连续载荷作用下悬臂梁的Airy应力函数解法

The airy stress function solution of a cantilever beam subjected to continuous load

依据应力函数的性质结合边界条件,求解连续载荷q(x)=ax2+bx+c作用下悬臂梁的平面应力问题,改变载荷方程的系数,可得到任意线性、二次分布载荷作用下的应力函数,该解析解是对弹性理论中相关经典例题的补充,求解计算表明,要得到更高次载荷分布情况的解析解将非常困难.

The plane stress problem was solved about the cantilever beam subjected to continuous load q （x）= ax2＋bx＋c based on the nature of stress function and boundary conditions. It can be received stress function at the random linear or second order load when changed the coefficients of the equation, then the analytic solutions is to supplement the classical example related to elastic theory. Study shows it is very difficulty to get the analytic solutions subjected to higher order load.