高精度微分求积曲梁单元的建立与应用

首先由能量原理导出曲梁弯曲问题的控制微分方程，在此基础上应用微分求积法原理分别给出了曲梁内点和端点的微分求积方程，由此形成曲梁单元的刚度方程，从而建立了微分求积曲梁单元，并给出了曲梁结构刚度方程的边界条件。通过算例分析，得到了微分求积单元法结构离散时应使单元数量少的原则和求解精度与单元长度比基本无关的性质。与有限元方法的结果比较表明，本文导出的曲梁单元是一种具有很高求解精度的单元。》

On a High-Accuracy Curved Differential Quadrature Beam Element and Its Applications

The governing differential equations for the bending of a curved beam are derived first by using the energy method and followed by the detailed derivations of the differential quadrature (DQ) equations at the inner and end points. Thus the stiffness equations of the curved beam are established. The boundary conditions for the curved beam structures are also given. Numerical examples are performed and the results are compared with the analytical solutions or with the data obtained by finite element method. It is shown that in the applications of the differential quadrature element method, one should use the number of DQ elements as small as possible in establishing the computational model. It is also shown that the results are insensitive to the element length and that the curved DQ beam element proposed in this paper has very high accuracy in both the generalized displacements and the generalized forces.