Civil Engineering Reference
In-Depth Information
and exhibit slow convergence with mesh refinement, which is especially a
problem with first-order tetrahedral elements. If they are required, an
extremely fine mesh may be needed to obtain results with sufficient
accuracy.
Similar to the behavior of shells, reduced integration can be used with
solid elements to form the element stiffness. The mass matrix and distributed
loadings use full integration. Reduced integration reduces running time,
especially in three dimensions. For example, element type C3D20 has 27
integration points, while C3D20R has eight integration points only. There-
fore, element assembly is approximately 3.5
more costly for C3D20 than
for C3D20R. Second-order reduced-integration elements generally pro-
vide accurate results than the corresponding fully integrated elements. How-
ever, for first-order elements, the accuracy achieved with full versus reduced
integration is largely dependent on the nature of the problem. Triangular
and tetrahedral elements are geometrically flexible and can be used in many
models. It is very convenient to mesh a complex shape with triangular or
tetrahedral elements. A good mesh of hexahedral elements usually provides
a solution with equivalent accuracy at less cost. Quadrilateral and hexahedral
elements have a better convergence rate than triangular and tetrahedral ele-
ments. However, triangular and tetrahedral elements are less sensitive to ini-
tial element shape, whereas first-order quadrilateral and hexahedral elements
perform better if their shape is approximately rectangular. First-order trian-
gular and tetrahedral elements are usually overly stiff, and fine meshes are
required to obtain accurate results. For stress/displacement analyses, the
first-order tetrahedral element C3D4 is a constant stress tetrahedron, which
should be avoided as much as possible. The element exhibits slow conver-
gence with mesh refinement. This element provides accurate results only in
general cases with very fine meshing. Therefore, C3D4 is recommended
only for filling in regions of low stress gradient to replace the C3D8 or
C3D8R elements, when the geometry precludes the use of C3D8 or
C3D8R elements throughout the model. For tetrahedral element meshes,
the second-order or the modified tetrahedral elements such as C3D10
should be used. Similarly, the linear version of the wedge element C3D6
should generally be used only when necessary to complete a mesh, and, even
then, the element should be far from any area where accurate results are
needed. This element provides accurate results only with very fine meshing.
A solid section definition is used to define the section properties of solid ele-
ments. A material definition must be defined with the solid section defini-
tion, which is assigned to a region in the finite element model.
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