板弯曲问题的群论方法

利用群论方法提出周期区域的分片正交多项式连续函数，在周期区域内利用正交分片多项式逼近位移函数可以大大地降低计算量。非周期区域的板可以通过附加边界载荷将其扩展成周期区域的板。利用此方法可以大大降低板弯曲问题的计算量。

Analysis of bending problem of plate system by group method

A periodic zone have infinite number of symmetry axes, the transmit group of symmetry can be approached by Abelian group. By using self-cognate operator, one can get the characteristic vectors of Abelian group space. These vectors are orthogonal to each other in normal representation of group. Acting the characteristic vector on the node bases function of finite element (that have no any symmetry), one can obtain the orthogonal bases of continuous segmentation function in periodic zone. The orthogonal continuous segmentation functions are continuously differential up to order 1 and orthogonal to each other. The detail of products of two bases and detail of its two differential functions in periodic zone are presented in the paper. The proposed orthogonal bases are applied to solve the bending problem of beam and plate system in periodic zone. The system other to periodic zone can be expanded to periodic zone by acting the additional forces in the boundary area, by using the energy method one can get the solution of expanded beam and plate structure (without considering the boundary condition). Considering the boundary condition one can get the solution of real beam and plate system. Some examples are presented in the paper, results show less calculation and good accuracy of the proposed method. The proposed method basically is one of finite element method, by orthogonal method the calculation is greatly reduced and the parallel calculation is easy to be carried out.