraint almost remains unchanged with out‐of‐plane constraint.     

影响约束阻尼结构阻尼性能的因素

采用自由梁振动法,研究阻尼层厚度、约束层材料及环境温度等三个变量,对约束阻尼结构阻尼性能的影响。结果表明：阻尼层厚度在1 mm～4 mm范围内,约束阻尼结构的阻尼性能随阻尼层厚度的增加而降低; 约束层材料分别为钢板、大理石板、砂浆板时,约束阻尼结构的阻尼性能不同;低温、高温环境均使约束阻尼结构阻尼值变小; 常温环境下,约束阻尼结构的阻尼值较大,复合损耗因子超过了0.154。     

TWO PARAMETER DESCRIPTION OF CRACK GROWTH INITIATION INCLUDING THICKNESS EFFECTS THROUGH PROBABILISTIC MODELLING

Abstract— The main object of this study is to apply the J-Q model in the transition region with emphasis on the thickness effects and the effects of constraint directly on the lower bound. If only cleavage without prior ductile growth is considered, then in the transition region the thickness effect may be small below a certain thickness. A model for predicting lower bounds from a limited number of data proposed by Stienstra and Anderson has been applied in connection with a J-Q constraint correction. The results are in good agreement with the predictions from a complete statistical analysis. A statistical analysis of the experimental data of cleavage without prior ductile growth, made after a J-Q constraint correction, shows that the latter is an appropriate procedure for evaluating small scale yielding fracture toughness of individual specimens or structures under such conditions.     

The influence of cross-sectional thickness on fatigue crack growth

For thin structures, fatigue crack growth rates may vary with the structure's thickness for a given stress intensity factor range. This effect is mainly due to the change in the nature of the plastic deformation when the plastic zone size becomes comparable with, or greater than, the cross-sectional thickness. Variations in the constraint affect both the crack tip plastic blunting behaviour as well as the fatigue crack closure level. Approximate expressions are constructed for the constraint factor based on asymptotic values and numerical results, which are shown to correlate well with finite element results. It is demonstrated that the present results not only permit predictions of the specimen thickness effects on fatigue crack propagation under spectrum loading, but also eliminate the need to determine the constraint factor by curve-fitting crack growth data.