## Mesh density

The mesh density parameter, md, determines mesh size. This parameter is used as follows. First, a characteristic dimension of the sectional shape, denoted Lr, is selected. Typically, this characteristic dimension is chosen to be the largest dimension of any of the components of the section and is divided by md to yields the characteristic size of an element, sr = Lr / md. The mesh generation program attempts to create, as closely as possible, quadrangular elements of size sr X sr .

As the mesh density increases, the total number of elements used in the discretization of the section increases and so does the computational cost. At the same time, the accuracy of the computation increases: the sectional stiffness matrix is computed with greater accuracy and the local, three-dimensional stress components also converge towards their exact value.

The figures below illustrate the effect of increasing the mesh density parameter, md, on the configuration of the mesh of a C-Section. The largest dimension of the section is the height of the web that will be divided into md elements. For md = 4 and 8, the web is divided into 4 and 8 elements, respectively, as shown in the left and right portions of fig. 1, respectively.  ##### Figure 1. Configuration of the mesh of C-Section for mesh density parameter, md = 4 and 8 for the left and right figures, respectively.

When the mesh density parameter is increased to md = 16, 16 elements are used for the height of the web, as expected, but two elements now appear through its thickness to keep the aspect ratio of the elements as square as possible, as illustrated in fig. 2. For md = 32, 32 elements are used for the height of the web and four elements now appear through the thickness of the web.  ##### Figure 2. Configuration of the mesh of C-Section for mesh density parameter, md = 16 and 32 for the left and right figures, respectively.

Finally, when the mesh density parameter is increased to md = 64, 64 and 8 elements are used for the height and thickness of the web, respectively, as illustrated in fig. 3. 