线性荷载作用下两端固支浅梁和短梁的解析解

Analytical Solution to Shallow Beam and Short Team with Fixed Ends under Linear Loading

针对已有的三种简化固定边界条件,通过半逆解法假设应力函数,求解了线性荷载作用下两端固支浅梁和短梁的解析解.运用有限元软件ANSYS分别对线性荷载作用下两端固支浅梁和短梁进行分析,与所求的解析解对比,结果表明,假设固定端截面中点两个方向的位移和固定端截面顶点纵向位移为零的简化边界条件和有限元结果符合较好,准确度较其它简化边界条件也更高,可以用于计算线性荷载作用下两端固支浅梁和短梁弯曲的位移和应力.

The analytical solution to the problem of shallow beam and short beam with fixed ends under linear loading is adopted in this paper, which uses three kinds of the assumption of the simplify boundary conditions available and the stress function by the way of semi-inverse method. The results of analytical solution are compared with the numerical results which are done by the finite software ANSYS in the situation of shallow beams and short beams. The comparison results show that the results for displacements and stresses under the simplify boundary conditions with displacements of middle point in two directions and in longitudinal direction of top point at the fixed ends equal zero are better than those of other existing sim- plify boundary conditions. The present solution can be used for the bending problems of shallow beams and short beams with fixed ends under linear loading.