Computational dynamics approach to the effect of damping on stability of a cantilevered column subjected to a follower force

The paper discusses on the basis of computational approach the effect of small damping on the theoretical flutter bounds of a cantilevered column subjected to a follower force. A cantilevered viscoelastic column having a tip mass is considered. The impulse responses of the column are studied by the mode superposition method to observe the growth rate of the motion. It is established that the growth rate of the motion of the nonconservative column with a larger but small size of damping is greater than that with the smaller. It is demonstrated that the gap between the flutter predictions made by considering and neglecting damping can be bridged by assuming the practical concept of stability, the stability in a finite time interval.     

On the design of Beck's column

The optimization of a single column subject to a follower load is studied. The shape of the column that maximizes the critical load for a given amount of material is found using optimization. The objective function is nonsmooth and there are also multiple local optima. Improved solutions to the optimization problem are found and compared to previous columns suggested in the literature. The sensitivity to perturbations in shape and refined discretization is also investigated.     

Stability of cylindrical shell panels subjected to follower forces based on a mixed finite element formulation

A mixed finite element formulation is developed from a weak variational priniciple. This formulation is applied to stability analysis of cylindrical shell structures subjected to follower loading. Bilinear trial functions are used for all field variables. The rectangular curved elements presented here satisfy the continuity requirements for the field variables at the element interface. Two examples of a cantilevered cylindrical shell panel under different kinds of loading are solved.     

Vibration and stability of a non-uniform double-beam subjected to follower forces

An analysis is presented for the vibration and stability of a non-uniform double-beam subjected to tangential follower forces distributed over the center line by use of the transfer matrix approach. For this purpose, the governing equations of the beam are written as a coupled set of first-order differential equations by using the transfer matrix of the beam. Once the matrix has been determined by numerical integration of the equations, the eigenvalues of vibration and the critical flutter loads are obtained. The method is applied to beams with linearly varying depths and breadths, subjected to a concentrated follower force, and the natural frequencies and flutter loads are calculated numerically, to provide information about the effects on them of varying cross-section span and stiffness of intermediate supports, and the slenderness ratio.     

Vision‐based autonomous convoying with constant time delay

This paper describes the design and experimental validation of a vision‐based vehicle‐following system that uses only onboard sensors to enable a convoy of follower vehicles to autonomously track the trajectory of a manually driven lead vehicle. The tracking is done using the concept of a constant time delay, in which a follower tracks the delayed trajectory of its leader. This constant‐time‐delay approach allows for new techniques to be used to estimate the speed and heading of the leader. Experiments were conducted with full‐sized military vehicles on a 1.3‐km test track. Successful field trials with one follower for 10 laps and with two followers for 13.5 laps, totaling over 30 km, are presented. © 2010 Government of Canada. Exclusive worldwide publication rights in the article have been transferred to Wiley Periodicals, Inc., AWiley Company.     

Optimum design of composite plate wings for aeroelastic characteristics using lamination parameters

The present paper treats the flutter and divergence characteristics of composite plate wings with various sweep angles. First, the effect of laminate configuration on the flutter and divergence characteristics is investigated for composite plate wings. To examine the effect of laminate configuration, the flutter and divergence characteristics are represented on the lamination parameter plane. Next, a minimum weight design of composite plate wings subjected to the constraints on the flutter and divergence speeds is conducted by using a genetic algorithm in which lamination parameters are used as design variables. The effectiveness of aeroelastic tailoring is demonstrated through the optimization results.     

Laterally braced wood beam-columns subjected to biaxial eccentric loading

This paper presents results of a study on the stability capacity and lateral bracing force of wood beam-columns subjected to biaxial eccentric compression loading. A numerical analysis model based on the column deflection curve method was developed. The model considers nonlinear parallel-to-wood-grain stress–strain relationship, size and stress distribution effects of wood strength, shear deformation, and the P-Delta effect of compression load. Material property tests and biaxial eccentric compression tests of wood beam-columns were conducted to provide input parameters and verification for the model. Good agreement was achieved. The adequacy of the 2% rule of thumb was also studied.     

基于混合策略改进的樽海鞘群算法

针对樽海鞘群算法(SSA)在求解复杂优化问题时存在的易陷入局部最优、收敛精度低等缺点,提出一种基于混合策略改进的樽海鞘群算法(ISSA).首先,采用Sobol序列实现樽海鞘种群的初始化,使初始种群在解空间中分布更加均匀,进而提高算法的全局寻优能力;其次,在领导者位置更新阶段引入步长控制因子,根据不同寻优时期自动调节领导者的搜索范围,有效平衡算法的全局搜索与局部搜索;然后,采用改进的透镜成像策略对领导者进行映射,避免算法陷入局部最优;此外,在追随者位置更新阶段,引入一种自主选择追随机制,改善追随者的盲从性,以提高算法的收敛精度;最后,与其他几种代表性优化算法在12个基准测试函数上进行仿真实验对比,并进行Wilcoxon秩和检验,实验结果表明所提出ISSA在收敛速度和精度上有明显提升,相较于其他优化算法具有更好的寻优效果和稳定性.另外,通过两个工程设计案例实验进行测试,进一步验证了所提出ISSA的可行性和适用性.     

Static and dynamic stabilities of a microbeam actuated by a piezoelectric voltage

In this paper, flutter and divergence instabilities of a cantilever, a clamped–clamped, and a cantilever with intermediate simply-support microbeam sandwiched by piezoelectric layers have been studied. By presenting a mathematical formulation and numerical solution, critical piezoelectric force for avoiding of the instability in a cantilever microbeam has been calculated and validated by known buckling capacity of Beck column. By applying a similar mathematical analysis it has been introduced a critical piezoelectric voltage for a clamped–clamped microbeam. It has been shown that for cantilever microbeams, increasing of the follower piezoelectric force leads to: first flutter and then divergence instabilities whereas in the clamped–clamped microbeams only divergence instability can be occurred. Also effects of the intermediate simply support position on the critical piezoelectric voltage of a cantilever microbeam have been investigated. It has been shown that for case when the intermediate simply support is near to the fixed end of the cantilever increasing of the follower piezoelectric force leads to flutter instability but for case when the intermediate simply support is near to the free end of the cantilever it leads to divergence instability.     

Estimation of dynamic buckling for composite columns with open cross-section

Local, global and interactive dynamic responses of thin-walled columns with open cross-sections subjected to pulse compressive loading of different shape are discussed.An analytical–numerical method has been proposed to analyse the dynamic buckling problem. The applied method is based on the asymptotic Koiter’s theory for conservative systems in the second-order approximation. In order to obtain equations of column walls, the non-linear theory of orthotropic thin-walled plates has been modified in such a way that additionally it accounts for all components of inertia forces.The results of calculations obtained with the analytical–numerical method have been compared with those attained from the finite element method. The results are in good agreement.     

Stress profiles in thin-walled prismatic columns subjected to crush loading-II. Bending

This paper extends the concept of a superfolding element, developed originally for axially loaded columns to the case of bending and combined bending/compression loading. A simple kinematic model of a column was constructed with four free parameters. Closed-form solutions were derived for the moment-rotation characteristics of square columns in the post-failure range and stress profiles in the most general case of a floating neutral axis. Considerable simplifications were obtained by assuming that the neutral axis stays within the tensile flange. It was shown that, in this case, the bending characteristics of a column, can in fact, be derived from the known characteristics of an identical column subjected to axial crush. High accuracy numerical calculations were run on a square column with three different width-to-thickness ratios to check the validity of various approximating assumptions. For all three cases considered, the simplified analytical solution was shown to predict the moment-rotation relationship with an absolute error not greater than 7%. Finally, the present method was generalized to arbitrarily shaped multi-cornered sheet metal columns.     

Robust structural optimization of plate wing corresponding to bifurcation in higher mode flutter

We propose a robust structural optimization of a plate wing that considers the bifurcation in higher mode flutter, which affects the robustness of an optimum design and the convergence of an optimization. In the optimization, the thickness distribution of a delta wing is considered to improve the critical dynamic pressure of supersonic flutter under the constant total mass. The convergence is improved by detaching the distance of eigenvalues between adjacent modes by the positive constant value in the optimization. Consequently, the critical dynamic pressure of the optimum design is six times larger than that of the uniform design. Moreover, to improve the robustness, the constraints are proposed to keep eigenvalues between adjacent modes apart by the specified distance which is composed of the sensitivity of the distance of eigenvalues. Numerical results indicate that the robustness of the optimum design is quantitatively obtained with the constraints. Presented at the Second China–Japan–Korea Joint Symposium on Optimization of Structural and Mechanical Systems (CJK-OSM3), Kanazawa, Japan, Oct. 30–Nov. 2, 2004.     

基于PXI的六分力硬件测试系统设计与实现

为满足大吨位固体火箭发动机地面试验对测试的需求,对固体火箭发动机性能参数以及测试原理进行了深入的研究,组建基于PXI总线的发动机推力矢量、发动机燃烧室压力、发动机壳体变形量的综合测试系统;并搭建系统的硬件平台及软件平台;试验结果表明,该系统能够反映固体火箭发动机地面试验的健康状态,采集的特征参量满足技术指标,具有高可靠性和易操作性等特点,能成功用于固体火箭发动机地面试验中的各种测试需要。     

Numerically efficient algorithm for compact microwave device optimization with flexible sensitivity updating scheme

An efficient trust‐region algorithm with flexible sensitivity updating management scheme for electromagnetic (EM)‐driven design optimization of compact microwave components is proposed. During the optimization process, updating of selected columns of the circuit response Jacobian is performed using a rank‐one Broyden formula (BF) replacing finite differentiation (FD). The FD update is omitted for directions sufficiently well aligned with the recent design relocation. As the algorithm converges, the alignment threshold is gradually reduced so that the condition for using BF becomes less stringent. This allows for further reduction of the number of EM simulations involved in the optimization process. The presented flexible Jacobian update scheme allows for considerable reduction of the computational cost with only slight degradation of the design quality. Robustness of the presented algorithm is validated through multiple optimization runs from random initial designs. The verification experiments are conducted for a range of microwave components, including a compact microstrip coupler as well as a three‐section compact microwave resonant cell‐based impedance transformer. The effects of the alignment threshold value on the computational efficiency of the algorithm and the design quality are investigated. Significant savings reaching 50% as compared to the reference algorithm are demonstrated.     

Shape sensitivity analysis with design-dependent loadings—equivalence between continuum and discrete derivatives

The purpose of this paper is twofold: (1) showing equivalence between continuum and discrete formulations in sensitivity analysis when a linear velocity field is used and (2) presenting shape sensitivity formulations for design-dependent loadings. The equations for structural analysis are often composed of the stiffness part and the applied loading part. The shape sensitivity formulations for the stiffness part were well-developed in the literature, but not for the loading part, especially for body forces and surface tractions. The applied loads are often assumed to be conservative or design-independent. In shape design problems, however, the applied loads are often functions of design variables. In this paper, shape sensitivity formulations are presented when the body forces and surface tractions depend on shape design variables. Especially, the continuum–discrete (C–D) and discrete–discrete (D–D) approaches are compared in detail. It is shown that the two methods are theoretically and numerically equivalent when the same discretization, numerical integration, and linear design velocity fields are used. The accuracy of sensitivity calculation is demonstrated using a cantilevered beam under uniform pressure and an arch dam crown cantilever under gravity and hydrostatic loading at the upstream face of the structure. It is shown that the sensitivity results are consistent with finite difference results, but different from the analytical sensitivity due to discretization and approximation errors of numerical analysis.     

基于响应面法的三维炮尾结构设计优化

为满足某炮尾结构布置的特殊需要,在输弹槽贯穿托弹板的开放式炮尾结构基础上,重新设计传力结构;采用基于响应面法（Response Surface Method,RSM）的多目标遗传算法NSGA-II寻找齿形传力结构的最优参数,通过编写Python脚本控制Abaqus内核实现自动前处理,对其进行有限元分析,并基于iSight实现多目标三维模型设计优化.该方法摒弃传统的二维优化三维验证的理念,将多目标遗传算法与RSM结合起来,在iSight中直接进行三维模型设计优化,可节省计算时间、提高计算效率、改善设计水平.     

Optimum design of Beck's column with a constraint on the static buckling load

The paper is concerned with optimization of a damped column subjected to a follower load. The aim is to determine the colum of least volume which has the same critical load as a uniform reference column. The stability analysis is based on the finite element method. The optimization problem is solved by sequential linear programming. By only including a constraint on the flutter load in the volume minimization, a very large volume reduction is possible but the static buckling load (by a pure conservative loading) becomes very small.In applications, it may be important that the optimal column also is capable of supporting a conservative load. Consequently, the volume is minimized with constraints on both the flutter load and the static buckling load. The constraint on the buckling loadp _b has the formp _b ^opt cp _b ⁰ , 0c1, where the upper index opt refers to the optimal design while the upper index 0 refers to the uniform initial design. It is found that, as the constantc approaches 1, the optimal column approaches the optimal Euler column of Tadjbakhsh and Keller (1962).Notation c slack parameter on the constraint on the static buckling load; defined by (9) - c _int,c _ext dimensionless internal and external damping parameters defined by (3) - d _j eigenvalue margin defined by (9) - d vector of time-independent nodal displacements and rotations - _e length of thee-th finite element - L total length of the column - vector of element lengths defined by (11) - m, m(x) mass distribution function - m _i design variables; the mass distribution function evaluated at the nodal points - upper and lower bounds on the design parameters - m design vector with elementsm _i - M mass matrix - N _e the number of finite elements used - p load parameter - Q load matrix - S stiffness matrix - t time - x distance along the column, measured from the clamped end - y lateral deflection of the column - y vector of nodal displacements and rotations - complex eigenvalue - b refers to buckling (static instability by conservative loading) - d refers to divergence (static instability by nonconservative loading) - f refers to flutter (dynamic instability by nonconservative loading)     

Reordering columns for smaller indexes

Column-oriented indexes—such as projection or bitmap indexes—are compressed by run-length encoding to reduce storage and increase speed. Sorting the tables improves compression. On realistic data sets, permuting the columns in the right order before sorting can reduce the number of runs by a factor of two or more. Unfortunately, determining the best column order is NP-hard. For many cases, we prove that the number of runs in table columns is minimized if we sort columns by increasing cardinality. Experimentally, sorting based on Hilbert space-filling curves is poor at minimizing the number of runs.     

Integration of design and manufacturing for structural shape optimization

This paper presents an integrated design and manufacturing approach that supports shape optimization of structural components. The approach starts from a primitive concept stage, where boundary and loading conditions of the structural component are given to the designer. Topology optimization is conducted for an initial structural layout. The discretized structural layout is smoothed using parametric B-Spline surfaces. The B-Spline surfaces are imported into a CAD system to construct parametric solid models for shape optimization. Virtual manufacturing (VM) techniques are employed to ensure that the optimized shape can be manufactured at a reasonable cost. The solid freeform fabrication (SFF) system fabricates physical prototypes of the structure for design verification. Finally, a computer numerical control (CNC) machine is employed to fabricate functional parts as well as mold or die for mass production of the structural component. The main contribution of the paper is incorporating manufacturing into the design process, where manufacturing cost is considered for design. In addition, the overall design process starts from a primitive stage and ends with functional parts. A 3D tracked vehicle roadarm is employed throughout this paper to illustrate the overall design process and various techniques involved.     

Optimum design of cantilever columns in the post buckling region with constraint on axial load—An optimality criterion approach

An optimality criterion and resizing formula for design variables are developed for obtaining minimum weight (volume if density is constant) of cantilever columns subjected to axial load constraints in the post-buckling region. A variational formulation is developed which forms the basis for the finite element analysis for the postbuckling analysis of cantilever columns. A method is presented to obtain absolute design variables from the converged design vector obtained through the resizing formula. Linear buckling constraints can be treated in the present study as special cases. Optimum configurations of cantilever columns of circular cross-section are obtained for three different axial load cases. Comparison of the present solution (linear buckling constraint) in the case of a cantilever column subjected to a concentrated tip load with a continuum solution shows the effectiveness of the present optimality criterion approach.