Nonlinear Static and Dynamic Analysis of Steel Structures with ...

Chapter 2 Finite element modeling with ABAQUS/Standard
primary effect of these modes is to eliminate the parasitic shear stresses that cause the
response of the regular first-order displacement elements to be too stiff in bending. In
addition, these modes eliminate the artificial stiffening due to Poisson's effect in bending
(which is manifested in regular displacement elements by a linear variation of the stress
perpendicular to the bending direction). In the nonhybrid elements—except for the plane
stress element, CPS4I—additional incompatible modes are added to prevent locking of the
elements with approximately incompressible material behavior. For fully incompressible
material behavior the corresponding hybrid elements must be used. Because of the added
internal degrees of freedom due to the incompatible modes (4 for CPS4I; 5 for CPE4I,
CAX4I, and CPEG4I; and 13 for C3D8I), these elements are somewhat more expensive
than the regular first-order displacement elements; however, they are significantly more
economical than second-order elements. The incompatible mode elements use full
integration and, thus, have no hourglass modes.
Shape considerations
The incompatible mode elements perform almost as well as second-order elements in many
situations if the elements have an approximately rectangular shape. The performance is
reduced considerably if the elements have a parallelogram shape. The performance of
trapezoidal-shaped incompatible mode elements is not much better than the performance of
the regular, fully integrated, first-order interpolation elements. Hence, there is a loss of
accuracy associated with distorted elements.
Using incompatible mode elements in large-strain applications
Incompatible mode elements should be used with caution in applications involving large
compressive strains. Convergence may be slow at times, and inaccuracies may accumulate
in hyperelastic applications. Hence, erroneous residual stresses may sometimes appear in
hyperelastic elements that are unloaded after having been subjected to a complex
deformation history.
Using incompatible mode elements with regular elements
Incompatible mode elements can be used in the same mesh with regular solid elements.
Generally the incompatible mode elements should be used in regions where bending
response must be modeled accurately, and they should be of rectangular shape to provide
the most accuracy. While these elements often provide accurate response in such cases, it
is generally preferable to use structural elements (shells or beams) to model structural
components.
2.1.6 Summary of recommendations for element usage
Make all elements as ―well shaped‖ as possible to improve convergence and accuracy.
If an automatic tetrahedral mesh generator is used, use the second-order elements
C3D10. If contact is present, use the modified tetrahedral element C3D10M if the
default ―hard‖ contact relationship is used or in analyses with large amounts of plastic
deformation.
If possible, use hexahedral elements in three-dimensional analyses since they give the
best results for the minimum cost.
For linear and ―smooth‖ nonlinear problems use reduced-integration, second-order
elements if possible.
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