Visual Basic을 활용한 二次元 有限要素 生成

A Two Dimensional Finite Elements Method by Visual Basic

A two dimensional finite element generation code has been developed attaching simple blocks with arbitrary solution degrees. The serendipity basis functions are employed to map elements between the computational domain and the physical domain. For blocks to be connected properly, a block should have a consistent numbering scheme for vertices, side nodes, edges and surfaces. Also, edge information such as number of elements and the progressive ratio for each direction should also be checked for interfaces to have unique node numbers. Having done so, user can add blocks with little worry about the orientation of blocks. In the construction of an element solution, the hierarchical basis functions are employed for a solution to have s continuity at the interface between blocks with different degrees. Since for the two dimensional cases the elements based on the hierarchical basis functions have some extra degrees of freedom at the edge node, the consistency of nodal degrees of freedom of each adjacent elements can be made rather easily than the other choice of basis functions. The present code has been made to handle this situation by adding the necessary degrees of freedom to the element with a lower degree. To verify the usefulness of the present scheme, examples for a two dimensional heat conduction problem are shown for blocks with different degrees.