摘要
利用Daubechies小波尺度函数作为有限元逼近空间的单元插值函数,构造了可用于动力分析的小波Ber-noulli-Euler梁单元,并建立了用于分析Bernoulli-Euler梁动力响应的小波有限元模型。为了检验该模型的计算精度与计算效率,文中对梁自由振动以及移动载荷下的受迫振动问题进行了数值实验,并与传统有限元模型的数值结果进行比较。结果表明,小波有限元法较之传统有限元法在结构总自由度相等的情况下,前者的计算精度更高;而在保证精度的情况下,前者大大提高了计算效率,从而为高效计算复杂梁结构动力学问题提供了一种新途径。
Wavelet scaling functions of Daubechies wavelet are utilized as the interpolation base functions of finite element approximation space. The wavelet BernoulliEuler beam element used for dynamic re sponse analysis is constructed. The wavelet finite element model （WFEM） which is applied to analyze the dynamic response of BernoulliEuler beam is built up. In order to test the calculation accuracy and compu tational efficiency of WFEM, free vibration problem and forced vibration problem under moving load are solved through the numerical experiments. The numerical results are compared with traditional finite ele ment model （FEM）. According to the results, WFEM is superior to FEM on the calculation accuracy when the total freedom of structure is equal. If the calculation accuracy is identical, WFEM can improve the computational efficiency greatly. The WFEM model will provide a high efficient calculation method for computing complex dynamics problem of beam structure.
出处
《力学季刊》
CSCD
北大核心
2012年第2期196-203,共8页
Chinese Quarterly of Mechanics
基金
国家自然科学基金(11172192)资助项目
