三维连续体结构仿生拓扑优化新方法

Wolff法则是指骨骼通过重建/生长,保证骨小梁方向趋于与主应力方向一致以不断地适应它的力学环境。根据Wolff法则,建立了一种新的拓扑优化的准则法。该方法的基本思想是:(1)将待优化的结构看作是一块遵从Wolff法则生长的骨骼,骨骼的重建过程作为三维连续体结构寻找最优拓扑的过程;(2)用构造张量描述正交各向异性材料的弹性本构;(3)重建规律为结构中材料的更新规律。通过引入参考应变区间,材料更新规律可解释为:设计域内一点处主应变的绝对值不在该区间时,该点处构造张量出现变化;否则,构造张量不变化,该点处于生长平衡状态。(4)当设计域内所有点都处于生长平衡状态时,结构拓扑优化结束。采用各向同性本构模型,即令二阶构造张量与二阶单位张量成比例,分析三维结构拓扑优化。实例进一步验证基于Wolf法则的连续体结构优化方法的正确性和可行性。     

基于类桁架材料模型的不确定荷载下结构拓扑优化

用区间分析方法研究了不确定荷载下结构拓扑优化方法。采用类桁架材料模型建立拓扑优化类桁架连续体结构。根据区间变量运算法则推导出不确定荷载下应力约束体积最小类桁架结构的拓扑优化方法。首先采用区间分析方法得到任一点的最不利荷载工况下应变状态。在此应变状态下,利用满应力准则优化类桁架材料中杆件的方向和密度。如此反复分析和优化,直至迭代收敛。最后由类桁架中杆件分布场可以近似离散得到桁架结构。通过几个数值算例验证了方法的有效性。数值算例显示了不确定荷载下的结构拓扑优化布局更合理。     

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。     

区间参数平面连续体结构频率非概率可靠性拓扑优化

研究了具有区间参数的平面连续体结构在固有频率非概率基频约束和频率禁区约束下的拓扑优化设计问题。考虑结构弹性模量、质量密度和频率约束限具有区间不确定性,根据SIMP材料插值方法和区间变量运算法则,构建了基于频率非概率可靠性约束的弯曲薄板和平面应力薄板结构的拓扑优化数学模型表达式,并给出了进化优化准则。算例及其结果表明文中模型和方法的有效性。     

一种基于非概率可靠性的结构水平集拓扑优化

该文在研究水平集拓扑优化方法的基础上,对具有区间参数的不确定性结构的非概率可靠性约束进行了分析,经对有限元公式的推导、变换,提出了包涵非概率可靠度信息的拟安全系数形式,从而将非概率可靠性约束问题显式化处理,使得优化过程形式简单、便于计算,避免了复杂的迭代运算。通过对算例中数据及拓扑图形的对比研究,表明该文中模型的合理性和方法的有效性。     

约束层阻尼短圆柱壳拓扑优化分析及实验研究

针对约束层阻尼短圆柱壳拓扑优化问题,采用基于模态应变能法的渐进结构优化算法（ESO）,引入独立网格滤波技术, 通过灵敏度分析,用ANSYS的参数化设计语言APDL编写拓扑优化程序,获得一定约束层阻尼材料用量的约束层阻尼最优拓扑构形,并对约束层阻尼材料的优化布局进行实验验证。研究表明该拓扑优化方法正确,用于短圆柱壳约束层阻尼材料布局优化具有较强的工程实用性。     

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。     

基于骨架提取的拓扑优化最小尺寸精确控制

受到可制造性的约束,拓扑优化技术目前多用于结构的概念设计,因此,研究直接面向加工制造的拓扑优化方法很有必要。该文基于启发式BESO(Bi-directional Evolutionary Structural Optimization)算法,提出了一种高效的可精确控制结构最小尺寸的拓扑优化方法。通过灵敏度插值,细化边界单元,改进BESO算法,解决边界不光滑问题;采用拓扑细化方法,提取拓扑结构的骨架构型;以此为基础,判定结构中不满足最小尺寸约束的部位,基于改进的BESO算法,实现拓扑优化结构的最小尺寸精确控制;此外,在优化过程中,通过松弛施加最小尺寸约束的方法,有效避免优化早熟问题。数值算例表明了该拓扑优化方法的有效性。     

稳态热传导结构非概率可靠性拓扑优化设计

研究具有区间参数的稳态热传导结构在散热弱度非概率可靠性约束下的拓扑优化设计问题。建立了以单元相对导热系数为设计变量,导热材料体积极小化为目标函数,满足散热弱度非概率可靠性为约束条件的稳态热传导结构的拓扑优化设计数学模型。基于区间因子法,推导出散热弱度的均值及离差的计算表达式。采用渐进结构优化法的求解策略与方法,并利用过滤技术消除优化过程中的数值不稳定性现象。通过算例验证文中模型及求解策略、方法的合理性和有效性。     

先进复合材料格栅圆柱壳优化设计的混合遗传算法

复合材料格栅加筋结构优化设计是一个属于多工况、多约束、连续变量和非连续变量混合的优化问题。对遗传算法与单纯形法作了相应的改进, 利用外罚函数法将受稳定性约束和应变约束的多约束优化问题转化为无约束优化。在此基础上, 提出了一种遗传算法与单纯形法相结合的混合遗传算法, 通过与其它文献结果和传统遗传算法结果对比, 证实了混合遗传算法的有效性。以受均匀侧压时复合材料格栅圆柱壳优化设计为例,分别讨论了不同格栅类型和有、无强度约束时的优化结果。分析表明, 整体稳定性是控制该结构安全度的最主要约束因素。本算法具有高效和方便的特点。      

A bidirectional evolutionary structural optimization algorithm for mass minimization with multiple structural constraints

A bidirectional evolutionary structural optimization algorithm is presented, which employs integer linear programming to compute optimal solutions to topology optimization problems with the objective of mass minimization. The objective and constraint functions are linearized using Taylor's first-order approximation, thereby allowing the method to handle all types of constraints without using Lagrange multipliers or sensitivity thresholds. A relaxation of the constraint targets is performed such that only small changes in topology are allowed during a single update, thus ensuring the existence of feasible solutions. A variety of problems are solved, demonstrating the ability of the method to easily handle a number of structural constraints, including compliance, stress, buckling, frequency, and displacement. This is followed by an example with multiple structural constraints and, finally, the method is demonstrated on a wing-box, showing that topology optimization for mass minimization of real-world structures can be considered using the proposed methodology.     

The optimal feedrate planning on five-axis parametric tool path with geometric and kinematic constraints for CNC machine tools

The optimal feedrate planning on five-axis parametric tool path with multi-constraints remains challenging due to the variable curvature of tool path curves and the nonlinear relationships between the Cartesian space and joint space. The methods for solving this problem are very limited at present. The optimal feedrate associated with a programmed tool path is crucial for high speed and high accuracy machining. This paper presents a novel feedrate optimisation method for feedrate planning on five-axis parametric tool paths with preset multi-constraints including chord error constraint, tangential kinematic constraints and axis kinematic constraints. The proposed method first derives a linear objective function for feedrate optimisation by using a discrete format of primitive continuous objective function. Then, the preset multi-constraints are converted to nonlinear constraint conditions on the decision variables in the linear objective function and are then linearised with an approximation strategy. A linear model for feedrate optimisation with preset multiple constraints is then constructed, which can be solved by well-developed linear programming algorithms. Finally, the optimal feedrate can be obtained from the optimal solution and fitted to the smooth spline curve as the ultimate feedrate profile. Experiments are conducted on two parametric tool paths to verify the feasibility and applicability of the proposed method that show both the planning results and computing efficiency are satisfactory when the number of sampling positions is appropriately determined.     

基于变频率区间约束的结构材料优化设计

针对频率约束的结构材料优化问题,基于结构拓扑优化思想,提出变频率区间约束的结构材料优化方法。借鉴均匀化及ICM(独立、连续、映射)方法,以微观单元拓扑变量倒数为设计变量,导出宏观单元等效质量矩阵及导数,进而获得频率一阶近似展开式。结合变频率区间约束思想,获得以结构质量为目标函数、频率为约束条件的连续体微结构拓扑优化近似模型;采用对偶方法求解。通过算例验证该方法的有效性及可行性,表明考虑质量矩阵变化影响所得优化结果更合理。     

约束阻尼板结构振动声辐射优化

根据经典薄板理论,建立约束阻尼板有限元模型,将其视作镶嵌于无限大刚性障板,利用Rayleigh积分法推导结构的辐射声功率及灵敏度表达式。以一阶峰值频率或频带激励下的声功率最小化为目标,约束阻尼材料体积分数为约束条件,建立拓扑优化模型,采用渐进优化算法,编制了优化计算程序,获得了约束阻尼材料的最优拓扑构型,并与全覆盖板及基板的辐射声功率进行了对比。研究表明：以声功率最小化为目标,对约束阻尼材料布局进行拓扑优化,能有效抑制结构的振动声辐射,为结构低噪声设计提供了重要的理论参考和技术手段。     

Comparison of robust,reliability-based and non-probabilistic topology optimization under uncertain loads and stress constraints

It is nowadays widely acknowledged that optimal structural design should be robust with respect to the uncertainties in loads and material parameters. However, there are several alternatives to consider such uncertainties in structural optimization problems. This paper presents a comprehensive comparison between the results of three different approaches to topology optimization under uncertain loading, considering stress constraints: (1) the robust formulation, which requires only the mean and standard deviation of stresses at each element; (2) the reliability-based formulation, which imposes a reliability constraint on computed stresses; (3) the non-probabilistic formulation, which considers a worst-case scenario for the stresses caused by uncertain loads. The information required by each method, regarding the uncertain loads, and the uncertainty propagation approach used in each case is quite different. The robust formulation requires only mean and standard deviation of uncertain loads; stresses are computed via a first-order perturbation approach. The reliability-based formulation requires full probability distributions of random loads, reliability constraints are computed via a first-order performance measure approach. The non-probabilistic formulation is applicable for bounded uncertain loads; only lower and upper bounds are used, and worst-case stresses are computed via a nested optimization with anti-optimization. The three approaches are quite different in the handling of uncertainties; however, the basic topology optimization framework is the same: the traditional density approach is employed for material parameterization, while the augmented Lagrangian method is employed to solve the resulting problem, in order to handle the large number of stress constraints. Results are computed for two reference problems: similarities and differences between optimized topologies obtained with the three formulations are exploited and discussed.