基于直接刚度法的弹性地基深梁单元

为研究弹性地基深梁的受力及变形性能,根据双参数弹性地基模型和Timoshenko深梁模型的基本方程,建立了弹性地基深梁挠度控制方程,求得了挠度方程全解,并给出了弹性地基深梁梁轴转角、截面弯曲转角及剪切角的表达式;结合节点位移条件,得到了位移系数;根据节点力方程建立了刚度平衡方程,给出了弹性地基深梁的刚度矩阵方程及均布荷载的等效节点力向量。在此基础上,分别计算了均布荷载、跨中集中力、两端集中力、两端集中力矩等荷载工况下的节点位移,求得弹性地基深梁挠度曲线,验证了本文给出的刚度矩阵方程及等效节点力向量的合理性及适用性。

Deep Beam Element on Elastic Foundation Based on Direct Stiffness Method

In order to analyze the mechanical behavior and deformation performance of deep beam on elastic foundation,the deflection control equation of deep beam on elastic foundation was deduced on the basis of basic equations of double-parameter elastic foundation model and Timoshenko deep beam model,by which its full solution was obtained.The expressions for the beam axis angle,the section flexural angle and the shear angle of deep beam on elastic foundation were developed.Combined with the displacement boundary conditions,the displacement coefficient was received.According to the nodal force equations,the stiffness balance equation was established,while the stiffness matrix equation and equivalent nodal force vector under uniform load for deep beam on elastic foundation were provided.On this basis,the nodal displacement under the uniform load,the concentrated load at the mid-span,the concentrated force at both ends,and the concentrated moment at both ends were calculated,respectively,to obtain the deflection curve of deep beam on elastic foundation,which verified the rationality and applicability of stiffness matrix equation and equivalent nodal force vector in this paper.