两端固定受均布载荷的短梁的平面应力解  

A Plane Stress Solution of Deep Beam with Fixed Ends Under Uniform Loading

作　　者：戴瑛[1] 嵇醒[1] 

机构地区：[1]同济大学航空航天与力学学院,上海200092

出　　处：《同济大学学报（自然科学版）》2008年第7期890-893,共4页Journal of Tongji University:Natural Science

基　　金：国家自然科学基金资助项目(10672122);上海市教委"曙光计划"资助项目;上海市重点学科建设项目(B302)

摘　　要：采用已有解析解的应力函数表达式,但改进了简化的固定边界条件,即假设固定端端面中点两个方向的位移和固定端端面顶点纵向位移为零,求得了两端固定受均布载荷的短梁的平面应力解析解.补充了有限元分析结果.所得结果与已有解析解的结果作了比较,表明改进后解析解的位移和应力与有限差分及有限元分析的结果符合得较好.比已有的解析解,准确度提高很多,能够用于计算两端固定短梁弯曲的变形和应力.The stress function of existing analytical solution for the problem of deep beam with fixed ends under uniform loading is adopted in this paper, but the assumption of the boundary conditions is different. The displacements of middle point in two directions and in longitudinal direction of top point at the fixed ends equal zero. The results of the present and the existing analytical solution are compared with the numerical results of finite difference and finite element analysis. The comparison result shows that the present results for displacements and stresses are better than that of the the existing analytical solution. So the present solution can be used for the bending problems d deep beams with fixed ends under uniform loading.

关 键 词：短梁 平面应力 应力函数 

分 类 号：O341[理学—固体力学] TB301[理学—力学]