中文摘要：

利用Jacobi椭圆函数得到了自由端受集中载荷悬臂梁大挠度弯曲问题的显式精确解，不同于由传统椭圆积分公式得到的解，该显式精确解给出梁中任意点的转角，由此可方便的得到梁弯曲后各点的位移。研究表明：由该解出发，可得到任意位置受集中载荷悬臂梁问题的解；对称性分析表明该解可直接用于两端简支或两端固支梁中点受集中载荷的情况。最后分别给出了载荷取一系列值时以上三种边界条件下梁弯曲的挠度曲线。

英文摘要：

Explicit exact solution of the large deformations of a cantilever beam under point load at the free tip was derived by using the Jacobi elliptic functions, and it was different from the conventional solution obtained by the elliptic integrals for it gave the rotation angle of any point in the beam by which the corre- sponding displacement can be obtained easily. The study shows that the solution of the cantilever beam with a concentrated load at any position in the beam can be obtained by the exact solution~ and symmetry analysis shows that the exact solution can be applied to simple and fixed beams with a concentrated load at middle point directly. Then the deflection curves for a series of different forces of the above 3 kinds of beams were given by the exact solution.