Civil Engineering Reference
In-Depth Information
(note that, by default, the nodes define the geometry) followed by definition of all
elements in terms of nodes. Many years ago, in the early development of the
finite element method, the tasks of node and element definition were labor
intensive, as the definitions required use of the specific language statements of a
particular finite element software system. The tasks were laborious, to say the
least, and prone to error. With currently technology, especially graphical user
interfaces and portability of computer-aided design (CAD) databases, these
tasks have been greatly simplified. It is now possible, with many FEA programs,
to “import” the geometry of a component, structure, or assembly directly from a
CAD system, so that geometry does not need to be defined. The finite element
software can then automatically create a mesh (
automeshing
) of finite elements
to represent the geometry. The advantages of this capability include (1) the finite
element analyst need not redefine the geometry; consequently, (2) the designer's
intent is not changed inadvertently; and (3) the finite element analyst is relieved
of the burden of specifying the details of the node and element definitions. The
major disadvantage is that the analyst is not in
direct
control of the meshing op-
eration.
The word direct is emphasized. In automeshing, the software user has some
control over the meshing process. There are two general types of automeshing
software, generally referred to as
free meshing
and
mapped meshing.
In free
meshing, the user specifies a general, qualitative mesh description, ranging from
coarse to fine, with 10 or more gradations between the extremes. The software
then generates the mesh accordingly. In mapped meshing, the user specifies quan-
titative information regarding node spacing, hence, element size, and the soft-
ware uses the prescribed information to generate nodes and elements. In either
method, the software user has some degree of control over the element mesh.
A very important aspect of meshing a model with elements is to ensure that,
in regions of geometric discontinuity, a finer mesh (smaller elements) is defined
in the region. This is true in all finite element analyses (structural, thermal, and
fluid), because it is known that gradients are higher in such areas and finer
meshes are required to adequately describe the physical behavior. In mapped
meshing, this is defined by the software user. Fortunately, in free meshing, this
aspect is accounted for in the software. As an example, refer back to Exam-
ple 9.4, in which we examined the stress concentration factor for a hole in a thin
plate subjected to tension. The solution was modeled using the free mesh feature
of a finite element software system. Figure 9.8b is a coarse mesh as generated by
the software. Geometry is defined by four lines and a quarter-circular arc; these,
in turn, define a single area of interest. Having specified the element type (in this
case a plane stress, elastic, quadrilateral), the area meshing feature is used to gen-
erate the elements as shown. It is important to note the relatively fine mesh in the
vicinity of the arc representing the hole. This is generated by the software auto-
matically in recognition of the geometry. The mesh-refined models of Fig-
ure 9.8c and 9.8d are also generated by the free meshing routine. From each of
these cases, we see that, not only does the number of elements increase, but the
