二维自由振动的有限元线法自适应分析新进展  

NEW PROGRESS IN SELF-ADAPTIVE FEMOL ANALYSIS OF 2D FREE VIBRATION PROBLEMS

作　　者：袁驷[1] 王永亮[1] 徐俊杰[1] 

机构地区：[1]清华大学土木工程系,土木工程安全与耐久教育部重点实验室,北京100084

出　　处：《工程力学》2014年第1期15-22,共8页Engineering Mechanics

基　　金：国家自然科学基金项目(51078199,50678093,50278046);长江学者和创新团队发展计划项目(IRT00736)

摘　　要：有限元线法(FEMOL)是一种优良的半解析、半离散方法,可将其比拟为广义一维问题,进而将一维有限元中单元能量投影(EEP)法及相应的自适应求解技术引入,使FEMOL由半解析方法变为完全解析、数值精确的方法。在对二维线性问题成功地实现了自适应FEMOL分析的基础上,该文进一步报道FEMOL自适应方法在二维自由振动问题中的成功应用和最新进展。该文简要介绍了FEMOL自适应分析二维振动问题的求解策略和技术,整套方法思路清晰、算法严谨、高效可靠,可以得到满足精度要求的自振频率和按最大模度量满足用户事先给定误差限的振型,均为数值精确解。该文给出的数值算例表明所提出的算法具有高效、稳定、通用、可靠的优良特性。The finite element method of lines （FEMOL） is a general and powerful semi-discretized method for BVPs. By viewing it as a generalized one-dimensional method, the well-established Element Energy Projection （EEP） method for super-convergence computation and the corresponding self-adaptive strategy in one-dimensional FEM can readily be incorporated into FEMOL, making the semi-discretized method to be a fully analytical and numerically exact method. Based on the earlier successful implementation of linear self-adaptive strategy in two-dimensional FEMOL analysis, the present paper intends to give a brief report of recent success and progress in adaptively solving two-dimensional free vibration problems. The paper briefly describes the main ideas of the self-adaptive strategy in the two-dimensional FEMOL analysis of free vibration problems, which forms a clean, simple, effective and reliable algorithm that can adaptively produce FEMOL results with accuracy of both the frequency and the mode satisfying the user specified error tolerance in a most restrict form. The numerical examples given show that the proposed method is highly efficient, stable, general and reliable.

关 键 词：有限元线法 自由振动 单元能量投影 超收敛 自适应 

分 类 号：O242.21[理学—计算数学]