中国机械工程
中國機械工程
중국궤계공정
CHINA MECHANICAl ENGINEERING
2015年
16期
2203-2207,2208
,共6页
可靠性%拓扑优化%隐式功能函数%响应面法
可靠性%拓撲優化%隱式功能函數%響應麵法
가고성%탁복우화%은식공능함수%향응면법
reliability%topology optimization%implicit performance function%response surface method
考虑工程实际中外载荷、材料属性等的随机不确定性对结构安全性的影响，研究了具有结构位移可靠性约束的拓扑优化设计。建立以柔度最小为目标、以单元相对密度为变量、具有材料体积分数约束和结构位移可靠性约束的拓扑优化数学模型；针对运用有限元数值计算方法时结构功能函数为隐式的情况，运用响应面法近似逼近结构真实的功能函数；利用简便高效的一次二阶矩法计算结构位移可靠度；采用内循环为确定性的拓扑优化、外循环控制结构材料体积分数的策略对连续体结构进行可靠性拓扑优化设计。通过两个算例与确定性拓扑优化结果进行比较，结果表明所提设计方法是高效可行的。
攷慮工程實際中外載荷、材料屬性等的隨機不確定性對結構安全性的影響，研究瞭具有結構位移可靠性約束的拓撲優化設計。建立以柔度最小為目標、以單元相對密度為變量、具有材料體積分數約束和結構位移可靠性約束的拓撲優化數學模型；針對運用有限元數值計算方法時結構功能函數為隱式的情況，運用響應麵法近似逼近結構真實的功能函數；利用簡便高效的一次二階矩法計算結構位移可靠度；採用內循環為確定性的拓撲優化、外循環控製結構材料體積分數的策略對連續體結構進行可靠性拓撲優化設計。通過兩箇算例與確定性拓撲優化結果進行比較，結果錶明所提設計方法是高效可行的。
고필공정실제중외재하、재료속성등적수궤불학정성대결구안전성적영향，연구료구유결구위이가고성약속적탁복우화설계。건립이유도최소위목표、이단원상대밀도위변량、구유재료체적분수약속화결구위이가고성약속적탁복우화수학모형；침대운용유한원수치계산방법시결구공능함수위은식적정황，운용향응면법근사핍근결구진실적공능함수；이용간편고효적일차이계구법계산결구위이가고도；채용내순배위학정성적탁복우화、외순배공제결구재료체적분수적책략대련속체결구진행가고성탁복우화설계。통과량개산례여학정성탁복우화결과진행비교，결과표명소제설계방법시고효가행적。
Considering the impacts of uncertain factors such as external loading,material property etc.on structural safety in engineering practice,the topology optimization design with the structural displacement reliability constrain was discussed.A mathematical of topology optimization was devel-oped,where the minimization of compliance was taken as objective function,the relative densities of el-ements were taken as design variables,the material volume fraction and structural displacement relia-bility were taken as constraints.The response surface method was implemented to approximately ap-proach its real performance function,for the situation that the structural performance function was implicit by using finite element numerical method.Then,the simple and efficient first order second moment method was used to obtain the structural displacement reliability.The strategy that inner loop was the deterministic topology optimization and the outer loop was to control the material volume fraction was implemented to carry out the reliability-based topology optimization of continuum struc-ture.Finally,two numerical examples were given to be compared with the results of deterministic to-pology optimization showing that the design method is efficient and feasible.
