高阶四边形单元的流形方法

HIGH ORDER RECTANGULAR ELEMENT OF MANIFOLD METHOD

在原有的三角形单元的流形方法的基础上,提出了高阶四边形单元的流形方法。该法简化了数学和物理网格,减少了小块物理覆盖的生成数量,采用解析解的单纯形积分,提高了应力和应变的计算精度。首先推导了四边形单元的权函数,并给出四边形单元的高阶位移方程的一般表达式。进一步推导了应变和应力以及单元的刚度矩阵等,最后通过具体实例验证了高阶四边形流形单元的计算应力和应变的准确性。

The high order displacement function of rectangular element of manifold method is developed based on the theory of manifold method. This new method can simplify the forming of the mathematical meshes and physical covers, reduce the number of small physical covers, and precisely calculate the strain and stress by using the simplex integration. The linear cover displacement function is mainly discussed. The stiffness matrix is formulated. The calculation results, with an example shown, demonstrate that high order rectangular element of manifold method can get more accurate strain and stress.