基于B样条函数的弹性地基梁内力反演研究

BACK ANALYSIS OF THE INNER FORCE OF ELASTIC FOUNDATION BEAM BASED ON B-SPLINE FUNCTION

位移是荷载作用下结构的外在响应,依据弹性地基梁的位移反演其内力在工程中具有重要意义。以非插值节点处的位移值作为边界条件对结构的位移数据点进行B样条插值,得到结构的位移样条函数;然后对位移样条函数求导,并根据曲率与弯矩间的物理关系和弯矩与剪力之间的微分关系,反算出荷载作用下结构的内力;最后将该方法运用于一简单算例,并将反算值与理论正算值进行对比,验证了所提方法的可行性。

Displacement is the external response of structure under load,so the back analysis of the inner force according to the displacement of elastic foundation beam is of great significance. In the paper, the B-spline interpolation was used to interpolate the displacement data of structure with data of non-interpolation node as boundary conditions,so as to obtain the spline displacement function of structure. The spline displacement function was derived,and according to the physical relation between curvature and bending moment and differential relation of bending moment and shear force,the inner force of structure under loads was obtained by back analysis. Finally,the method proposed in the paper was applied to a example,and its feasibility was verified through the comparison between back calculated values and theory calculated values.