In creating an accurate representation of a wing in a FEM, it is common to explicitly model spar caps in order to properly capture the load sharing between those caps and the surrounding wing skin. There are several different modelling techniques - including different element types, reference planes, and orientations. On the analysis side in HyperX, there are just as many options in the way of reference plane definition and Design Property assignment. Each of these decisions can change the contribution of spar caps to the overall wing CG.
This article reviews several options for modeling spar caps in the FEM, the corresponding HyperX setup, and offers insight on the pros and cons.
The table below briefly summarizes each model configuration, HyperX Design Property and reference plane setup, and corresponding analysis implication.
All configurations are explained based on the example wing section indicated below.
The first configuration uses CROD elements to represent spar caps. These elements are aligned with the nodal reference plane of the shell elements representing the wingskin - which is the midplane of the skin. The corresponding HyperX setup for the CROD elements involves assigning a cap beam Design Property and 'Top' reference plane. The shell elements can inherit any Design Property and should maintain a reference plane consistent with the FEM - Midplane. This setup is summarized in the table line item below.
A visual mock-up of this setup is shown below. Notice that the CROD elements (blue) do not do anything to contribute to the wing CG. Their location at the shell midplane does not change the distance from that reference plane to the wing CG.
Compared to the other configurations reviewed in this article, there is a larger distance from the skin CG to the wing CG in both directions. This results in a less accurate representation of the spar cap contribution to the overall wing stiffness in either direction, EI1 and EI2 respectively.
The second configuration uses horizontal CBAR elements to represent spar caps. These elements are aligned with the nodal reference plane of the shell elements representing the wingskin - which is the midplane of the skin. The corresponding HyperX setup for the CBAR elements involves assigning a web beam Design Property and 'Top' reference plane. The shell elements can inherit any Design Property and should maintain a reference plane consistent with the FEM - Midplane. This setup is summarized in the table line item below.
A visual mock-up of this setup is shown below. Notice that the CBAR elements (blue) have centroids that are closer to the overall wing CG in the 2-direction. Their location at the shell midplane does not change the distance from that reference plane to the wing CG in the 1-direction.
Compared to the other configurations reviewed in this article, there is a larger distance from the skin CG to the wing CG in the 1-direction. This results in a less accurate representation of the spar cap contribution to the overall wing stiffness in the 1-direction, EI1. But, in the 2-direction, this distance is shorter. This results in a more accurate representation of the spar cap contribution to the overall wing stiffness in the 2-direction, EI2.
Note
For thin wings (EI1 << EI2), the accuracy of the EI1 contribution of the caps has more impact than that of the EI2 contributions of the cap
The second configuration uses vertical CBAR elements to represent spar caps. The tops of these elements are aligned with the nodal reference plane of the shell elements representing the wingskin - which is the midplane of the skin. The corresponding HyperX setup for the CBAR elements involves assigning a cap beam Design Property and 'Top' reference plane. The shell elements can inherit any Design Property and should maintain a reference plane consistent with the FEM - Midplane. This setup is summarized in the table line item below.
A visual mock-up of this setup is shown below. Notice that the CBAR elements (blue) have centroids that are closer to the overall wing CG in the 1-direction. Their does not change the distance from that reference plane to the wing CG in the 2-direction.
A special-case of this configuration - in which the skins are to be sized as stiffened panels - is shown below. The only change here is that the shell elements must have a stiffened-panel Design Property with a reference plane set at "Top Face - Midplane" (as this is always the assumption for stiffened panels).
Compared to the other configurations reviewed in this article, there is a shorter distance from the skin CG to the overall wing CG in the 1-direction. This results in a more accurate representation of the spar cap contribution to the overall wing stiffness in the 1-direction, EI1. But, in the 2-direction, this distance is longer. This results in a less accurate representation of the spar cap contribution to the overall wing stiffness in the 2-direction, EI2.
Note
For thin wings (EI1 << EI2), the accuracy of the EI1 contribution of the caps has more impact than that of the EI2 contributions of the cap
The fourth configuration uses vertical CBAR elements to represent spar caps. The tops of these elements are aligned with the nodal reference plane of the shell elements representing the wingskin - which is the IML of the skin. The corresponding HyperX setup for the CBAR elements involves assigning a cao beam Design Property and 'Top' reference plane. The shell elements can inherit any Design Property (aside from stiffened panel) and should maintain a reference plane consistent with the FEM - at the bottom of the elements. This setup is summarized in the table line item below.
A visual mock-up of this setup is shown below. Notice that the CBAR elements (blue) have centroids that are closer to the overall wing CG in the 1-direction.
Compared to the other configurations reviewed in this article, this is the configuration with the shortest distance from the skin CG to the wing CG in the 1-direction. This results in the most accurate representation of the spar cap contribution to the overall wing stiffness in the 1-direction, EI1. But, in the 2-direction, this distance is larger. This results in a less accurate representation of the spar cap contribution to the overall wing stiffness in the 2-direction, EI2.
Note
For thin wings (EI1 << EI2), the accuracy of the EI1 contribution of the caps has more impact than that of the EI2 contributions of the cap
Based on the explanations above, Collier Aerospace engineers recommend Configuration #4, as it is the most accurate method to take advantage of the additional stiffness contribution of the cap elements to overall wing stiffness. However, this configuration is only applicable to unstiffened panel concepts (plates, laminates, sandwiches). If the wing skins are to be stiffened panel, then Configuration 3b is the best (and only) option.