B样条函数法的任意荷载近似计算方法

An Approximate Calculation Method for Arbitrary Loads Using B-Spline Function Method

为优化B样条函数法数值计算流程,提升解决复杂荷载问题的能力。本文基于B样条函数法,通过与相关文献数值算例结果进行比较分析,研究任意荷载的新型计算方法。论文以解圆柱壳结构模型为数值算例,基于文中提出的计算方法,构建出三组不同的单方向荷载逼近函数,分别求解得到特殊点的位移、弯矩、轴力,以及位移和内力沿坐标轴方向的分布,与精确解(扁壳解法)进行比较研究,分析近似计算方法的精确性与实用性。结果显示,在特殊点处二次插值方法的相对误差均低于1.5%,三次、四次插值方法的相对误差均低于0.6%,沿坐标轴方向的分布与精确解均一致,表明本方法具有精度高、处理复杂荷载简便、易于程序编写、构造函数灵活等特点。本方法用逼近函数替代原函数便于数值积分的想法,为未来B样条函数法处理复杂荷载提供新思路。

In order to optimize the numerical calculation process of B-spline function method and improve the ability to solve complex load problems,this paper,based on the B-spline function method,proposes a new calculation method of arbitrary load,by comparing and analyzing the results of numerical examples in the relevant literature.Taking the solution of cylindrical shell structure model as a numerical example,using the calculation method proposed in this paper,three groups of different one-way load approximation functions are constructed,and the displacement,bending moment,axial force,and the distribution of displacement and internal force along the coordinate axis at special points are obtained respectively.The accuracy and practicability of the approximate calculation method are analyzed by comparing with the accurate solution(shallow shell solution).The results show that the relative errors of quadratic interpolation method are less than 1.5%at special points,and the relative errors of cubic and quartic interpolation methods are less than 0.6%.The distribution along the coordinate axis is consistent with the exact solution,which shows that this method has the characteristics of high accuracy,simple handling of complex loads,easy programming,flexible constructor and so on.The idea that the approximation function is used to replace the original function for numerical integration in this method provides a new idea for the future B-spline function method to deal with complex loads.