结构畸变比能处理的应力约束全局化的连续体结构拓扑优化

该文根据von Mises强度准则的畸变比能本质,计算单元畸变比能替代应力约束;依照应力全局化策略,定义结构畸变比能约束概念,求解应力约束下重量最小的连续体结构拓扑优化问题,急剧地减少了应力约束。构造许用应力和结构最大应力的比值含参数幂函数,对约束限进行动态修正。基于ICM(Independent Continuous and Mapping,独立、连续、映射)方法,采用指数型快滤函数建立了结构在畸变比能约束下的结构拓扑优化模型,并选取精确映射下的序列二次规划进行求解。数值算例表明:采用修正的结构畸变比能的应力全局化策略,对于结构拓扑优化问题的求解是有用和高效的。该文提出的方法对解决工况间存在病态载荷的问题也是有益的。     

应力约束全局化处理的连续体结构ICM拓扑优化方法

由于应力约束按单元计,加之多工况,使得连续体结构拓扑优化由于约束数目太多,导致应力敏度分析计算量太大而无法接受。基于第四强度理论提出了应力约束条件全局化处理的方法,化为全局替代约束——总应变能约束,用ICM方法对总应变能约束条件下的连续体结构拓扑优化进行建模及求解,其过程分为三步:第一步选择最大应变能对应的工况,在给定重量下求出最小结构总应变能;第二步提出一个数值经验公式,借助第一步的结果,计算出各工况下的许用总应变能;第三步以第二步计算出来的各工况的许用总应变能作为约束,以重量为目标建立模型并求解。顺便指出,第二步的处理方法可以处理载荷相差特别大的情况,即病态载荷情况。数值算例表明:全局性应力约束可以更好地得到传力路径,对于处理多工况问题具有优势。     

ICM应力全局化方法克服连续体拓扑优化的载荷病态

在连续体结构拓扑优化中,由于载荷通常非常复杂,存在一种类似于结构分析中总刚病态的载荷病态现象。引起载荷病态的原因是由于大多数拓扑优化算法没有考虑大载荷、小载荷间的不同影响,使得小载荷的传力路径在优化过程中消失。该文对载荷病态问题进行了剖析,并将其分为三种情况:1)多工况间有载荷病态,但工况内无载荷病态;2)仅在工况内有载荷病态;3)多工况间有载荷病态,同时某工况内也有载荷病态。为解决载荷病态问题,该文提出了应变能策略,利用应力全局化的ICM方法,逐一采用不同的补充方法解决了上述三种载荷病态问题。对多工况下应力约束的连续体结构拓扑优化问题,应力全局化意指基于第四强度理论将局部性应力约束转化为全局性的应变能约束。数值算例表明:全局性的应变能约束代替局部性应力约束可以更好地得到传力路径,并能更方便地处理各种复杂载荷病态问题。     

屈曲与应力约束下连续体结构的拓扑优化

基于ICM(独立、连续、映射)方法建立了以结构重量最小为目标,以屈曲临界力、应力同时为约束的连续体拓扑优化模型:采用独立的连续拓扑变量,借助泰勒展式、过滤函数将目标函数作二阶近似展开;借助瑞利商、泰勒展式、过滤函数将屈曲约束化为近似显函数;将应力这种局部性约束采用全局化策略进行处理,即借助第四强度理论、过滤函数将应力局部性约束转化为应变能约束,大大减少了灵敏度分析的计算量;将优化模型转化为对偶规划,减少了设计变量的数目,并利用序列二次规划求解,缩小了模型的求解规模。数值算例表明:该方法可以有效地解决屈曲与应力约束共同作用的连续体拓扑优化问题,能够得到合理的拓扑结构,并有较高的计算效率。     

位移约束刚架拓扑优化的非线性有无复合体方法

为了提高基于物理模型的结构拓扑优化的寻优效率, 该文提出了非线性有无复合体, 以刚架结构在位移约束下的拓扑优化为例, 进行了结构重量目标函数极小化的数学模型建立和程序实现。与线性有无复合体不同, 非线性有无复合体是无限多个无穷小的“有单元”和“无单元”各自长度的非线性组合。由于每个梁单元“有”单元长度和“无”单元长度之和的不变性, 其拓扑变量可以用“有”单元的总长度予以表达。推导了结构重量、位移约束同结构拓扑变量的显式函数, 建立了优化模型。使用线性规划算法求解了相应的优化模型, 算例表明, 该文方法的寻优效率得到了提高。同作为数学变换的ICM(独立、连续和映射)方法比较, 该文提出的作为物理模型的方法, 二者在解决结构拓扑优化上具有异曲同工之效：后者的“有”单元长度的非线性关系替代了前者的单元重量、位移约束中的过滤函数。数学变换方法与物理模型方法的异同点更是耐人寻味。 方法     

具有形状和应力约束的连续体结构拓扑优化及其在框架结构设计中的应用

本文研究了在形状和应力约束下的连续体结构拓扑优化问题,采用满应力法求解保证了应力约束的满足;根据对形状的要求,固定部分单元不被删除,强迫最优拓扑满足设计要求。对框架结构进行了计算,结果表明了算法的正确性。     

横向力作用下的悬臂桁架结构拓扑优化

研究了应力约束下最小重量悬臂梁桁架结构的拓扑优化设计。根据Michell理论,首先用解析方法和有限元方法建立满应力类桁架连续体结构。然后选择其中部分杆件形成离散桁架作为近最优结构,并建立桁架的拓扑优化解析表达式。采用解析方法证明最优拓扑结构的腹杆中间结点在节长的四分之一位置。最后采用解析和数值方法对自由端受集中力和侧边受均布力作用的桁架进一步拓扑优化,确定了桁架的节数和每节的长度,最后得到拓扑优化桁架结构。得到的拓扑优化桁架比工程上普遍采用的45°腹杆桁架的体积少20%以上。     

Simulations of a stress and contact model in a chemical mechanical polishing process

A two-dimensional axisymmetric quasi-static contact finite element model for the chemical mechanical polishing process (CMP) was established. The von Mises stress on the wafer surface was investigated. The findings indicate that the profile of the von Mises stress correlated with that of the removal rate. The larger the elastic modulus of the pad or the smaller the elastic modulus of the carrier film, the larger is the maximum von Mises stress. The thicker the pad or the thinner the film, the smaller is the maximum von Mises stress. The larger the load exerted on the carrier, the greater is the maximum von Mises stress.     

A Method of Material Optimization of Cementless Stem Through Functionally Graded Material

Ideally, a bone implant should be such that it exhibits an identical response to loading as real bone and is also biocompatible with existing tissue. A stiff stem, which is usually made of titanium, shields the proximal bone from mechanical loading (stress shielding). On the other hand, decreasing the stem stiffness increases the proximal interface shear stress and the risk of proximal interface failure. Therefore the purpose of this study is to solve these conflicting requirements in order to have more uniform interface shear stress distribution and less stress shielding through the concept of functionally graded material (FGM). FGM is a kind of advanced composite materials, which changes its composition and structure gradually over one or two directions of its volume, resulting in corresponding changes in the properties of the material. This study is divided into two parts; in the first part, the finite element analysis and optimization technique are used to design the stem as one-dimensional FGM, while in the second part, the stem is designed as two-dimensional functionally graded material. The aim of both designs is to overcome the above mentioned problems. In the case of part one (one-dimensional FGM), the gradation of elastic modulus is changed along the vertical direction (model 1) and along the horizontal direction (model 2), in order to find the optimal gradation direction. It is found that the optimal design is to change the elastic modulus gradually from 110 GPa (Hydroxyapatite) at the top of the stem to 1GPa (Collagen) at the bottom (model 1). This optimal gradation decreases stress shielding by 83%, while reduces the maximum interface shear stress by 32% compared to homogenous titanium stem. However, in the second part (two-dimensional FGM, model 3) the materials of optimal design are found to be hydroxyapatite, Bioglass, and collagen. This design leads to the same stress shielding reduction as in model 1, while at the same time, the maximum interface shear stress is reduced by 45% and 63% compared to the optimal one-dimensional FGM design and homogenous titanium stem, respectively.     

Thermal-stress reduction for a Czochralski grown single crystal

In this paper an optimal-control approach for thermal-stress reduction inside a Czochralski-grown single crystal is presented. Using the lateral heat flux as a control variable, an optimal-control formulation for minimizing thermal stress with a given crystal shape is derived. Since the thermal stress is also affected by the lateral shape of crystals during growth, the level of the stress can be reduced by growing crystals into a suitable shape. Using the lateral shape as a control variable, a similar optimal-control formulation for stress reduction is derived. In both cases, the von Mises stress is used as an objective function for the constrained optimization problem. Euler–Lagrange equations are derived using the calculus of variations and Lagrange multipliers. Various stress-reduction strategies are explored by solving the Euler–Lagrange equations numerically.     

Von mises approximation of the critical value of a test

In this paper we propose a von Mises approximation of the critical value of a test and a saddlepoint approximation of it. They are specially useful to compute quantiles of complicated test statistics with a complicated distribution function, which is a very common situation in robustness studies. We also obtain the influence function of the critical value as an alternative way to analyse the robustness of a test.     

The effects of strength models in numerical study of metal plate destruction by contact explosive charge

Based on a complete mathematical model, the authors set up a problem of metal plate destruction by contacting explosive charge in highly nonlinear dynamic software AUTODYN and solved in two cases using the Johnson–Cook and von Mises strength models. The numerical simulation results were compared with the experimental results and showed a good fit of numerical calculations versus experiments by using the von Mises strength model. The study also shows that the Johnson–Cook strength model, if applied unreasonably, will lead to large errors, which would help to avoid mistakes in the future high speed impact study.