均布载荷作用下各向异性固支梁的解析解

Analytical Solution for Fixed-Fixed Anisotropic Beam Subjected to Uniform Load

针对均布载荷作用下的各向异性梁在两端固支条件下的平面应力问题,给出了一个求解应力和位移解析解的方法.该方法构造了一个含待定系数的应力函数,通过Airy应力函数解法,给出了含待定系数的应力和位移通式.对固支端边界条件采用两种处理办法.利用应力和位移边界条件,确定应力函数中的待定系数,得到了应力和位移的解析表达式.结果表明,该解析解与有限元数值结果相比,两者较为吻合.该解析解是对弹性理论中相关经典例题的补充.

The analytical solutions of the stresses and displacements were obtained for fixed-fixed anisotropic beams subjected to uniform load. A stress function involving unknown coefficients was constructed, and the general expressions of stress and displacement were obtained by means of Airy stress function method. Two types of the description for the fixed end boundary condition were considered. The introduced unknown coefficients in stress function were determined by using the boundary conditions. The analytical solutions for stresses and displacements were finally obtained. Numerical tests show that the analytical solutions agree with the FEM results. The analytical solution supplies a classical example for the elasticity theory.