用C_n群解梁弯曲问题

Solving the Bending of Beam by Using C_n Group

应用Cn 群的表示理论 ,将分布多项式分解为正交特征分布多项式 .周期函数采用正交特征多项式逼近 .将均匀梁结构延拓并加上附加载荷 ,使梁的位移化为周期函数 .利用正交特征分布多项式 ,逼近梁的位移函数 .应用能量法求在载荷作用下梁位移的各个多项式的系数 ,通过边界条件确定附加载荷的大小 .所述方法基本上为有限元方法 ,其逼近精度与有限元是一致的 .此方法在求解中应用正交函数 ,因而大大减低有限元的计算量 .该计算量与边界元相仿 .

The representation theory of C n group is applied to the decomposition of distributed polynominals into distributed polynomial with characteristic of orthogonality, which is adopted for approximating periodic function. A homogeneous structure of beam is in continuation and bears additional load; and the displacement of the beam is converted into periodic function. Thus the authors use distributed polynomial with orthogonal characteristic for approximating displacement function of the beam; and apply energy method for solving coefficient of each polynomial reflecting dispacement of beam under the action of load; and draw support from boundary condition for determining the size of additional load. The method mentioned above is basically the finite element methoel with the same approximation accuracy. The method apply orthogonal functions in its solving. As a result, its amount of calculation is less than that of finite element method but is similar to that of buoundary element method.