The Quadrilateral Region

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The Quadrilateral Region |

The mesh generation for any two-dimensional domain into elements should start with the division of the body in consideration into quadrilateral or triangular regions. These regions are then subdivided either into triangle or quadrilateral finite elements. The subdivision between regions should be located where there is a change in geometry or material properties. GFAS uses a group of eight-node (quadratic) quadrilateral regions to define the body under consideration, being capable of modeling two-dimensional domains that are composed of rectangles and triangles having second-order curved boundaries. The element nodes are numbered and optimization of the matrix bandwidth to reduce the computer storage and calculation time can be performed by the program using internal re-numbering of the system equations.

The region available in GFAS is the quadratic quadrilateral. This element is quite versatile, it can be used as a rectangle, general quadrilateral, or as a triangle as shown in Figure 2. Two sides of the quadrilateral are used to define one side of the triangular region. The eight nodes that define the region must be numbered as shown in the Figure 2. Node 1 is always at the coordinate location ξ=η=-1. Note that one of the corner nodes (node 5 in Figure 2) will always be on the hypotenuse of the triangular region. The region is then subdivided either in triangular elements or quadrilateral elements using the mapping technique.

Fig. 2. Possible regions for the quadrilateral. Nodes numbering. |

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