非线性梁静力学问题的小波有限元方法研究  

Research on the Wavelet-based Finite Element Method for the Static Problem of Nonlinear Beam

作　　者：曹建华 郭东旭 褚园 Cao Jianhua;Guo Dongxu;Chu Yuan(College of Mechanical Electronic Engineering,Huangshan University,Huangshan 245021,China)

机构地区：[1]黄山学院机电工程学院,安徽黄山245041

出　　处：《黄山学院学报》2023年第3期10-16,共7页Journal of Huangshan University

基　　金：高校优秀青年人才支持计划项目(gxyq2020053);安徽省仿真设计与现代制造工程技术研究中心开放项目(SGCZXYB1802);黄山学院人才引进科研启动项目(2020xkjq002)。

摘　　要：针对小应变适度挠度的非线性梁,采用变分法和小波有限元离散了其微分方程,推导了其对称和不对称刚度矩阵,结合复数步进法生成切线刚度矩阵,求解了梁中点的位移。结果表明:采用不对称刚度矩阵以及复数步进法生成切线刚度矩阵,与传统有限元对比,小波有限元迭代次数少,数值收敛快,而切线刚度矩阵的显式表达式并不能使迭代收敛。小波有限元数值结果精确可靠,且在两端可移铰接和两端简支边界条件下,其迭代收敛所花时间大幅减少。In this paper,the differential equations of the nonlinear beam with small strain and moderate rotation are discretized by using variational method and wavelet-based finite element method,and the symmetric and asymmetric stiffness matrices are obtained.The tangent stiffness matrix is generated by applying the complex-step method.The displacement of the middle point of the beam is solved.The wavelet-based finite element obtains fast convergence by using asymmetric stiffness matrix and numerical method to generate tangent stiffness matrix.The results show that,compared with traditional finite element method,wavelet-based finite element has fewer iterations and faster numerical convergence,while the explicit expression of tangent stiffness matrix cannot make the iteration converge.The numerical results of wavelet-based finite element analysis are accurate and reliable,and the iterative convergence time is significantly reduced under the movable hinge and simply-supported boundary conditions at both ends.

关 键 词：非线性 梁 小波 有限元 

分 类 号：O321[理学—一般力学与力学基础] O327[理学—力学]