均布载荷作用下正交各向异性固支梁的解析解  

Analytical solution for fixed-end orthotropic beams subjected to uniform load

作　　者：黄德进[1] 丁皓江[1] 王惠明[1] 

机构地区：[1]浙江大学土木工程学系

出　　处：《浙江大学学报（工学版）》2006年第3期511-514,共4页Journal of Zhejiang University：Engineering Science

基　　金：国家自然科学基金资助项目(10472102;10432030)

摘　　要：针对均布载荷作用下正交各向异性梁在两端固支条件下的平面应力问题,求解了应力和位移的解析解.在求解过程中,构造了一个含待定系数的应力函数,通过Airy应力函数解法,给出了应力和位移的表达式.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解结果.结果表明,该解析与由Nastran程序计算的有限元数值结果相比,解析解落在有限元数值的附近,两者较为吻合.该解析解对于跨高比较大的梁有较高的精度,并可退化到各向同性梁的结果.For the plane stress problem of fixed end orthotropic beams subjected to uniform load, the analytical solutions of stress and displacement were resolved. A stress function involving several unknown coefficients was constructed in the solution process, and the stress and displacement expressions were obtained through traditional Airy stress function methodology. After the fixed end boundary condition was treated with two methods, the unknown coefficients in stress function were determined with stress and displacement boundary conditions, and the analytical solutions were achieved. The results show that compared with finite element method （FEM） numerical solutions by Nastran codes, the analytical solutions are close to and agree well with the FEM solutions. The analytical solutions can reach high precision for the beams with large span height ratio, and can be degenerated into isotropic results.

关 键 词：固支梁 正交各向异性 应力函数 解析解 

分 类 号：O343.1[理学—固体力学]