论文部分内容阅读
本文以三次样条函数和傅氏级数作为求解空间的基函数,应用基于复阻尼理论的Lagrange方程求计算粘弹性层状半无限地基在表面单位简谐力作用下的动力柔度阵。这种半解析半离散方法,将二维问题降为一维数值问题处理,同时利用了样条函数良好的插值性能和傅氏级数的正交性,大幅度节省计算工作量和内存要求,便于利用微机实现,并具有较高的计算精度,从而为进一步建立复杂地基的动力刚度阵和研究结构与地基相互作用问题提供一个简便有效的数值计算工具。
In this paper, the cubic spline function and Fourier series are used as the basis functions of the solution space. The Lagrange equation based on the complex damping theory is applied to calculate the dynamic compliance matrix of viscoelastic layered semi-infinite ground under the action of surface unit harmonic forces. This semi-analytical and semi-discrete method reduces the two-dimensional problem to one-dimensional numerical problem processing. It also takes advantage of the good interpolating performance of the spline function and the orthogonality of the Fourier series, greatly reducing computational workload and memory requirements. It is easy to be implemented by microcomputer and has high calculation accuracy. It provides a simple and effective numerical calculation tool for further establishing the dynamic stiffness matrix of complex foundation and studying the interaction between structure and foundation.