基于节点切平面解耦列式的一步逆成形法  

One-step Inverse Approach Based on Decoupled Formulation in Nodal Tangent Plane

作　　者：周平[1] 胡平[2] 张健伟[2] 张向奎[2] 

机构地区：[1]吉林大学汽车工程学院,长春130022 [2]大连理工大学工业装备结构分析国家重点实验室,大连116024

出　　处：《机械工程学报》2010年第22期24-30,共7页Journal of Mechanical Engineering

基　　金：国家高技术研究发展计划(863计划;2009AA04Z101);国家自然科学基金重点(10932003);国家重点基础研究发展计划(973计划;2010CB832700)资助项目

摘　　要：对基于传统的整体坐标系列式的一步逆成形法进行改进,提出一种基于节点切平面解耦列式的一步逆成形有限元模拟算法。该算法利用虚功原理的坐标系无关性,将虚功方程建立在节点局部坐标系上,实现刚度方程在节点法向和切平面内的解耦。与传统列式法相比,解耦列式法避免了立壁单元投影刚度阵引起的数值问题,因此提高了迭代求解的精确性和收敛性。通过弯曲薄板的展平问题对解耦列式法的误差进行定量分析,表明该法满足精度要求。将该算法嵌入自主研发的金网格分析系统(Kingmesh analysis system,KMAS),并以方盒件为例,将传统列式法和解耦列式法的结果分别与基于增量有限元求解器LS-DYNA求解结果进行对比,验证了解耦列式法的有效性。An one-step inverse approach based on decoupled formulation in nodal tangent plane is proposed to improve the method based on traditional formulation in the global coordinate system.In this algorithm,considering the coordinate independency of principle of virtual work（PVW）,stiffness equations are decoupled in nodal normal direction and nodal tangent plane by establishing the PVW equation in the nodal local coordinate system.Compared with traditional formulation,decoupled formulation avoids the numerical problems caused by projected stiffness matrix of vertical element,thus it improves the accuracy and convergence of iteractive solution.By flattening analysis of bending thin plate,quantitative analysis of the error of decoupled formulation shows that the algorithm meets the required precision.Finally,the decoupled formulation is integrated into King mesh analysis system（KMAS） software.By numerical simulation on square box,and comparisons among traditional formulation,decoupled formulation and incremental algorithm with LS-DYNA solver,the effectiveness of the decoupled formulation is verified.

关 键 词：一步逆成形法 虚功原理 解耦列式 塑性形变理论 

分 类 号：TG156[金属学及工艺—热处理] TG386[金属学及工艺—金属学]