Optimization of bolt thread stress concentrations

Designs of threaded fasteners are controlled by different standards, and the number of different thread definitions is large. The most commonly used thread is probably the metric ISO thread, and this design is therefore used in the present paper. Thread root design controls the stress concentration factor of threads and therefore indirectly the bolt fatigue life. The root shape is circular, and from shape optimization for minimum stress concentration it is well known that the circular shape is seldom optimal. An axisymmetric Finite Element formulation is used to analyze the bolted connection, and a study is performed to establish the need for contact modeling with regard to finding the correct stress concentration factor. Optimization is performed with a simple parameterization with two design variables. Stress reduction of up to 9% is found in the optimization process, and some similarities are found in the optimized designs leading to the proposal of a new standard. The reductions in the stress are achieved by rather simple changes made to the cutting tool.     

大展弦比机翼中液压管路的抗大变形设计与优化方法

提出了一种大展弦比机翼管路的抗大变形设计与优化方法。首先建立了大展弦比机翼平板-不同布局管路的装配简化模型;然后分析了在机翼大变形下,管道的弯曲位置、弯曲半径、横向距离、弯曲角度等几种不同布局参数,对管路根部应力、最大应力和卡箍处变形的影响关系。结果表明:弯曲位置与横向距离对应力有较大影响,弯曲位置靠近机翼根部可以降低管道根部应力,但是最大应力显著增加,横向距离的增加可以降低管路根部应力以及最大应力;弯曲位置和弯曲半径对卡箍处变形有较大影响,随着弯曲位置从机翼板根部向变形处移动,卡箍处变形量均先减小后增加,弯曲半径的增加会降低卡箍处变形量。采用遗传算法得到在机翼大变形下最优的管形布局,结果表明,卡箍附近最大应力比直管降低了51%。     

Accuracy and stability of a set of free‐surface time‐domain boundary element models based on B‐splines

An analysis is given for the accuracy and stability of some perturbation‐based time‐domain boundary element models (BEMs) with B‐spline basis functions, solving hydrodynamic free‐surface problems, including forward speed effects. The spatial convergence rate is found as a function of the order of the B‐spline basis. It is shown that for all the models examined the mixed implicit–explicit Euler time integration scheme is correct to second order. Stability diagrams are found for models based on B‐splines of orders third through to sixth for two different time integration schemes. The stability analysis can be regarded as an extension of the analysis by Vada and Nakos [Vada T, Nakos DE. Time marching schemes for ship motion simulations. In Proceedings of the 8th International Workshop on Water Waves and Floating Bodies, St. John's, Newfoundland, Canada, 1993; 155–158] to include B‐splines of orders higher than three (piecewise quadratic polynomials) and to include finite water depth and a current at an oblique angle to the model grid. Copyright © 2000 John Wiley & Sons, Ltd.     

基于改进的双向渐进结构优化法的应力约束拓扑优化

工程结构设计时经常需要限制最大名义应力,以避免发生断裂或疲劳破坏,一个有效的策略是采用拓扑优化方法. 常规的双向渐进结构优化法(bi-evolutionary structural optimization, BESO)不能有效求解应力约束拓扑优化问题,为此本文提出一种改进的双向渐进结构优化方法,处理体积和应力约束下的最小柔顺性问题. 引入基于K-S函数的全局应力度量,以减小大量局部应力约束引起的计算代价. 采用拉格朗日乘子法将应力约束函数引入到目标函数,然后由二分法确定合适的拉格朗日乘子的值使得应力约束得到满足. 而且,详细推导了基于BESO方法的应力约束拓扑优化模型及其灵敏度列式,最后通过三个典型拓扑优化算例验证改进方法的有效性. 为展示考虑应力约束的优点,将应力约束设计与传统的基于刚度的设计进行了比较. 结果表明, 改进的BESO方法优化迭代过程稳健,获得了边界灰度单元很少的清晰的拓扑构型,并实现了有效降低应力集中效应的设计.      

Application of smoothing spline approximations in problems on identification of creep parameters

Conclusion It is desirable to use approximated cubic splines to obtain reliable processing of experimental data on creep and for identification of creep parameters. The spline approximation makes it possible to allow for such characteristic features of creep as the three-stage nature of the process of deformation and the scattering of Theological properties of materials; it also makes it possible to computer the first and second derivatives for an arbitrary point in time to obtain the corresponding speed and acceleration of the creep process. Translated from Prikladnaya Mekhanika, Vol. 33, No. 6, pp. 52–61, June, 1997.     

Design of Beams Subjected to Random Loads

Nonuniform Timoshenko beams subjected to a given stationary random excitation are considered. The general equations relating the spectral density function of the response to the cross spectral density of the load are derived. The optimal shape of the beam is defined as the shape which, for given constant volume of the beam, minimizes the maximum root-mean-square value of the bending stresses in the beam. The shape of the beam is described by a limited number of orthogonal design functions, and their optimal combination is found by sequential linear programming with move limits. From numerical results it is seen that slight modifications of the beam shape give a considerable reduction of maximum r.m.s. stress for most loading cases.     

Free vibration of layered cylindrical shells filled with fluid

The vibration of the layered cylindrical shells filled with a quiescent, incompressible, and inviscid fluid is analyzed. The governing equations of the cylindrical shells are derived by Love’s approximation. The solutions of the displacement functions are assumed in a separable form to obtain a system of coupled differential equations in terms of the displacement functions. The displacement functions are approximated by Bickley-type splines. A generalized eigenvalue problem is obtained and solved numerically for the frequency parameter and an associated eigenvector of the spline coefficients. Two layered shells with three different types of materials under clamped-clamped (C-C) and simply supported (S-S) boundary conditions are considered. The variations of the frequency parameter with respect to the relative layer thickness, the length-to-radius ratio, the length-to-thickness ratio, and the circumferential node number are analyzed.     

基于余弦样条函数的有限点阵法

应用节点影响域的概念,提出了基于余弦样条函数的有限点阵方法.利用余弦样条函数的性质,通过张量积的形式构造余弦样条函数正则解空间,用于逼近场函数,余弦样条基的线性组合使得边界条件处理如同有限元法一样方便.余弦样条与边界型方法结合,可用于求解不规则域问题.数值实例的计算结果表明,文中方法避免了高阶多项式构造形函数所带来的数值振荡,解的连续性不受限制,为改进计算精度而加密点阵所导致的计算量增加量较少,计算收敛快.     

Laser surface-contouring and spline data-smoothing for residual stress measurement

We describe non-contact scanning with a confocal laser probe to measure surface contours for application to residual stress measurement. (In the recently introduced contour method, a part is cut in two with a flat cut, and the part deforms by relaxation of the residual stresses. A cross-sectional map of residual stresses is then determined from measurement of the contours of the cut surfaces.) The contour method using laser scanning is validated by comparing measurements on a ferritic steel (BS 4360 grade 50D) weldment with neutron diffraction measurements on an identical specimen. Compared to lower resolution touch probe techniques, laser surface-contouring allows more accurate measurement of residual stresses and/or measurement of smaller parts or parts with lower stress levels. Furthermore, to take full advantage of improved spatial resolution of the laser measurements, a method to smooth the surface contour data using bivariate splines is developed. In contrast to previous methods, the spline method objectively selects the amount of smoothing and estimates the uncertainties in the calculated residual stress map.     

Performance analysis and application of grid interpolation techniques for fluid flows

Although it is common for automated image processing techniques to claim subpixel accuracy in the identification of particles, or centroids of displacements of groups of particles, additional errors are inevitably introduced when and if these data are reinterpolated back onto a grid mesh whose nodes lie at different locations from the original data. Moreover, these errors can be large compared to the errors introduced in the original image processing step.Two different techniques, convolution with an adaptive Gaussian window (AGW), and a two-dimensional thin-shell spline (STS), have been compared and contrasted for interpolating irregularly spaced data onto a regular grid. Both techniques are global interpolators; the Gaussian kernel applies an ad hoc choice of smooth function, while the thin-shell spline minimises a global functional proportional to the Laplacian of the velocity field. In this way, the smoothness constraint on the spline coefficients may be thought of as akin to a viscous smoothing of the fluid flow.Performance curves are given, enabling the investigator to make an informed choice of interpolating routine and grid interpolation parameters to minimise the interpolation errors, given various external constraints. Some illustrative example applications on real experimental data are described. In general, the importance of matching the interpolation technique to the characteristics of the original data is stressed. It is also pointed out that a correct interpretation of grid interpolated data must be based on a basic knowledge of the performance characteristics of that interpolator. Finally, recommendations are made concerning the development of surface spline techniques for problems involving large numbers of data points.     

3D-Simulation of human walking by parameter optimization

The simulation of human gait is a complex dynamical problem that requires accounting for energy consumption as well as dealing with a redundantly actuated multibody system. If muscle forces and generalized coordinates are parameterized, optimization techniques allow the simulation of the muscle forces and of the walking motion. An optimization framework is presented for non-symmetrical gait cycles found in the presence of one-sided gait disorders. The motion of each leg is independently parameterized for a whole walking cycle. The non-linear constraints used to fulfill the equations of motion and the kinematical constraints of the different walking phases are implemented in an efficient way. Fifth-order splines are used for the parameterization to reduce the oscillatory behavior coming from non-periodicity conditions. To achieve the computational performance required for three-dimensional simulations, the spline interpolation problem has been split in two parts, one is performed in a preprocessing stage and the other during the optimization. Numerical differentiation via finite differences is avoided by implementing analytical derivatives of the splines functions and of the contractile element force law. The results show good numerical performance, and the computational efficiency for 3D-simulations with one-sided gait disorders is highlighted.     

全螺栓装配式钢框架外挂轻质墙板有限元分析

基于一体化轻质保温装饰墙板全螺栓装配式钢框架的抗震性能试验研究,本文采用商业有限元软件ABAQUS对结构进行了精细化非线性有限元分析。研究了结构的滞回性能、结构能力、应力分布以及失效模式等,提出了在柱脚和龙骨间设置加劲肋的改进设计方案,并对诸如顶底L型件水平板和竖向板螺栓数量、加劲肋形式、结构高跨比以及轴压比等关键设计参数进行了拓展分析。结果表明,采用本文有限元建模方法能够精准地模拟试验的滞回性能,极限承载力与试验最大差值为8.86%,模型失效模式及应力分布与试验现象高度吻合;柱脚和龙骨间加劲肋使柱脚内外翼缘协同变形,减小翼缘局部屈曲,避免龙骨连接处焊缝的应力集中,显著提升了结构承载力;通过优化顶底L型件的螺栓数量和加劲肋形式等设计参数,可进一步提升结构能力;实际工程中应合理控制结构高跨比和轴压比,以满足抗震设防要求。     

Externally pressurized air journal bearing with multiple supply holes

A theoretical analysis is made to predict the load carrying capacity, flow requirement, and stiffness of an externally pressurized air lubricated journal bearing with several supply holes. The load, flow, and stiffness, expressed in dimensionless parameters, are presented for various bearing design parameters and eccentricity ratios. The design procedure of one such bearing either for maximum load capacity or for maximum stiffness is indicated.     

加筋路径驱动的板壳自适应等几何屈曲分析

加筋薄壁结构常被用于航空航天结构的轻量化设计.随着结构尺寸和几何特征的增加,需要更加精细的网格来满足分析精度的要求.传统的等几何方法采用NURBS张量积形式的拓扑结构,使得在分析过程中难以实现局部细化,而全局细化则会增加不必要的自由度.为了提升加筋板壳结构的数值分析精度和效率,提出一种基于RPHT (rational polynomial splines over hierarchical T-meshes)样条的加筋板壳自适应等几何屈曲分析方法.样条网格可以沿着加筋路径进行自适应的局部细化,有效提升低自由度下加筋板壳结构等几何屈曲分析的精度.首先,蒙皮和筋条分别采用RPHT样条曲面和NURBS样条曲线进行建模,几何建模与数值仿真采用统一的几何语言,实现建模与分析的一体化.其次,采用几何投影算法和样条插值算法实现筋条与蒙皮之间的高效高精度强耦合,并建立基于加筋路径驱动自适应网格细化方法.最后,曲线加筋板和网格加筋壳两个算例验证本方法的高效性和鲁棒性,通过与基于NURBS的等几何分析进行对比,本方法能够明显降低分析模型的总自由度.     

Spline collocation approach to boundary value problems

A well-known Stokes problem is discussed by a cubic spline collocation method. Two consecutive cubic splines are obtained for the problem. The results by this method are compared with those of an orthogonal collocation method. The selection of the length of the subintervals of the range of the boundary value problem is also justified. The results obtained by these two methods are compared with the analytic solution. The methods involve simple algebra, and hence the calculations do not require the help of a computer. Necessary error analysis has been carried out.     

Optimal airfoil shapes for low Reynolds number flows

Flow over NACA 0012 airfoil is studied at α = 4^° and 12^° for Re?500. It is seen that the flow is very sensitive to Re. A continuous adjoint based method is formulated and implemented for the design of airfoils at low Reynolds numbers. The airfoil shape is parametrized with a non‐uniform rational B‐splines (NURBS). Optimization studies are carried out using different objective functions namely: (1) minimize drag, (2) maximize lift, (3) maximize lift to drag ratio, (4) minimize drag and maximize lift and (5) minimize drag at constant lift. The effect of Reynolds number and definition of the objective function on the optimization process is investigated. Very interesting shapes are discovered at low Re. It is found that, for the range of Re studied, none of the objective functions considered show a clear preference with respect to the maximum lift that can be achieved. The five objective functions result in fairly diverse geometries. With the addition of an inverse constraint on the volume of the airfoil the range of optimal shapes, produced by different objective functions, is smaller. The non‐monotonic behavior of the objective functions with respect to the design variables is demonstrated. The effect of the number of design parameters on the optimal shapes is studied. As expected, richer design space leads to geometries with better aerodynamic properties. This study demonstrates the need to consider several objective functions to achieve an optimal design when an algorithm that seeks local optima is used. Copyright © 2008 John Wiley & Sons, Ltd.     

A kind of bivariate spline space over rectangular partition and pure bending of thin plate

The mechanical background of the bivariate spline space of degree 2 and smoothness 1 on rectangular partition is presented constructively.Making use of mechan- ical analysis method,by acting couples along the interior edges with suitable evaluations, the deflection surface is divided into piecewise form,therefore,the relation between a class of bivariate splines on rectangular partition and the pure bending of thin plate is established.In addition,the interpretation of smoothing cofactor and conformality con- dition from the mechanical point of view is given.Furthermore,by introducing twisting moments,the mechanical background of any spline belong to the above space is set up.     

Effect of air injection method on the performance of an air lift pump

Air lift pump performance was investigated experimentally for different submergence ratios (the ratio between the immersed length of the riser and its total length) using different air injection footpiece designs. For this purpose an air lift pump with a riser 200 cm long and 2.54 cm in diameter, was designed and tested. Nine different air injection footpiece designs were used at four submergence ratios with different air injection pressures (from 0.2 to 0.4 bar). An area of 10 mm² was chosen and divided into nine injection hole arrangements (1, 2, 3, 4, 6, 15, 25, 34 and 48 holes) to cover the whole experimental range. Four submergence ratios were used for this work: 0.75, 0.7, 0.6 and 0.5. The experimental results showed a marked effect on the pump performance when operated with different types of injectors at different submergence ratios. The results indicated that the disk with three holes (D3) gives the highest efficiency at nearly all submergence ratios. Moreover, it is found that there is a suitable disk design for maximum water flow rate at every submergence ratio. Further, the highest efficiency resulted at the largest used submergence ratio, namely 0.75. The pump capacity and efficiency were found to be functions of air flow rate, lift ratio, and injection pressure.     

Optimization of tensegrity structures

This paper concerns the design of tensegrity structures with optimal mass-to-stiffness ratio. Starting from an initial layout that defines the largest set of allowed element connections, the procedure seeks the topology, geometry and prestress of the structure that yields optimal designs for different loading scenarios. The design constraints include strength constraints for all elements of the structure, buckling constraints for bars, and shape constraints. The problem formulation accommodates different symmetry constraints for structure parameters and shape. The static response of the structure is computed by using the nonlinear large displacement model. The problem is cast in the form of a nonlinear program. Examples show layouts of 2D and 3D asymmetric and symmetric structures. The influence of the material parameters on the optimal shape of the structure is investigated.