OptiStruct® 结构优化 方献军 Altair China April 2015

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1 OptiStruct® 结构优化 方献军 Altair China support@altair.com.cn April 2015
Welcome to OptiStruct training! The instructor should describe the environment, rest room, kitchen, etc… The objective today is to introduce what is and how to use OptiStruct. This training will give you too basic overview about optimization too. We hope you enjoy these 2 days and take advantage of this fabulous tool when you get back to your company. Information about the class and instructor: Name, company and position! What the attendee know about Optimization and HyperWorks! Why he is attending this course! On your computer four is a folder named training on your desktop, on this folder you will find all electronic files you need: Manual: Folder with the manual in pdf format: Book with chapters and exercises. PPT_pdf: Folder with the powerpoint slides on pdf format Model Files: Folder with all model files that will be used during the exercises. Solved: Folder with the final files from the exercises. On your desk you should have a folder with a CD that has all these files and the PowerPoint printed as handouts to take notes during the exposition.

2 Agenda Day 1 Day 4 Day 2 Day 5 Day 3 Free Size Optimization
Optimization Strategies Introduction Day 4 Theoretical Background Optimization Interface and Setup Optimization Parameter and Control Topology Optimization Sensitivity Analysis .fem File and .out File Complex Response A Complete Process : CAD to CAD Optimization with Nonlinear Case Day 2 ESLM Optimization Multi Model Optimization Topology Optimization Using Inspire Day 5 Morphing of HyperMorph Shape Optimization Optimization with Super Element Day 3 Combine Optimization Reliability-based Optimization Free Shape Optimization Composite Optimization Topography Optimization Size Optimization

3 日程安排 第1天 第4天 第2天 第5天 第3天 自由尺寸优化 优化策略 简介 理论背景 优化设置界面 优化卡片与控制参数 拓扑优化
灵敏度分析 .fem 文件 和.out文件 复杂响应创建 一个完整的流程：从 CAD 到 CAD 非线性工况优化 第2天 ESLM优化 多模型优化 使用Inspire进行拓扑优化 第5天 HyperMorph网格变形 形状优化 含超单元模型的优化 第3天 组合优化 基于可靠性的优化 自由形状优化 复合材料优化 形貌优化 尺寸优化

4 Day 4 Agenda Optimization Parameter and Control Sensitivity Analysis
Complex Response Optimization with Nonlinear Case ESLM Optimization Multi Model Optimization Today we will cover the first part of a product development, called Concept Design. The idea is to give you an INTRODUCTION A HyperWorks Overview How OptiStruct is integrated with the other HyperWorks solvers. An OptiStruct overview FEA, MBD and Optimization. 2 examples where OS was used to optimize a design. THEORETICAL BACKGROUND Optimization Design Variable Response Objective Constraint Feasible and unfeasible Gradient-base method Sensitivity Analysis Move Limit Adjustment Constraint screening Regions Discrete DV OPTIMIZATION INTERFACE AND SETUP Model Definition Structure Subcase Information Section Bulk Data Section Optimization Cards OPTIMIZATION Setup Optimization Panel Optimization Menu Model Browser How to Setup an Optimization on HyperMesh CONCEPT DESIGN Topology Optimization Exercise: step by step on a 2D model Exercise: A Solid Control arm. Topography Optimization Exercise: Determine the optimum hard drive disc slider suspension beads. Free-size Optimization

5 优化迭代过程 收敛准则是什么？ 如何提高运算速度？ 灵敏度的计算和意义是什么？

6 Important Application Techniques
Sound optimization problem definition Trade between objective and constraints Avoid unstable responses (e.g., lowest buckling eigenvalue) Constraint screening Divide regions using insights Number of retained constraints in a region (DSCREEN) Convergence control Default may not fit all problems (e.g., insensitive objective) Reduce if converges too quick and unsure about the result Move limits Sound adaptive algorithm in place A good tuning mechanism for ‘tough’ problems

7 收敛准则 正则收敛：连续两次迭代满足收敛准则 软收敛：相邻两次迭代设计变量变化小或没有变化
相邻两次迭代目标函数变化小于容差（默认为0.5%，OBJTOL） 且约束条件违反小于1% 软收敛：相邻两次迭代设计变量变化小或没有变化 也可由最大迭代步数控制，DESMAX（默认30，拓扑优化中使用制造约束则为80）

8 Additional Optimization Considerations
Constraint Screening (DSCREEN) Screening - specify normalized threshold value Temporarily ignores constraints which are less than the normalized threshold value during optimization Regionalization - specify maximum number of constraints to be retained for a given region Considers user specified number of most violated constraints for each load case and region id. Essential in situations where there are many constraints E.g. Stress constraints for shape/size optimization. If too many constrained responses are screened, it may take considerably longer to reach a converged solution or, in the worst case, it may not be able to converge on a solution if the number of retained responses is less than the number of active constraints for the given problem.

9 Additional Optimization Considerations
Constraint screening: Critical constraints in and out of retained sets? Yes – adjust constraint screening regions and criteria Bad steps - bad approximation quality? Potentially unstable response? Reduce move limits to increase approximation fidelity Convergence difficulty: A necessary tool for large problems Key - region separation Number of retained constraints (defined by DSCREEN) Does not reduce the number of active constraints When no other choice, use very small move limits Optimality can not be achieved in this case

10 Constraint Screening Plate sizing optimization Minimizing weight
Design variables: Thickness of three zones Constraints: Vertical displacements ≤ 0.06

11 Constraint Screening Plate sizing optimization
Constraint screening – Scenario I One region for all grids Retained constraints – 20 (default) 15 iterations Objective: → 117.6 Constraint violation: 125% - 870% - 0%

12 Constraint violation: 125% - 0%
Constraint Screening Plate sizing optimization Constraint screening – Scenario II Three regions Retained constraints – 20 (default) 4 iterations Objective: → 117.5 Constraint violation: 125% - 0%

13 Constraint Screening Plate sizing optimization
Constraint screening – Scenario III One region Retained constraints – 20 (default) Move limits DELSIZ 0.1 (default 0.5) 16 iterations Objective: → 117.9 Constraint violation: 125% - 0%

14 DSCREEN

15 Move limit Adjustments
design moves away from its initial point in the approximate optimization used to protect the accuracy of the approximations Small move limits lead to smoother convergence You can set the initial move limit for Size and Shape optimization DOPTPRM, DELSHP DOPTPRM, DELSIZ DOPTPRM, DELTOP Typical for approximation optimization are 20% Advanced approximation: up to 50% Move limits are automatically adjusted by OptiStruct，may not be greater than this initial move limit

16 灵敏度分析

17 灵敏度分析

18 灵敏度分析

19 灵敏度分析

20 灵敏度分析

21 灵敏度分析 尺寸优化/形状优化(变量个数远少于约束个数)：直接差分法 拓扑优化（变量个数远大于约束个数）:伴随变量法 灵敏度输出
OUTPUT,MSSENS SENSITIVITY OUTPUT,HGSENS OUTPUT,H3DTOPOL、OUTPUT,H3DGAUGE

22 灵敏度文件格式 尺寸和形状优化可以输出每一迭代步的灵敏度，后辍为.slk，可以修改“New”这一列的数据
每一个响应都会有列灵敏度数据。如果响应被约束，则会给出上/下限。Response reference 是由变量的reference值求出的结果 三种不同方法计算响应值 线性插值 倒数插值 混合法（灵敏度正，与线性法相同；灵敏度负，与倒数法相同）

23 优化控制选项 DOPTPRM 最大迭代次数，默认30/80 目标函数收敛容差 百分比 最小成员尺寸 尺寸优化的move limit 初值
目标函数收敛容差 百分比 离散变量选项（1，2，3）离散优化；先连续再以最优为初始点离散；连续优化； 最小成员尺寸 尺寸优化的move limit 初值 最小层厚 初始材料质量分数 形貌和形状优化的move limit 初值 最大的外层循环次数(MBD,ESLM) 最小单元密度 拓扑和自由尺寸优化的move limit 初值 时间步扫描策略(1：屏蔽部分step，0:所有step都包含在内) 离散参数。（0，2.0）壳单元；3 .0体单元 全局的屈曲约束（0，1） 时间步扫描容差(当ESLSOPT=1) 越小，保留的step越少 控制棋盘格现象（0，1） 在优化中需要考虑的屈曲因子阶数（15以上） 形状优化算法（1，2），当形状不变时使用2 效果与CHECKER类似 1D单元的离散参数 优化算法选择，DUAL：概念优化方法。MFD：尺寸和形状 显示动力学优化所保留的step数 隐示动力学优化所保留的step数 几何非线性优化所保留的step数 网格重划开关 近似算法选择，对于大模型或832错误建议使用REDUCED选项

24 优化重启动、拓扑优化重分析 控制.sh文件输出频率 优化重启动用于优化突然中止或优化不收敛，大模型等一些特殊的情况。
优化问题重启动需要两个文件：filename.fem (包含输入文件)和 filename.sh (包含最后一个完成迭代步的设计变量信息) 控制.sh文件输出频率

25 优化重启动、拓扑优化重分析 在优化分析完成之后进行重新分析来初步验证优化结果。
优化问题重分析需要两个文件：filename.fem (包含输入文件)和 filename.sh (优化之后的sh文件)

26 Complex Response Internal Responses External Responses
DRESP1: Result of a design analysis iteration DRESP2: Combinations of responses Design Response via equations (DEQUATN) for design optimization Can be one of: DESVAR, DTABLE, DGRID, DRESP1, DRESP1L, DRESP2… External Responses DRESP3 , in combination with LOADLIB I/O option Definition of responses through user-defined external functions Barebones functions for Fortran and C, HyperMath Excel File

27 内置响应 Subcase Independent Linear Static Analysis Normal Modes Analysis
Mass, Volume Fraction of mass, Fraction of design volume Center of gravity Moments of inertia Weighted compliance Weighted reciprocal eigenvalue Combined compliance index Von Mises stress in a topology or free-size optimization Bead discreteness fraction Linear Static Analysis Static compliance and displacement Static stress, strain of homogeneous material Static stress and strain of composite lay-up Static failure in a composite lay-up Static force Normal Modes Analysis Frequency Linear Heat Transfer Analysis Temperature Linear Buckling Analysis Buckling factor Frequency Response Function Frequency response displacement, velocity, acceleration Acoustic Analysis Acoustic pressure Multi-body Dynamics Analysis MBD displacement, velocity, acceleration, force Fatigue Analysis Damage Life Random Analysis PSD and RMS responses User Responses Function External

28 约束和目标定义：工况相关 如果响应是某一特定工况结果，则目标和设计约束需要定义为与工况相关的。 工况相关响应 工况无关 响应(全局)
柔度，频率，位移，应力，应变，力，复合材料响应 这些响应的函数包含其它与工况相关的响应 工况无关 响应(全局) 质量，质量分数，体积，体积分数，重心，惯性矩，加权柔度，加权频率，柔度指数。 这些响应的函数。 使用某个工况下的柔度，频率，位移，应力，应变，力，复合材料响应而组成的函数。

29 Exercise 4a: using DRESP2
Objective: Min. Mass Design Variables: shell thickness Constraints: Stress of design parts<65Mpa Relative displacement<0.2 The relative displacement means the displacement from Node P to plane ABC(determined by Node A, B and C). So the point is how to calculate the distance from P to plane ABC. design1 design2

30 Relative displacement
θ Initial coordinate : … Node displacement: … Distance between two nodes after deformation：

31 Setting in OptiStruct Equation 1: Distance between two nodes after deformation Equation 2: Relative displacement between node P and plane ABC Responses dxA, dyA, dzA,….: the components of displacement of node A, B, C and P PA, PC, AC, BC : the distance between two nodes Dr: Relative displacement

32 Results

33 DRESP3定义 rresp[0] = 0.0; 外部自定义函数响应 支持Fortran或C的外部函数
支持HyperMath函数或Excel文件定义外部响应 外部C函数建立要求： 函数名必须全部为小写或者大写，不能大小写混合 下划线禁止使用 名字长度小于8个字节 将Fortran或C函数转换为dll文件 int mysum(int* iparam, double* rparam, int* nparam, int* iresp, double* rresp, int* nresp, char* userdata) { int i; rresp[0] = 0.0; for (i=0; i<*nparam; i++) rresp[0] = rresp[0] + rparam[i]; } rresp[1] = rresp[0]/(*nparam); return 0;

34 DRESP3 响应名 函数名 返回的响应编号 返回的响应个数 外部文件类型：FLIB, CLIB, HLIB

35 DRESP3定义 DRESP3 LOADLIB—加载动态链接库文件 DRESP3—用户自定义外部函数
DRESP FSUM CLIB MYSUM DRESP DRESP MSUM CLIB MYSUM DRESP DESOBJ(MAX)=10 DCONSTR

36 Exercise 4b: using DRESP3
目标： min. 应变能 拓扑优化 约束条件： 体积分数< 0.5 质量和<1.5e-7t 质量平均<1e-7t 使用DRESP3计算两个部分质量和以及平均值

37 显式方法定义Excel外部响应 显式方法可以定义任意复杂的EXCEL表 DRESP3卡片显式指定输入项和输出项
LOADLIB DRESP3 ELIB dresp3_excel.xlsx DRESP FUNC ELIB MYFUNC DRESP DESVAR CELLIN B3 THRU B6 CELLIN C10 CELLOUT E10

38 练习 4c: Excel文件创建DRESP3响应
LOADLIB DRESP3 ELIB 'Book1.xlsx' DESOBJ(min)=3 BEGIN BULK DRESP s STRESS ELEM SVM DRESP s STRESS ELEM SVM DRESP s STRESS ELEM SVM DRESP s STRESS ELEM SVM DRESP s STRESS ELEM SVM dresp3,3,wa,ELIB,SHEET1 +,dresp1,1,2,4,5,6 +,cellin,a2,b2,c2,d2,e2 +,cellout,f2 Excel文件和fem文件放在同一目录下时不需要写文件路径

39 非线性工况的优化 F OptiStruct直接支持非线性准静态工况（Quasi-static nonlinear）的优化
所有优化方法均支持 非线性材料不能作为拓扑优化的设计空间 OptiStruct支持显式工况的优化 基于RADIOSS模型文件 可以HyperMesh中完成设置，也可直接在RADIOSS文件中添加卡片完成 显式问题由RADIOSS求解，优化计算由OptiStruct完成 OptiStruct F

40 带接触优化 分别用contact和cgap单元来模拟圆柱与孔之间接触，并对其进行拓扑优化。
练习4d：含接触的优化（…/4d_CONTACT_OPTIMIZATION/contact_opt.hm）

41 ESLM 优化 OptiStruct专注于结构设计，以其强大的拓扑优化、形貌优化、自由尺寸优化、尺寸优化、形状优化、自由形状优化等技术实现结构的最优化设计。在汽车、机械和轨道交通领域， OptiStruct 广泛应用于轻量化设计、强度提升、降噪和减振。在建筑和土木工程领域， OptiStruct则呗应用于寻找最佳的结构布局。 应用OptiStruct先进的等效静态载荷技术（Equivalent Static Load Method，ESLM）可进行运动机构零件优化设计和非线性优化。

42 ESLM(Equivalent static load method)方法
Analysis Dynamic Problem Load time history Radioss Block Optimization Static Problem Equivalent static loads Optistruct Load Design variables Start Nonlinear Analysis fteq = Kdt Load set feq0 feq1 feq2  feqn Time Step t0 t1 t2  tn time displacement Calculate equivalent static loads Update design variables Solve linear static response optimization No Yes Converged Stop

43 基于MBD工况的优化 OS-2098: Topology Optimization of an Excavator Arm Model
优化目标：刚度最大化 约束条件：体积分数上限 设计变量：单元密度

44 OptiStruct +MBD优化

45 练习4e: 基于显式工况的尺寸和形状优化 Analysis Type: EXPDYN
Material: Steel (Johnson-Cook Elastic Plastic) Imposed displacement 30 mm in 10 ms This is an example of a slide built from the corporate presentation, built within the new template style. Impactor Force u Impdisp

46 练习4e: 基于显式工况的尺寸和形状优化 Optimization Problem Formulation:
Objective Function: Minimize Mass Optimization Goal: Impactor force has to follow a linear target force in a specific range between +/- 25 kN (see next slide) Design variables: Thickness (Gauge) Shape This is an example of a slide built from the corporate presentation, built within the new template style. 5 Shapes 1 Gauge Spring Element (Optimization Response) to measure the Impactor Force

47 练习4e: 基于显式工况的尺寸和形状优化 K, Gradient Target Force: K= 60/30=2 Optimization Function : f(x,y)=abs(abs(Spring_Force)-abs(K*Imposed_Disp)) Optimization Constraint: f(x,y) < 25 kN The constraint is a function of displacement Softer crashbox resulting in a smaller impactor force in the next nonlinear loop

48 练习4e: 基于显式工况的尺寸和形状优化 Thickness [mm] Shape [mm] ~ Δ m [%]
Constraint Violation Run 1 1.2 – 3.1 2 / -2 57 No Run 2 47 Yes Run 3 3.2 / -3.2

49 练习4e: 基于显式工况的尺寸和形状优化

50 直接基于RADIOSS文件的ESLM优化
可自动创建ESLM模型，自动调用RADIOSS计算 操作方法 定义RADIOSS的filename_0000.rad 和filename_0001.rad 用文本编辑器新建一个filename.rad文件，内容包含设计变量,响应，约束和目标函数的卡片 开始菜单或命令行运行OptiStruct，选择filename.rad文件，加“-rad”选项 $ALTAIR_HOME/hwsolvers/scripts/optistruct.bat <name>.rad –rad 限制 拓扑优化目前仅支持壳单元 某些响应不支持（比如 截面力、加速度不支持） ESL方法本身的理论不足

51 输入文件(与OptiStruct 卡片类似)
Objective /DESOBJ Constraints /DCONSTR Responses /DRESP1 Design variables /DESVAR, /DSIZE, /DTPL, /DTPG, /DSHAPE, /DVGRID Relate design variable with properties /DVPREL1

52 示例

53 特性 Design variables: Responses: Coverage of RADIOSS keywords:
Shape/Freeshape; Size (shell thickness, beam section area etc) Free-size optimization (do not support composite); Topology optimization (do not support composite or solids) ; Responses: displacement, strain(including plastic strain), stress, internal energy and volume/mass; Coverage of RADIOSS keywords: Material laws (linear properties): 0,1,1,2,3,6,10,13,16,21,22,23,24,27,32,33,35,36,38,42,43,44,48,49,50,52,54,57,60,62,63,64,65,66,70,72,73,7,76,78,82 Properties: 1,2,3,6,8,13,14,45 Elements: SHELL, SH3N, BRICK, BRIC20, TETRA4, TETRA10, PENTA6, BEAM, TRUSS, SPRING Connections: RBE2, RBE3, RBODY Interface: type 2/5/7/11/20/24

54 多模型优化技术 – 动力和目标 多模型优化（MMO）主要用于同时优化多个部件或者有相同设计变量的不同设计 多模型优化主要考虑性能和扩展性
简化有多个部件或者存在要求冲突的优化设计流程 模型可以是完全不同，或者共享部分相同设计 模块可以设置独立的目标和约束，也可以定义全局的响应 多模型优化主要考虑性能和扩展性

55 多模型优化技术 – 应用场景 不同的模型，相连接的部分是可优化区域 相同的设计，不同的网格模型（如，粗细）
相似的模型，有基于工况的参数配置和部件属性（如，阻尼） hm HSt 不同的模型，有组合的目标和约束 不同的模型，共用部分相同的设计 以上所有场景的组合 …

56 多模型优化 – 案例一 两个模型,一个模型是另一个模型的局部细化

57 多模型优化 – 案例二 板的两端固支，中部受侧向载荷作用。 考虑两个设计，两端的设计一致中间不一样（体积相同） 要求优化结果为对称设计
总单元数37,440个 优化目标：柔度最小 优化约束：体积百分比<=0.3 制造约束：使用最小成员尺寸约束

58 多模型优化 – 案例二 实际设计中可能存在多种设计方案 同一个部件可能用于不同场合，例如同一组发动机支架可能用于不同车型不同发动机的安装
Problem definition Plate clamped at both ends and subjected to a lateral load around its center Two versions of the plate are considered, with the end-plates being common to both models, while the middle sections are different (same initial volume) Asymmetrical model to generate more interesting designs Total of design elements Optimization setup Minimize the compliance with a maximum volume fraction of 0.3 Minimum member size control is activated Single objective formulation is applied in the SMO case Multi objective formulation is applied in the MMO case 单模型优化 多模型优化

59 多模型优化– 案例三 悬臂梁，末端有垂向载荷 根据长度不同，有短梁和长梁两个版本，两个模型共用右端的设计 共51,200设计单元
最小化柔度，体积分数约束0.3 最小成员控制和拔模方向约束 单目标应用在单模型优化 多目标应用在多模型优化

60 多模型优化– 案例三 单模型优化 多模型优化

61 MPI配置 Implemented within a MPI-based framework (SPMD parallelization)
Conceptually, optimization only necessitates the knowledge of the underlying mathematical problem, hence the simplistic overview: One master process handles the optimization tasks Slave processes handle the analysis and sensitivity analysis tasks for each model Processes exchange design variables, responses and sensitivities Launched from the solver script or from the run manager GUI optistruct –mmo [MPI_TYPE] –np [N] [MASTER_DECK] [OS_ARGS] Number of processes must be equal to the number of models plus one Initiated through the so-called “master” or “setup” input deck Lists the models to include in the multi-model optimization ASSIGN,MMO,<MODEL_NAME>,<INPUT_DECK> Optionally contains limited control cards and bulk data cards

62 设计变量 Sizing and shape design variables
Design variables (DESVAR) with identical IDs are linked together Dependent design variables (DLINK) are supported Discrete design variables (DDVAL) are supported Covers properties (DVPREL), materials (DVMREL) and elements (DVCREL) Topology and free-sizing design variables Design variables (DTPL/DSIZE) with identical IDs are linked together Similar to pattern repetition with implicit master/slave(s) relationship(s) Standard manufacturing constraints, such as member size control or draw direction, are supported Topography design variables Design variables are not linked together, but topography optimization can be carried on each model independently

63 Implementation – Objectives and Constraints
Responses All existing solution sequences and response types are supported Global equation (DRESP2) and external (DRESP3) responses may be defined in the master deck to combine responses originating from individual models DRESPM identifies the responses and models being combined Example: equation calculating the total mass of two models DRESP MASS SUM DRESPM MMO3P MMO2P Objectives and constraints Global objectives and constraints may be defined in the master deck Single objectives are combined into a multi-objective formulation, with reference values (DOBJREF) being automatically assigned based on the analysis values Individual models are not required to have an objective, as long as there exists at least one objective within the combined optimization problem Automatic screening is supported

64 练习4f: 桥梁的多模型优化 Folding bridge Bridge closed Bridge opened

65 ≠ 练习4f: 桥梁的多模型优化 MODELE 1 MODELE 2 OptiStruct OptiStruct CONCEPT 1
Folding bridge : standard optimization MODELE 1 MODELE 2 OptiStruct OptiStruct CONCEPT 1 CONCEPT 2 ≠

66 练习4f: 桥梁的多模型优化 MODELE 1 MODELE 2 OptiStruct Common results
Folding bridge : standard optimization MODELE 1 MODELE 2 OptiStruct Common results

67 Master文件

68 使用脚本写出Master文件 WriteMasterFileforMMO.tcl