考虑混合约束的柔顺机构拓扑优化设计

为了满足制造工艺和静强度要求,提出一种综合考虑最小尺寸控制和应力约束的柔顺机构混合约束拓扑优化设计方法。采用改进的固体各向同性材料插值模型描述材料分布,利用多相映射方法同时控制实相和空相材料结构的最小尺寸,采用最大近似函数P范数求解机构的最大应力,以机构的输出位移最大化作为目标函数,综合考虑最小特征尺寸控制和应力约束建立柔顺机构混合约束拓扑优化数学模型,利用移动渐近算法求解柔顺机构混合约束拓扑优化问题。数值算例结果表明,混合约束拓扑优化获得的柔顺机构能够同时满足最小尺寸制造约束和静强度要求,机构的von Mises等效应力分布更加均匀。     

平面整体式三自由度全柔顺并联机构拓扑优化构型设计及振动频率分析

通过建立并联原型机构的微分雅克比矩阵方程,实现平面整体式三自由度全柔顺并联机构与并联原型机构之间的矢量同构映射。在此基础上,建立平面整体式3-PRR型全柔顺并联机构SIMP拓扑优化模型,并采用优化准则算法,结合矢量同构映射方程,进行了平面整体式3-PRR型全柔顺并联机构同构构型设计,通过应力分布和前四阶振动固有频率仿真对比研究表明：所采取的拓扑优化设计方法使平面整体式全柔顺并联机构具有一定的均布刚度和较好的振动抑制性能,且对其振动频率的分析可为机构尺寸优化及振型优化提供了重要的依据。同时,微运动特性的仿真表明其与传统并联原型机构之间的运动学同构性一致。该结果对平面整体式全柔顺并联机构的构型拓扑优化设计有实际意义。     

基于映射的拓扑优化最大尺寸控制方法

拓扑优化方法经过几十年的发展,已成功应用于机械工程、航空航天、电磁等领域的构型设计中。然而,由于制造工艺的限制,拓扑优化结果通常无法直接应用,需根据工艺要求进行修改,因此在拓扑优化模型中考虑制造约束成为重要的研究方向。其中,尺寸控制广泛存在于大部分制造工艺中,主要包括最小尺寸控制与最大尺寸控制。该文提出了一种基于映射的拓扑优化最大尺寸控制方法,构造了一种新的映射模型,对结构中不满足最大尺寸约束的中心单元密度进行惩罚,在不引入任何约束条件的情况下实现了对结构最大尺寸的控制。此外,该文将该方法中的惩罚转变为一个全局约束条件后与具有最小尺寸控制功能的拓扑优化鲁棒列式相结合,实现了对构件的最大最小尺寸协同控制。数值算例表明了该方法的有效性。     

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。     

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。     

多工况应力约束下的拓扑优化格栅

提出一种多工况应力约束下格栅结构的拓扑优化方法。优化目标结构是由无限细无限密的梁(或肋)构成的类格栅连续体(或加肋板)。采用正交异性增强复合材料模型模拟该类格栅连续体(或加肋板)的本构关系。以梁在结点处的密度和方向作为设计变量。根据有限元分析结果,采用满应力准则法优化各单工况下材料分布。按照多工况下材料的方向刚度与各单工况下材料的方向刚度最大值的差值最小为原则建立多工况下梁(或肋)的拓扑优化分布。经过少量迭代就可以建立优化的材料连续分布场。最后以3个算例演示拓扑优化的过程,并给出结点处梁的密度和方向分布。     

考虑重叠过滤及稳定性约束的桁架拓扑优化方法

从工程实际的角度来说,一般不允许结构形式中包含重叠单元。目前桁架拓扑优化的基结构法在选定基节点的情况下一般不建重叠单元,这导致可行域缩小,使优化不能找到更优解,人为增删杆件缺乏科学依据。针对该问题,该文对重叠给出准确的数学描述,建立包含重叠杆的基结构,利用Heaviside函数将拓扑变量连续化处理,使之在优化过程中可以获取目标函数、约束函数的敏度信息,同时考虑在拓扑优化中加入基频约束以避免出现机构,并加入稳定性约束防止出现压杆失稳,通过优化模型实现重叠过滤。最后通过两个案例计算证明可以找到更优解,验证了该方法的有效性。     

飞机起落架扭力臂拓扑优化设计和分析

飞机起落架是一种能够实现飞机起飞,降落,滑跑和停放的重要装置,而扭力臂是飞机起落架中的关键部件.本论文以梁架式起落架中的简单支柱式起落架作为研究对象,基于Solidworks建立飞机扭力臂的有限元模型,在满足强度和刚度要求下,根据实际工程要求对模型进行优化.优化后的飞机起落架模型相比于原先模型减重39.80％,质量减少...     

基于制造工艺约束的数控插齿机中床身拓扑优化设计

为解决立式数控插齿机中床身的拓扑优化结果在工程上加工制造困难的问题,建立了带有制造工艺约束的拓扑优化模型,采用OptiStruct对中床身进行拓扑优化设计,得到了约束条件含有体积分数及同时含有体积分数和制造工艺的2种拓扑优化结果.对比分析了2种拓扑优化结果,表明基于制造工艺约束的拓扑优化设计的中床身结构有更好的铸造性能...     

3-UPU柔顺并联机构构型拓扑优化设计与实验测试

目的为了设计出具有x,y和z方向纯平动的微纳级精密定位装置。方法首先,运用旋量与逆螺旋理验证所设计的传统3-UPU并联机构运动特性;采用封闭矢量映射原理构建3-UPU并联机构的微分Jacobian,实现各关节与动平台的空间映射关系。然后,定义优化问题的目标函数为结构刚度,约束函数为体积比,运动特性条件为微分Jacobian构造3-UPU柔顺并联机构的SIMP模型,并运用优化算法计算。最后,基于Ossmooth对优化构型进行CAD模型的提取,完成运动特性的力学仿真分析,此外,通过3D打印制造处理后的CAD模型,并完成运动特性的实验测试。结果仿真可得,优化后的构型柔度值从58.324 mm/N下降到25.993 mm/N;一阶固有频率从964.64 Hz提高到1362.26 Hz;沿x,y和z方向的微运动特性分别达到2.488,6.512,9.185μm;3-UPU柔顺并联机构优化构型的微运动特性与理论解处于同一微米级,并运用实验测试进行了验证。结论拓扑优化设计的构型具有微米级运动特性和微米定位精度,实验测试结果验证了该优化技术的可行性。     

Topology synthesis of large‐displacement compliant mechanisms

This paper describes the use of topology optimization as a synthesis tool for the design of large‐displacement compliant mechanisms. An objective function for the synthesis of large‐displacement mechanisms is proposed together with a formulation for synthesis of path‐generating compliant mechanisms. The responses of the compliant mechanisms are modelled using a total Lagrangian finite element formulation, the sensitivity analysis is performed using the adjoint method and the optimization problem is solved using the method of moving asymptotes. Procedures to circumvent some numerical problems are discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

Topology optimization of compliant mechanisms using the homogenization method

A procedure to obtain a topology of an optimal structure considering flexibility is presented. The methodology is based on a mutual energy concept for formulation of flexibility and the homogenization method. A multi-objective optimization problem is formulated as an application of compliant mechanism design. Some examples of the design of compliant mechanisms for plane structures are presented. © 1998 John Wiley & Sons, Ltd.     

Topology optimization of compliant mechanisms using pairs of curves

The structural topology optimization approach can be used to generate compliant mechanisms for some desired input–output requirements. The success of the optimization depends on the structural geometry representation scheme used. In this paper, a novel representation scheme is proposed. The representation scheme is characterized by pairs of curves that are used to connect Input/Ouput (I/O) regions of the structure. Each pair of curves includes a normal curve and a fat curve. The areas bounded by the pair of curves define the material distribution between them. All I/O regions are connected to one another (either directly or indirectly) by pairs of curves in order to form one single connected load-bearing structure. A genetic algorithm for constrained and multiobjective optimization is then applied with the representation scheme of the structure in the form of a graph. Simulation results from a displacement inverter and a displacement redirector indicate that the presented representation scheme is appropriate.     

Robust topology optimization of compliant mechanisms with uncertainties in output stiffness

This work addresses the topology optimization approach to design robust compliant mechanisms with respect to uncertainties in the output stiffness, when compared to the traditional deterministic approach. To this end, two formulations are proposed: probabilistic and nonprobabilistic. The probabilistic formulation minimizes a joint objective function of expected output displacement plus a measure of its standard deviations, for given statistical distribution of the output stiffness. The nonprobabilistic formulation is written as minimization of a joint function of the median of output displacements, plus the width of the intervals that contains the extreme values of the output displacements, for a given interval of output stiffness. The Monte Carlo simulation method is used to evaluate expected values and standard deviations of output displacements in the probabilistic formulation and to assess results obtained with the deterministic approach. It is shown that both formulations lead to designs where output displacements are less sensitive to variations of output stiffness when compared to the traditional deterministic approach. Furthermore, as an additional benefit, it is observed that large variations of output stiffness can hinder the appearance of one-node connected hinges, usually found in the deterministic design of compliant mechanisms.     

Hierarchical optimization for topology design of multi-material compliant mechanisms

Multi-material topology optimization enables potential design possibilities in the multiphysics and structural designing fields. In this article, a bi-level hierarchical optimization method is introduced to address the multi-material design of compliant mechanisms. The hierarchical optimization develops decomposition approaches allowing the original complex multi-material optimization problem to be reduced to set of low-order single-material optimization sub-problems. The solution of the complex multi-material problem is found as a vector of the single-material sub-problems solutions. All the local sub-problems are solved with the solid isotropic material with penalization method independently, and a stiffness spreading technique is worked out to coordinate components of the global solution of the original problem. Several numerical examples are presented to demonstrate the validity of this method.     

Topology optimization of compliant circular path mechanisms based on an aggregated linear system and singular value decomposition

This paper proposes a topology optimization method for the design of compliant circular path mechanisms, or compliant mechanisms having a set of output displacement vectors with a constant norm, which is induced by a given set of input forces. To perform the optimization, a simple linear system composed of an input force vector, an output displacement vector and a matrix connecting them is constructed in the context of a discretized linear elasticity problem using FEM. By adding two constraints: 1, the dimensions of the input and the output vectors are equal; 2, the Euclidean norms of all local input force vectors are constant; from the singular value decomposition of the matrix connecting the input force vector and the output displacement vector, the optimization problem, which specifies and equalizes the norms of all output vectors, is formulated. It is a minimization problem of the weighted summation of the condition number of the matrix and the least square error of the second singular value and the specified value. This methodology is implemented as a topology optimization problem using the solid isotropic material with penalization method, sensitivity analysis and method of moving asymptotes. The numerical examples illustrate mechanically reasonable compliant circular path mechanisms and other mechanisms having multiple outputs with a constant norm. Copyright © 2011 John Wiley & Sons, Ltd.