论文部分内容阅读
基于液化土层中桩-土相互作用的Winkler模型,将桩等效为Rayleigh梁,构造了Rayleigh梁单元在轴力作用下自由振动和屈曲分析的精确形函数,建立了Winkler基础上考虑轴力的Rayleigh梁精确有限单元,得到了单元刚度矩阵、单元几何刚度矩阵和单元质量矩阵的表达式,建立了相应的精确有限元法。通过修正精确有限元的整体离散控制方程,得到成层液化土中单桩-土-结构系统的自由振动与屈曲分析的精确有限元离散方程,并就成层液化土中单桩-土-结构系统的固有频率和屈曲载荷进行了数值计算,通过与解析结果的比较,说明了本文精确有限元法的可靠性和合理性。研究表明,常规梁单元是精确梁单元的一个特例,采用精确有限元,无需细分网格就可以进行精确固有频率与屈曲载荷等的计算。
Based on the Winkler model of pile-soil interaction in liquefied soil, the pile is equivalent to a Rayleigh beam, and the exact shape function of Rayleigh beam element under free axial motion and buckling analysis is established. Based on the Winkler model, The Rayleigh beam finite element is obtained. The expressions of element stiffness matrix, element geometric stiffness matrix and element mass matrix are obtained, and corresponding accurate finite element method is established. The accurate finite element discretization equation of free vibration and buckling analysis of single-pile-soil-structure system in layered liquefiable soil is obtained by modifying the integral discrete governing equations of accurate finite element method. The natural frequency and buckling load of the system are numerically calculated. The comparison of the results with the analytical results shows the reliability and rationality of the accurate finite element method in this paper. The research shows that the conventional beam element is a special case of an accurate beam element. The precise finite element method can be used to calculate the exact natural frequency and buckling load without subdivision mesh.