二次抛物线形曲线梁平衡与几何解析方程

目的对形心轴线为二次抛物线形曲线梁的内力、几何方程进行理论分析与公式推导.方法应用矢量几何与微分学理论,推导出平面二次曲线梁在空间分布力系作用下的内力、几何解析方程,其表达式方程最终可表示为全局坐标系下的解析函数.结果为了验证其正确性,在最后通过令参数取值趋向于极限值,其内力、几何方程恰好回归到直梁表达方程形式.结论本例推导所采用的构件形式是不考虑截面尺寸的平面曲线构件,得到的只是在各横截面位置处的内力、曲率表达形式,并不涉及到应力在横截面内的具体分布问题.

Analytical Equations on Polynomial Curved Beam

Applying theories of Vector geometry and differential calculus,this paper aims to infer the internal force and geometry equations for curved beam,whose axis curve is parabola and being distributing-load.The equations can be described with functions in Cartesian Coordinate System.In order to testify whether these equations are correct,this paper,by making the parameters approach limits,designs to get the internal force and geometric equations to completely regress to those for straight beam.The curved beam employed in this paper is regarded as a space curve,without taking the section size into consideration,what we obtained is just the internal force and curvature expressions in different section,and concrete distribution of stress in sections is not related.