The objective of this report is to discuss the effects the linear and non-linear tension
has on the analytical model of a cube.
For the first problem, it was required to sketch a cube of specific dimensions. The
cube was assigned specific materials of young modulus of E=110 Mpa and Poisson
ratio of v=0.35
The cube was then assigned linear and non-linear tension modes and the results
compared for both cases.
Finite element results from Abaqus:
In fig.1, a contour plot of the displacement along the x-axis is present for both linear
and non-linear tension cubes.
In a linear element the displacement across the element is considered linear. In
other words, you can use simple interpolation between nodes to find the
displacement at any point on a linear element.
Non-linear here means that the curve load-displacement is no more proportional.
As seen in table 1 above:
– For Linear Geometry: The Nominal stain, nominal stress and force per nodes are
approximately equal in both cases for the abaqus and theoretical results.
– For Non-Linear Geometry: The true strain, strain along y-axis and true stress are
approximately equal in both cases for the abaqus and theoretical results.
– The nodal force for the non-linear geometry is non accurate when comparing the
abacus results and theoretical results.
Table 1, demonstrates the effect the NLGEOM mode has on an analytical model of a
cube under specific boundary conditions.
Furthermore, the two plots in fig4 & fig5 further demonstrates the differences in results the
NLGEOM mode has on results. It also shows that for the geometric non linearity, the strain
varies as well as the displacement as the application of the load becomes non uniform.
Problem 2
In problem 2, a point load of 1.3933 mm was applied to the corner of a cube. For case 1, the
cube was meshed with element type C3D8, which is a full integration hexahedral element.
For the second case, Von -Mises results are compared for both cases.
The maximum stress with element type C3D8 is almost four times greater than the
maximum stress with element type C3D8
This highlights the important of choosing the right element type to mesh the design,
as it has a large impact on the Von-misses (deformation) results and analysis.
Hourglass term come into picture if you are using reduced integration elements.
Because of under integration you will get spurious modes, which needs to be
avoided as it produces meaningless results.
Due to the complexity of distribution of the point stress on the cube corner, the
design required an element type to be analysed accurately by using fully integrated
elements not reduced integration.
As seen in fig.6, there is almost an error in the formation representation given
assigning as an element type to the mesh.
The results above in fig.6 verify that Hourgalssing can be addressed by using fully
integrated elements.
Problem 3
In problem 3, the task is to highlight the differences and limitation between the element
choices on Abacus. The following three elements will be compared to the theoretical
? Reduced integration hexahedral (brick) element (C3D8R)
? Full integration linear hexahedral (brick) element(C3D8)
? Incompatible element (C3D8I)
A concentrated force will be applied with magnitude of 8000N to the vertices of a set of
The force will results in the downward bending of the beam and a step will be created for
analysis of at least 20 incriminations.
The results from the 3 simulations will be presented along with plots of the shape of the
deformed beam.
Lastly, there will be a brief discussion of results and comparisons with theoretical
The reduced integration results for deflection compared to the theoretical calculation are
off by a margin of about 10 mm which is very inaccurate and proves that the reduced
integration is not accurate and a bad choice for trying to predict the bending response of a
On the other hand the full and incompatible integration seem to be quite accurate when
compared to the theoretical results in fig. and table. 2and fig.8 .This proves that full and
incompatible integration are both good choices for predicting the beams bending response
and deflection along the deformed beam.
However in fig.7, there is an inaccuracy in the stress values for the full integration elements.
Therefore, the incompatible integration would be more accurate in interpreting accurate
overall results for the deflection of the beam. As it couses enhancements to the
deformation gradients which allow a first-order element to have a linear variation of the
deformation gradient across the element’s domain.
To conclude, element choices have proven to have a missive impact on the results obtained
form abacus. Choosing the right element type is crucial when analysis a design on abacus, as
the integrity of the results might be effected and impact greatly on the performance of the
designed model.