【摘要】 针对集中荷载作用下正交各向异性悬臂梁的平面应力问题,研究了固端边界条件对位移的影响。对于固端边界条件的处理,Timoshenko和Goodier给出了两种形式。首先,采用第二种形式,基于Lekhniskii各向异性弹性理论应力解答,推导出位移分量的解析解;然后,在文献已有的部分结果的基础上求出第一种形式的x方向位移解析解;最后,求出两种固端边界条件处理形式的位移差别。位移解析解与有限元数值解进行了比较,两者吻合良好。数值算例表明,材料各向异性程度、跨高比和材料弹性主轴方向对位移差别有明显的影响。更多还原

【Abstract】 The effects of the fixed-end boundary conditions on the displacement are studied for the plane stress problem of an orthotropic cantilever beam subjected to a single force.The fixed-end boundary conditions are treated by two kinds of methods presented by Timoshenko and Goodier.From Lekhniskii’s anisotropic elasticity solutions of stresses,the displacement expressions are obtained according to one of the methods treating the fixed-end boundary conditions.Based on the part solution under another kind of fixed-end boundary condition obtained in reference,the displacement expression in x direction is also derived and then the displacement difference under the two kinds of fixed-end boundary conditions is presented.The analytical displacement results are compared with those calculated by the finite element method(FEM) and the agreement between them is satisfactory.Numerical example shows that the displacement difference is dependent on the anisotropy ratio,the span-to-thickness ratio and the principal directions of elasticity.更多还原