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基于小波函数特有的多分辨特性,Daubechies小波在处理工程中的应力大梯度、强非线性和奇异问题方面具有较强优势。限于联系系数的计算广度不够,目前Daubechies小波有限元法的应用仅限于杆、梁以及地基系数为常数的弹性地基梁等方面的计算中。在基于m法的桩基础计算中,假定地基系数为线性函数,故挠曲线微分方程中荷载项的地基系数为线性变量,但与此相关的联系系数的计算方法及计算结果尚未见文献报导,无法应用Daubechies小波法进行求解。针对桩基础计算模型的特点,提出和推导了一类基于m法的可用于桩基础计算的小波联系系数,首次将Daubechies小波应用于桩基础的计算中。并利用上述结果,对桩基础的典型模型进行计算。结果表明,所推导出的Daubechies小波新型联系系数结果正确,基于Daubechies小波有限元法可精确求解桩基础的受力。
Based on the unique multiresolution property of wavelet function, Daubechies wavelet has strong advantages in dealing with large gradient stress, strong nonlinearity and singularity problems in engineering. Limited to the calculation of the contact coefficient is not enough breadth, the current application of the Daubechies wavelet finite element method is limited to the calculation of poles, beams and elastic foundation beams with constant foundation coefficient. In the calculation of pile foundation based on m method, the ground foundation coefficient is assumed to be a linear function, so the foundation factor of the load term in the deflection curve differential equation is a linear variable. However, the calculation method and calculation result of the correlation coefficient related to this method have not been reported in the literature, Can not solve Daubechies wavelet method. Aimed at the characteristics of the pile foundation calculation model, a class of wavelet coefficients based on m method which can be used in pile foundation calculation is proposed and deduced. For the first time, Daubechies wavelet is applied to the calculation of pile foundation. Using the above results, a typical model of pile foundation is calculated. The results show that the new contact coefficient of Daubechies wavelet derived is correct. Based on Daubechies wavelet finite element method, the stress of pile foundation can be accurately solved.