修正组合近似法及其在车架刚度重分析中的应用  

Modified Combined Approximations and the Application in Reanalysis of Vehicle Frame Stiffness

作　　者：黄观新[1] 王琥[1] 高国强[1] 李光耀[1] 

机构地区：[1]湖南大学汽车车身先进设计与制造国家重点实验室,长沙410082

出　　处：《机械工程学报》2011年第18期86-92,共7页Journal of Mechanical Engineering

基　　金：国家自然科学基金(10902037);国家高技术研究发展计划(863计划;2009AA044501);中央高校基本科研业务费;国家重点基础研究发展计划(973计划;2010CB328005);湖南省自然科学基金(11JJA001)

摘　　要：重分析是指在结构修改之后不需要重新求解平衡方程,仅需要根据初始计算结果对修改后的问题进行求解,并能够在保证计算精度的前提下,大幅度提高计算速度。针对重分析法在有限元计算中可能出现的奇异性问题,通过奇异值分解法(Singular value decomposition,SVD)对重分析法中的组合近似法(Combined approximation,CA)进行修正。修正后的重分析算法,能够解决刚度矩阵奇异的问题,并能够保持CA法的重分析精度。为验证算法的有效性,采用修正后的重分析方法对圆柱壳和车架刚度分析进行仿真测试。测试结果表明,修正后的重分析方法在解决奇异性问题的同时,能够保证重分析的计算效率和计算精度。由两个数值算例的结果对比可知,当刚度矩阵奇异性比较高时,常用的以矩阵的伪逆代替逆的方法不可行。由此可知,修正后的重分析算法在解决奇异性问题时具有相当的优越性。Reanalysis is used for analyzing the modified structure according the initial analysis results instead of solving the equilibrium equations.It can greatly improve calculation efficiency with enough accuracy.This study proposed a modified reanalysis method by integration of singular value decomposition（SVD） and combined approximation（CA） for the singularity problems.The modified reanalysis method can solve the problem of singular stiffness matrix,as well as keep the accuracy of CA method.To validate the feasibility of the modified reanalysis,a cylinder shell example and real vehicle frame stiffness are performed by the proposed method successfully.Test results demonstrated that the modified reanalysis method can solve the singular problems efficiently with accuracy.And,by comparing the results of the two numerical examples,when the stiffness matrix has high singularity,the common method replacing the inverse by the pseudo inverse is not feasible.Therefore,the modified reanalysis method has advantages in solving singular problems.

关 键 词：逼近组合法 奇异值分解法 重分析 病态方程组 

分 类 号：U270[机械工程—车辆工程]