超静定型钢桁架优化设计的面积比法

满应力准则是对超静定型钢桁架进行优化设计的有效方法．但这种方法的主要缺点在于收敛速度很慢甚至不收敛,这给设计工作带来很大的不便．对问题进行了研究,在“型钢压杆稳定设计直接法”的基础上,提出了满应力优化设计的一种新方法——面积比法,有效地提高了设计过程的收敛速度,降低了设计成本,供有关结构设计人员参考．     

几何规划的最速下降法

本文把无约束极值问题中的最速下降法应用到几何规划的集约迭代中,从而控制和加快了收敛速度。用该法计算了两杆桁架和平面腹板梁的优化设计问题取得满意的结果。     

考虑压杆稳定性时二杆桁架的优化设计

从材料力学中一个简单桁架结构的优化设计问题入手,讨论了考虑压杆稳定时二杆桁架的优化设计问题.     

基于敏度分析的拉压不同模量桁架问题的数值分析

利用光滑函数技术,提出光滑化的拉压不同弹性模量问题的应力应变关系,与有限元方法相结合,建立了拉压不同模量一维连续体与桁架结构的数值求解模型,推导了敏度计算公式,采用Newton-Raphson算法进行求解.数值结果表明,本文算法具有较高的计算精度和收敛速度.     

关于规定荷载下柱截面设计方法的探讨

桁架和柱的设计中,常碰到压杆的稳定问题,这一问题在不知杆的截面尺寸情况下,是以试算的方法确定杆的临界力,然后确定截面尺寸.本文给出了常见型钢杆件、松元木杆件受压时稳定问题的图解法,设计者可依据其荷载、支承情况迅速地查出所需截面尺寸或型钢型号.     

基于IGA-SIMP法的连续体结构应力约束拓扑优化

建立了一种IGA-SIMP框架下的连续体结构应力约束拓扑优化方法。基于常用的SIMP模型,将非均匀有理B样条（NURBS）函数用于几何建模、结构分析和设计参数化,实现了结构分析和优化设计的集成统一。利用高阶连续的NURBS基函数,等几何分析（IGA）提高了结构应力及其灵敏度的计算精度,增加了拓扑优化结果的可信性。为处理大量局部应力约束,提出了基于稳定转换法修正的P-norm应力约束策略,以克服拓扑优化中的迭代振荡和收敛困难。通过几个典型平面应力问题的拓扑优化算例表明了本文方法的有效性和精确性。应力约束下的体积最小化设计以及体积和应力约束下的柔顺度最小化设计的算例表明,基于稳定转换法修正的约束策略可以抑制应力约束体积最小化设计中的迭代振荡现象,获得稳定收敛的优化解;比较而言,体积和应力约束下的柔顺度最小化设计的迭代过程更加稳健,适合采用精确修正的应力约束策略。     

基于IGA-SIMP法的连续体结构应力约束拓扑优化

建立了一种IGA-SIMP框架下的连续体结构应力约束拓扑优化方法。基于常用的SIMP模型,将非均匀有理B样条(NURBS)函数用于几何建模、结构分析和设计参数化,实现了结构分析和优化设计的集成统一。利用高阶连续的NURBS基函数,等几何分析(IGA)提高了结构应力及其灵敏度的计算精度,增加了拓扑优化结果的可信性。为处理大量局部应力约束,提出了基于稳定转换法修正的P-norm应力约束策略,以克服拓扑优化中的迭代振荡和收敛困难。通过几个典型平面应力问题的拓扑优化算例表明了本文方法的有效性和精确性。应力约束下的体积最小化设计以及体积和应力约束下的柔顺度最小化设计的算例表明,基于稳定转换法修正的约束策略可以抑制应力约束体积最小化设计中的迭代振荡现象,获得稳定收敛的优化解;比较而言,体积和应力约束下的柔顺度最小化设计的迭代过程更加稳健,适合采用精确修正的应力约束策略。     

函数变换下的满应力设计方法

本文从函数变换下函数高阶展式出发,推出了无穷个满应力公式,在空间桁架结构和平面框架结构中分别进行了16种情况下的满应力实现,并进行了相应的数值实验,得到了关于收敛较快公式的初步结论。     

基于类桁架连续体的结构拓扑优化方法与应用

以各向异性连续体为基结构,采用类桁架连续体材料模型进行结构拓扑优化。以材料在结点位置的密度和方向作为优化设计变量,使材料在设计域内连续分布。并以此建立材料的弹性矩阵和刚度矩阵。优化过程没有抑制中间密度,这从根本上避免了许多拓扑优化方法普遍存在的单元铰接、棋盘格现象以及单元依赖性等数值不稳定问题。采用满应力准则法,借助有限元结构分析,经过少量迭代,建立优化的材料连续分布场,即类桁架连续体结构。由于首先建立的拓扑优化结构是各向异性连续体,从而得到更大优化空间。然后可以结合工程实际需要将其转化为离散的拓扑优化杆系结构。最后,以1个经典Michell桁架和3种形式的拱桥为数值算例,演示了其结构拓扑优化过程。     

基于可靠性约束的结构优化设计技术研究

建立结构重量最小化、可靠度为约束的优化模型。将结构近似为串联可靠度模型，每个元件作为一失效单元；由应力状况建立元件的失效函数。采用一次二阶矩法求解元件的可靠性指标；用元件失效概率的和来表示结构失效概率；将结构失效概率的允许值平分给元件，建立设计变量的显示迭代式，并用满可靠度法进行修正，获得最终设计结果。在开展结构静强度优化设计的同时，对元件在线弹性范围内的屈曲可靠性优化设计问题做了初步的研究。桁架结构和机翼盒段结构的可靠性优化结果表明，与现有方法相比，本文提出的方法在具有较高精度的同时，极大地提高了优化设计的效率。     

On the optimal shape of compressed rotating rod with shear and extensibility

In this paper, the optimal shape of a compressed rotating rod which maintains stability against buckling is presented. In the rod modeling, extensibility along the rod axis and shear stress is taken into account. Using Pontryagin's maximum principle, the optimization problem is formulated with a fourth order boundary value problem. The optimally shaped compressed rotating (fixed-free) rod has a finite cross-sectional area on the free end. This shape is qualitatively different from that suggested by the Bernoulli-Euler theory with zero cross-sectional area on the free end. In addition, the Bernoulli-Euler theory overestimates the buckling load, and this effect is more significant in the optimally shaped rod than for the corresponding constant cross-sectional rod consisting of the same material volume and length. In order to show this effect, it is necessary to use a generalized constitutive model which takes real material properties, such as axial extensibility and shear stress into account. Particularly, the solution of this generalized problem, obtained for thin rods, approaches the classical solution predicted by the Bernoulli-Euler theory.     

Does generalized elastica lead to bimodal optimal solutions?

This paper answers the following question. A compressed rod clamped at both ends is assumed to rotate with a constant angular velocity. In the sense of classical Bernoulli–Euler elastica theory, the shape of the lightest rod, stable against buckling, is bimodal (i.e. associated with two buckling modes). What will be the case if we introduce more physical information in the rod model by assuming that it can suffer not only flexure but also compression and shear?     

The strongest rotating rod

By using the Rayleigh quotient, we present the variational formulation for the strongest rotating rod stable against buckling. This variational formulation is converted to fifth-order singular non-linear boundary value problem. The optimal shape and the critical rotating speed are determined with special numerical-analytical integration procedure. We found the explicit linear relation between the volume and the squared critical speed. Although, in general, the linear stability problem for the optimal rotating rod does not have purely discrete spectra, we show that in the present case, the critical speed is determined with lowest eigenvalue. This fact verifies our optimization strategy based on a linear spectral problem.     

型钢柱(压杆)稳定设计的直接法

在稳定设计中,根据已知轴向荷载来确定型钢柱的截面尺寸,当前国内外均采用试算的方法,设计过程非常繁琐。本提出一种确定型钢柱截面尺寸的简捷方法-直接法,使设计工作摆脱了繁琐的试算,大大提高了计算效率。     

Tangential interaction of elastic spherical particles in contact

The elastic interaction of spherical particles is studied. The distribution of the stress, normal to the contact plane, is determined by the rod model suggested recently, which is applicable in the more wide range of deformations as compared with the classical Hertz law. In the rod model context an inner part of compressed particles is regarded as an elastic cylindrical rod, which radius is equal to the contact radius. The rod reaction is added to the normal particle interaction corresponding with the Hertz solution. The resulting normal force passes into the Hertz solution for infinitesimal deformations and gives stronger particle repulsion for finite deformations. Here we solve the Mindlin problem for the rod model, i.e., derive the tangential interaction of initially compressed particles when a relative displacement takes place. The analytical expressions, which determine the total displacement of the sphere’s centers and the corresponding tangential force, are derived. So, the generalization of the classical Mindlin law is obtained for the rod model.     

形状记忆合金相变塑性的统一本构理论

本文根据单品相变时其宏观(长程)切应变(等效应变)与外加切应力(等效应力)问的幂函数关系假定,建立了形状记忆合金多晶体相变塑性的统一细观本构理论,它推广了现有细观本构理论的结果,消除了现有理论中存在的当外加偏应力趋于零时自由能函数的不连续性和宏观塑性变形的不连续性。这一本构理论将能统一地描述在不同温度和载荷下记忆合金所呈现的各种行为。     

Cr4Mo4V轴承钢滚动接触疲劳和磨损性能研究

通过球棒滚动接触疲劳(RCF)试验机,研究了Cr4Mo4V轴承钢在4050润滑油润滑和0.18滑滚比条件下的滚动接触疲劳和磨损性能.结果表明:Cr4Mo4V钢的应力-寿命(S-N)曲线数据分散性较大,疲劳寿命随着应力增加呈下降趋势.Cr4Mo4V钢滚动接触磨损主要为磨料磨损,黏着磨损和疲劳磨损,随着应力和时间增加磨损体积增加,滚道凹槽深度达到17μm.通过光学显微镜(OM)和扫描电子显微镜(SEM)观察试样棒剖面与滚道交界处疲劳裂纹,发现疲劳破坏类型主要有两种:起源于表面的剥落(SOF)和起源于白蚀区的剥落(WSF).通过滚道径向切割抛光酸蚀显示Cr4Mo4V钢滚动接触疲劳影响区,随着应力和循环接触次数的增加,在次表层依次发现黑蚀区(DER)、白蚀区(WEA)和蝴蝶组织(BW).表面碳化物的剥落坑,黏着磨损和疲劳磨损的凹坑导致了表面起裂、白蚀区和蝴蝶组织中的碳化物和夹杂导致微裂纹的产生,链状碳化物使裂纹往深处扩展.     

On the Optimal Shape of a Compressed Rotating Rod

By using Pontryagin's maximum principle we determine the shape of the lightest compressed rotating rod, stable against buckling. It is shown that the cross-sectional area function is determined from the solution of a nonlinear boundary value problem. A variational principle for this boundary value problem is formulated and a first integral is constructed. The optimal shape of a rod is determined by numerical integration.     

钢筋砼叠合梁受力特性分析

本运用成熟的电算模拟方法,计算得到二阶段受力钢筋砼叠合梁在不同受力阶段的截面应力分布规律及钢筋的应力变化规律,分析得到二阶段受力时钢筋砼叠合＾「１」的受拉钢筋应力超前,受压区砼应变迟后逐渐缓解的实质为截面应力重分布的结果。