基于改进粒子群的薄壁变截面刚架临界载荷优化算法

针对大型变截面薄壁结构的稳定问题,以一类任意约束对称结构受非对称载荷的单跨刚架为研究对象,结构拆分为相关铁木辛柯（Timoshenko）梁,结合差分原理和最优化方法,以每段刚架的每个离散点挠度、临界载荷、轴力、剪力和梁端弯矩为设计变量,建立求解满足边界条件的非线性差分方程模型,提出基于优胜劣汰粒子更新的粒子群（IPSO）临界载荷优化算法。运用JAVA编程语言编制对应优化程序,分析典型算例并核实ABAQUS仿真结果。研究表明,本文提出的优化算法获得了有效的变形位型和高精度的临界载荷计算,能更好地描述刚架受力下位型和载荷的力学关系,进一步为工程设计与分析提供支持。     

基于改进粒子群的薄壁变截面刚架临界载荷优化算法

针对大型变截面薄壁结构的稳定问题,以一类任意约束对称结构受非对称载荷的单跨刚架为研究对象,结构拆分为相关铁木辛柯(Timoshenko)梁,结合差分原理和最优化方法,以每段刚架的每个离散点挠度、临界载荷、轴力、剪力和梁端弯矩为设计变量,建立求解满足边界条件的非线性差分方程模型,提出基于优胜劣汰粒子更新的粒子群(IPSO)临界载荷优化算法。运用JAVA编程语言编制对应优化程序,分析典型算例并核实ABAQUS仿真结果。研究表明,本文提出的优化算法获得了有效的变形位型和高精度的临界载荷计算,能更好地描述刚架受力下位型和载荷的力学关系,进一步为工程设计与分析提供支持。     

简支梁大挠度弹性后屈曲载荷与变形的优化算法

针对简支梁结构大挠度后屈曲载荷与变形的计算问题,本文提出了一种直接求解其后屈曲载荷和变形的优化算法。在简支梁处于大挠度屈曲平衡状态下,将梁结构划分为有限子段,以待求后屈曲载荷为设计变量,根据起点的边界条件和每个子段满足的弯矩变形公式,累积计算出其他各个节点的坐标,以得到的终点坐标满足的边界条件构建目标函数模型。在此基础上,通过MATLAB编制优化程序分析了两个典型算例,并将理论结果与相关软件的计算结果进行对比,从而证明了本文算法的正确性。本文算法求解过程简单、快速,具有一定的实用性,为变截面结构大挠度弹性屈曲稳定性问题的研究提供了参考。     

多约束膜结构截面优化及在MSC/Nastran上的程序实现

将准则法和数学规划法相结合,借助满应力准则将应力约束转化为动态尺寸约束,利用单位虚载荷法将位移约束转化为设计变量的显式表达式建立优化模型,然后用数学规划法求解;采用无量纲设计变量实现设计变量连接,对膜结构的厚度进行优化设计;根据对偶理论,应用对偶规划精确映射原问题,再按泰勒展式建立对偶问题的二阶近似。为了提高优化效率,采用射线步调整结构性态,运用粗选有效约束技术筛选约束,并采用主、被动变量循环确保收敛稳定。以MSC／Nastran软件作为结构分析的求解器,以MSC／Patran软件作为开发平台,完成了膜结构截面优化程序。对膜结构的单变位、多变位的结构优化问题进行了优化计算,并与MSC／Nastran优化模块的计算结果进行比较。算例结果表明程序的可靠性、高效性和稳定性以及理论算法的优越性。     

拉索预应力空间网格结构的优化设计

本文讨论了以结构自重为目标函数,以拉索张力和杆件截面尺寸为设计变量,考虑应力和位移约束的拉索预应力空间结构的优化设计问题,建立了该结构优化设计的数学模型。提出了解决该优化问题的二级优化算法。从本文的两个算例可以看出,二级优化算法有较好的计算效率和收敛性,便于工程应用。     

轴向功能梯度Timoshenko变截面梁的屈曲分析

运用插值矩阵法研究了不同边界条件下轴向功能梯度材料变截面Timoshenko梁的屈曲性能问题。基于Timoshenko梁基本理论,将轴向功能梯度变截面Timoshenko梁临界荷载的计算转化为一组变系数常微分方程特征值问题,然后运用插值矩阵法可一次性地计算出轴向功能梯度变截面梁在不同边界条件下的屈曲临界荷载。当区间划分点数n为80时,在不同的边界条件下均质材料等截面Timoshenko梁量纲为一的临界荷载的本文计算值与解析解有7位有效数字相同,轴向功能梯度Timoshenko锥形梁量纲为一的临界荷载的本文计算值与已有文献计算结果有3~5位有效数字相同,数值计算结果表明了本文方法的有效性和较高的计算精度。同时,本文方法可获取相应的挠度模态函数,而且对于材料梯度函数和截面几何轮廓的具体形式无任何限制条件。     

桁架结构非概率可靠性形状优化设计

采用区间变量描述不确定参数,提出一种桁架结构非概率可靠性形状优化方法。建立了以截面尺寸和节点坐标为设计变量,以结构重量为目标函数,具有非概率可靠性指标约束的桁架结构形状优化数学模型。采用量纲归一化对截面尺寸和节点坐标进行了变量统一;运用均值点法对功能函数进行泰勒线性近似求解得到相应的非概率可靠性指标,并采用序列二次规划算法对优化模型进行求解。三个算例分析结果表明,算例均能快速稳定地收敛到最优解,结果符合工程结构设计经验,验证了本文所提方法的准确性和有效性。     

多层次联合的结构优化设计

多层次联合结构优化问题,通常含有不同种类的设计变量,例如,当构件的截面和结构的形状同时优化时,设计变量就可分为截面类设计变量{X_s)}和几何类设计变量{X_g}。对这类问题,本文提出一个有效的求解策略。优化过程的每一步迭代都由商个子问题组成:(1)优化截面类设计变量{X_8}以减少重量,使约束趋于临界;(2)优化几何类设计变量{X_g}以放松约束,为下一轮迭代提供条件。本文的方法收敛较快且具有较好的稳定性。     

多层次联合的结构优化设计

多层次联合结构优化问题,通常含有不同种类的设计变量,例如,当构件的截面和结构的形状同时优化时,设计变量就可分为截面类设计变量{X_(?)}和几何类设计变量{X_g}。对这类问题,本文提出一个有效的求解策略,优化过程的每一步迭代都由两个子问题组成:(1)优化截面类设计变量{X_8}以减少重量,使约束趋于临界:(2)优化几何类设计变量{X_g}以放松约束。为下一轮迭代提供条件。本文的方法收敛较快且具有较好的稳定性。     

阶梯形变截面圆拱和圆环稳定计算的有效方法

利用等截面圆弧曲杆的稳定微分方程和本文导出的弯矩一般表达式，建立了静水压力作用下阶梯变截面圆拱和圆环稳定分析的代数方程组，得到了解析计算临界载荷的特征方程．算例表明本文方法简单有效     

端部切向载荷作用下的压杆失稳分析及其应用

细直杆件在压应力作用下会产生横向屈曲即失稳．直杆撞击刚性平面或拉断卸载后将形成压缩波，因承载压缩载荷的长度增加可以引起失稳．冲击速度转换的压应力沿着杆件切线方向，该处弯矩和剪力为零；而众多文献设定的失稳段固支边界条件并不准确．基于精确的杆件变形曲率方程得到端部载荷指向杆件中固定点时的受压失稳条件，得到其极限状态即载荷沿杆端切向作用时失稳长度相当于两端简支的1.5 倍．对于钢丝绳拉断形成的冲击失稳，载荷恒定而长度增加，可以产生高阶屈曲即在侧向出现多次曲折，并基于尼龙-橡胶带的模拟试验给出了定性说明．     

Buckling and post-buckling of extensible rods revisited: A multiple-scale solution

An exact non-linear formulation of the equilibrium of elastic prismatic rods subjected to compression and planar bending is presented, electing as primary displacement variable the cross-section rotations and taking into account the axis extensibility. Such a formulation proves to be sufficiently general to encompass any boundary condition. The evaluation of critical loads for the five classical Euler buckling cases is pursued, allowing for the assessment of the axis extensibility effect. From the quantitative viewpoint, it is seen that such an influence is negligible for very slender bars, but it dramatically increases as the slenderness ratio decreases. From the qualitative viewpoint, its effect is that there are not infinite critical loads, as foreseen by the classical inextensible theory. The method of multiple (spatial) scales is used to survey the post-buckling regime for the five classical Euler buckling cases, with remarkable success, since very small deviations were observed with respect to results obtained via numerical integration of the exact equation of equilibrium, even when loads much higher than the critical ones were considered. Although known beforehand that such classical Euler buckling cases are imperfection insensitive, the effect of load offsets were also looked at, thus showing that the formulation is sufficiently general to accommodate this sort of analysis.     

Stability analysis of gradient elastic beams by the method of initial value

The buckling of a bar is studied analytically on the basis of a simple linear theory of gradient elasticity in the frame of the method of initial values. The method of initial values provides the values of the displacements and stress resultants throughout the bar once the initial displacements and initial stress resultants are known. We use probably for the first time the method of initial values to get critical loads of a strain gradient beam under completely different boundary conditions at the two end faces of the beam. Exact carryover matrix is presented for the classical beam and gradient beam analytically. The first mode shapes of classical beam and gradient beam are plotted. The method of initial values is also applied to the beams with variable cross-section. The priorities of the method of initial values are depicted. The variational approach gives a sixth-order ordinary differential equation for a beam in buckling. The additional boundary conditions are used to obtain critical loads. It is observed that critical loads increase dramatically for increasing values of the gradient coefficient.     

Axisymmetric compressive buckling of multi-walled carbon nanotubes under different boundary conditions

The paper studies the axisymmetric compressive buckling behavior of multi-walled carbon nanotubes (MWNTs) under different boundary conditions based on continuum mechanics model. A buckling condition is derived for determining the critical buckling load and associated buckling mode of MWNTs, and numerical results are worked out for MWNTs with different aspect ratios under fixed and simply supported boundary conditions. It is shown that the critical buckling load of MWNTs is insensitive to boundary conditions, except for nanotubes with smaller radii and very small aspect ratio. The associated buckling modes for different layers of MWNTs are in-phase, and the buckling displacement ratios for different layers are independent of the boundary conditions and the length of MWNTs. Moreover, for simply supported boundary conditions, the critical buckling load is compared with the corresponding one for axial compressive buckling, which indicates that the critical buckling load for axial compressive buckling can be well approximated by the corresponding one for axisymmetric compressive buckling. In particular, for axial compressive buckling of double-walled carbon nanotubes, an analytical expression is given for approximating the critical buckling load. The present investigation may be of some help in further understanding the mechanical properties of MWNTs.     

Characteristic-value analysis for plastic dynamic buckling of columns under elastoplastic compression waves

The characteristic-value analysis of plastic dynamic buckling is presented for columns under the action of elastoplastic compression wave caused by an axial-step load. Two critical conditions constituting a dynamic instability criterion are derived on the basis of transformation and conservation of energy. The governing equations, the boundary conditions and the continuity conditions derived by the use of the first critical condition are the same as those given by the adjacent-equilibrium criterion and are insufficient for determining two characteristic parameters involved in the governing equations. A supplementary restraint equation for buckling deformations at the plastic-wave front and the elastic-wave front is derived by the use of the second critical condition. Then, a couple of characteristic equations for two characteristic parameters are derived on the condition that the governing equations have non-trivial solutions satisfying the boundary conditions, the continuity conditions and the supplementary restraint equation. The critical-load parameters, dynamic characteristic parameter (exponent parameter of inertia term) and dynamic buckling modes are calculated from the solutions of the characteristic equations.     

面内阶跃载荷下矩形薄板的塑性动力屈曲

对于面内阶跃载荷作用下矩形薄板的塑性动力屈曲问题,将临界应力和屈曲惯性项指数参数作为双特征参数求解。由相邻平衡准则导出失稳控制方程,由动力屈曲发生瞬间的能量转换和守恒准则,导出波阵面上的屈曲变形补充约束条件。失稳控制方程、边界条件、塑性波阵面上的连续条件和补充约束条件构成了定量求解两个特征参数和动力屈曲模态的完备条件。研究了矩形薄板塑性动力屈曲过程中板的厚宽比、冲击载荷大小、屈曲模态和临界屈曲长度之间的关系。     

热载荷作用下梯度多孔材料梁弯曲及过屈曲力学行为的研究

基于Bernoulli-Euler梁理论,引入物理中面解耦了复合材料结构的面内变形与横向弯曲特性,研究了梯度多孔材料矩形截面梁在热载荷作用下的弯曲及过屈曲力学行为．假设沿梁厚度方向材料的性质是连续变化的,利用能量法推导了矩形截面梁的控制微分方程和边界条件,并用打靶法对无量纲化的控制方程进行数值求解．利用计算得到的结果分析了材料的性质、热载荷、边界条件对矩形截面梁非线性力学行为的影响．结果表明,对称材料模型下,固支梁与简支梁均显示出了典型的分支屈曲行为特征,而其临界屈曲热载荷值均会随着孔隙率系数的增加而单调增加．非对称材料模型下,固支梁仍显示出分支屈曲行为特征,但其临界屈曲热载荷不再随着孔隙率系数的变化而单调变化;而对于两端简支梁,发生了弯曲变形,弯曲挠度随载荷的增大而增大．     

DYNAMIC BUCKLING BEHAVIOR OF MULTI-WALLED CARBON NANOTUBES SUBJECTED TO STEP AXIAL LOADING

This paper studies the dynamic buckling behavior of multi-walled carbon nanotubes (MWNTs) subjected to step axial loading.A buckling condition is derived,and numerical results are presented for MWNTs u...     

Analysis and optimization against buckling of beams interacting with elastic foundation

We consider an infinite continuous elastic beam that interacts with linearly elastic foundation and is under compression. The problem of the beam buckling is formulated and analyzed. Then the optimization of beam against buckling is investigated. As a design variable (control function) we take the parameters of cross-section distribution of the beam from the set of periodic functions and transform the original problem of optimization of infinite beam to the corresponding problem defined at the finite interval. All investigations are on the whole founded on the analytical variational approaches and the optimal solutions are studied as a function of problems parameters.