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Submodeling Beams Can Be a Force to Be Reckoned With

Full Beam Model vs. Submodel Displacements - Force vs. Displacement vs. Mixed Method |FEA Consulting
February 28, 2017 By: Peter Barrett

Previous CAE Associates blog posts: Using Submodels to Give Adam a Leg to Stand OnTips & Tricks for Submodeling with Boundary Contact Surfaces and Modal Submodeling, have demonstrated the merits and ease of use of submodeling under a variety of applications. In this post, I will demonstrate the value of utilizing beam-to-solid submodeling, illustrating the value of combining both displacement and force loading interpolation.

Accurate evaluation of potential fatigue and fracture of complex structural connections is achievable with a refined local finite element mesh. However, for large structures such as bridges and offshore platforms, it is impossible to achieve this type of modeling resolution for the entire model, not to mention over the large number of loading combinations.  All beam finite element models are a very effective way of isolating the peak forces and moments at the critical design joints. Detailed local 3-D models are an efficient way of developing the detailed stress and stress intensities in the local connections, where empirical solutions typically used are not always practical, or are often overly conservative.  The local models are only as good as their boundary conditions. Beam-to-solid submodeling provides an effective method of creating accurate 3-D detailed models of the connection region of concern by utilizing the true force/displacement field from the global analysis model.

In classic solid-to-solid submodeling, first introduced in ANSYS in the late 1970’s, the submodel boundary node displacements are computed independently on a node by node basis via interpolation, based on their location in the global model element displacement field. Beam-to-solid submodeling utilizes a similar interpolation of beam forces and moments from the global analysis. However, with the beam global model, there is no displacement field to interpolate onto the solid element boundary nodes. Thus, instead of applying displacements directly to the boundary nodes, a series of constraint equations or multi-point constraint equation contact elements are used to distribute the interpolated forces and moments and/or displacements and rotations from the beam element to the boundary face(s) of the solid elements.

The recently released ANSYS version 18 has added a highly automated easy-to-use submodeling procedure for beam-to-solid submodeling that can be implemented using either a force/moment of displacement/rotation approach via “drag and drop” on the project schematic. 

This beam-solid submodeling procedure is illustrated in Figures 1 through 3 with a stress analysis of a welded steel tubular frame structure commonly seen in the offshore industry. The all beam model of the full frame calculates displacements, rotations, forces and moments throughout the frame over the full range of loads. A review of either nominal beam stresses or peak forces and moments isolates the critical connection. A local 3-D solid submodel is then generated as a totally independent finite element model but geometrically positioned consistent with the global analysis geometry. The member free-ends are positioned a few diameters away from the joints in all directions.  Transferring loads from the global model to the submodel is performed using either forces and moments or displacements and rotations at each member end. These loads are interpolated from the global beam model to the ends of the submodel section cuts. Bonded contact elements are then automatically generated to apply these loads to the solid element free surfaces. Guidelines on selecting either force of displacement submodeling loads are summarized below.

Beam-to-Solid Force Submodeling

  • Typically, forces are best suited for the cases where the local model might have a stiffness mismatch due to the inexact modeling of the member connections, including local fillets, that can be added in the submodel.
  • For static models where force submodeling is used on all cut boundary surfaces make sure that rigid body motion is eliminated.  A combination of weak springs and inertia relief can be used to maintain equilibrium.
  • When weak springs are added to the model, be sure to check for unrealistic spring reactions.
  • Stresses should be reasonable with this method since forces are accurate, but the displacements from this method are likely to be arbitrary, due to rigid body motion. (See the left image of Figure 1, above).
     
Figure 2 - Full Beam Model vs. Submodel Von Mises Stress (psi) - Force vs. Displacement vs. Mixed Method


Beam-to-Solid Displacement Submodeling

  • Displacement loading prevents rigid body motion to provide the most stable submodel.
  • Reactions at the support cuts are typically easily extracted and compared with global model for validation.  In many cases these will not match due to the stiffness mismatch. This mismatch is illustrated by comparing columns three and four in the Figure 3 chart.
  • Displacements will be accurate, but since the forces are not exact, expect some error in the stress calculation. (See Figure 2 middle image)
     
Figure 3 - Full Beam Model vs. Submodel Load/Reaction for Force vs. Displacement vs. Mixed Method



Beam-to-Solid Mixed Displacement/Force Submodeling (Figure 3)

  • A hybrid approach would be to use a displacement boundary on one free end to prevent Rigid Body Motion Restraint and the define forces/moment loads on the remaining cuts.
  • The force constraints on all other boundaries allows for minor stiffness mismatch and thus maintaining the force balance.Reaction force comparisons at the single displacement support provide validation of the model.
  • Displacements are correctly predicted throughout since the submodel is constrained at one end. (See third image of Figure 1)
  • Since forces and displacements are accurate, the stresses are most accurate for this method. (see right image of Figure 2)

Figure 3 provides a summary of the applied forces and/or reaction forces for each of the 3 methods discussed above. The mixed method is recommended since it will produce the most accurate stress and displacement data. Utilizing the automated Workbench V18 tool makes testing each of these three methods very easy for the analyst. I welcome hearing about others’ experiences in utilizing beam-to-solid submodeling.