摘要
从几何变形角度出发,使用插值理论推导了Euler-Bernoulli梁单元的完整的二阶位移场.使用三次Her-mite插值函数建立了单元的横向一阶位移场,一次Lagrange插值函数构造了单元的轴向位移场,进而在单元的横向位移场和纵向位移场中包含了因单元截面转动而产生的附加位移,从而将Euler-Bernoulli梁单元的位移场表达为结点位移的二次函数,可用于杆系的非线性静、动力学分析.
From the geometric deformation viewpoint, the complete second-order displacement field of Euler-Bernoulli beam element is deduced using the interpolation theory. In this regard, the transverse first-order displacement field is established using the cubic Hermite interpolation function, whereas the axial displacement field is constructed via the first-order Lagrange interpolation function. Furthermore, the additional displacement derived from the rotation of elemental cross- sections is contained in the transverse and longitudinal displacement fields. Based on this understanding, the bespoke displacement fields are expressed as the quadratic function of nodal displacement. Therefore, this approach can be applied for the nonlinear static and dynamic analyses on beam systems.
出处
《中国工程机械学报》
2011年第4期416-420,共5页
Chinese Journal of Construction Machinery
