均布荷载作用下正交各向异性悬臂梁固端边界条件对位移的影响

EFFECTS OF BOUNDARY CONDITIONS AT FIXED-END ON DISPLACEMENT OF A UNIFORMLY LOADED ORTHOTROPIC CANTILEVER BEAM

本文采用Timoshenko和Goodier处理固端边界条件的两种方法,探讨均布荷载作用下正交各向异性悬臂梁固端边界条件对位移的影响。根据Lekhniskii各向异性弹性理论应力解答,推导在第二种固端边界条件下的位移分量的解析解,并在文献已有部分结果的基础上求出第一种固端边界条件下的x方向位移解析解,然后得出两种固端边界条件下的位移差别。数值算例中将得出的位移解析解与有限元数值解进行比较,两者吻合良好,然后讨论材料各向异性程度、跨高比和材料弹性主轴方向对位移差别的影响。

The effects of the fixed-end boundary conditions on the displacement of an orthotropic cantilever beam subjected to uniform load are analyzed by way of Timoshenko and Goodier ＇s method of treating fixed-end boundary condition. According to one kind of the fixed-end boundary condition, the displacement expressions are obtained by using Lekhniskii＇s anisotropic elasticity solutions of stresses. Based on the part solution of another fixedend 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. In the numerical example the analytical displacement results are compared with those calculated by the finite element method （FEM） and agreement between them is satisfactory. Several sets of numerical results are presented to show the effects of anisotropy ratios, the span-to-thickness and principal directions of elasticity.