用椭圆积分法求解轴线可伸长梁的弹性曲线

Elastica of beams with extensible axis derived by elliptical integration

基于轴线可伸长梁(杆)的几何非线性控制方程,采用椭圆积分法推导出了两端简支梁过屈曲状态的解析解,给出了更为精确的载荷 变形特征关系.其中反映了梁的长细比对过屈曲变形的影响.结果表明,当长细比趋近于无穷大时轴线不可伸长假设才精确成立.

Based on the geometrically nonlinear governing equations of extensible beams/rods, an analytical solution for the post-buckling of a simply supported beam is derived by using elliptical integral method. More accurate characteristic relationships between the load and the deformations are presented, in which the influence of the slenderness on the buckling deformations are illustrated. The results show that the axially inextensible assumption of the beam comes absolutely true only when the slenderness approaches to the limit of infinity.