Plate and Laminate Element Offsets

This has always been a fun topic. In this post, we will look at some important aspects related to plate and laminate element offsets.

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What happens when we use plate and laminate element offsets? Before we get into that, what exactly is an offset?

For example, consider the simple laminate in the featured image above. The laminate may be fastened to a T-beam or extrusion flanges using rivets or hi-loks. Or, it may be bonded using structural adhesive to the top surface of the beam or extrusion. Whatever the case maybe, when we model this joint we need to account for the actual position of the components with respect to each other. This is done using offsets. But offsets also induce moments.

In this post we will look at some sample models with offsets defined in different ways. We will look at how the offsets affect the results. We will use hypothetical models, we are doing this just to understand the “what if” conditions, so this is more of a hypothetical study than a real life situation.

Plate and Laminate Element Offsets Study – The Basics:

Our hypothetical models consist of two components:

  • A laminate with 10 fiberglass plies, each ply is 0.01″ thick and thus making up a 0.1″ thick solid laminate. The laminate is modeled as a symmetric 10 ply laminate, [0/+-45/90/0]s
  • An aluminum alloy “T” extrusion, 0.1″ thick flanges and 0.1″ thick web modeled as beam elements at the mid line of the laminate elements
    • The T extrusion will include an inherent offset of the nodal or bending axis from its shear center axis.
    • The effect of this has been covered in the beam bar elements shear center effect blog post, click to read more on this topic
  • Let us assume, for analytical purposes, that the two parts act in union due to bonding, or connected with a couple of CBUSH elements acting as rivets.

By default, the plate or laminate nodes lie on the mid plane of the plate, the total plate/laminate thickness is equally distributed on either side of the mid plane of nodes. However, it is important to remember that any applied load along the nodal plane will result in an induced moment due to any offset.

We are using a single set of nodes to model the laminate T-Beam assembly. In case of the two laminate plates connected with CBUSH elements representing rivets, each laminate has its own plane of nodes. To model the components in their correct physical position in the assembly we can define a plate offset from its original midplane. Or, a line element offset for the extrusion, this moves it down in addition to its shear center offset.

Plate and Laminate Element Offsets Study – Common Boundary Conditions:

  • In each case, a single center node is fixed in all directions. All remaining nodes are free to move and rotate in any direction. Is this situation a real life situation? Not really.
  • In each case, the edges at the far and near side of the laminate are loaded with a total edge force of 500 lbs each in the opposite directions. This could be a similar load that comes from a fuselage barrel pressurization on the skin panels, but the skin panels are always supported with stringers. This pressure could be as high as 9 to 12 psi.

Plate and Laminate Element Offsets Study – Case 1:

In this case, we have just the laminate component. One center node is fixed, the short edges are loaded as indicated below. There are no offsets, the laminate nodes lie at the mid plane. Obviously, this model results in a simple symmetric stretch of the laminate along the laminate’s long axis, or the ‘zero’ degree material angle. The poisson’s effect results in a symmetric contraction along the short axis, as shown in the Figure below. There is no bending effect of the laminate. So this is our base case.

Plate and Laminate Element Offsets Case1
Figure 1: Plate and Laminate Element Offsets Case1

Before we get into the remaining cases, let us dig into the different offset types.

Plate and Laminate Element Offsets Study – Offset Types:

There are two types of offsets. The figure below explains how a regular plate offset is defined, and how a laminate offset is a bit different from a regular shell element offset.

Plate and Laminate Element Offsets Type
Figure 2: Plate and Laminate Element Offsets Types

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The plate offset (top dialog box in Figure 2) will simply move the neutral plane based on the offset value, this can be a positive or a negative number. But let us assume that a positive number represents a plate offset. So a 0.05″ plate offset will move the plate above the flanges of the T-Beam.

But when we talk about a laminate bottom surface offset, it is a bit different. The bottom surface is the bottom of ply 1. So if we have an unsymmetric layup, or if ply pick ups and drop offs exist, this offset will make sure that each layup bottom surface is aligned properly based on the part design. By default if you leave it blank or unchecked, the value is -t/2, where ‘t’ is the total laminate thickness. This means that the bottom surface is t/2 inches below the neutral plane.

For example, if there is a bonded doubler on one side, or a ply drop off on that side at different locations, the same laminate bottom surface offset in the different layups will ensure that all the bottom surfaces are aligned with each other. On the other hand, if you define a positive value in this offset field, then it is just like a plate offset and moves the bottom surface above the nodal plane.

Plate and Laminate Element Offsets Study – Case 2:

In this case, we offset the T-Beam by 0.1″. The same loading as case 1 is applied. The offset pushes the T-Beam elements down by 0.1″ in addition to the shear center offset of the beam nodal axis. Therefore, any axial load applied at the laminate edges will result in a downward displacement of the laminate edges.

The plot below shows an exaggerated plot of vertical displacements. If the laminate edges are constrained from moving down or simply supported, there is a possibility of tension loads developing in the rivets or hi-loks. So this is may be important for analysis.

Plate and Laminate Element Offsets Case2
Figure 3: Plate and Laminate Element Offsets Case2

Plate and Laminate Element Offsets Study – Case 3:

In the final case, we have two laminate plates. The top plate is offset by 0.1″ resulting in a gap of 0.1″ between the plates. This is done only to examine the effect of the offset. Three CBUSH elements are used to connect the two plates together. The bottom plate is completely fixed. And the top plate is only constrained by the CBUSH elements with 100,000 lb/in stiffness in all translational DOF. The same loading is applied on the top plate short edges. The result is that the edges of the top laminate lift up due to the induced moment from the offset. This also results in a small tension load in the outer CBUSH elements (about 5lb) and a compressive load (10lb) at the center CBUSH element.

Plate and Laminate Element Offsets Case3
Figure 4: Plate and Laminate Element Offsets Case3

The point of all the cases above is to try and understand what offsets do and how to interpret those results properly.

Obviously, if the plate is simply supported at all edges like the aircraft skin panels are, then there is no significant impact. But in locations with stringer reinforcements, using either structural adhesives or fasteners, the moment due to the axial load and beam offsets, and the resulting peel off loads may require some level of thought in terms of stress analysis. The fact the fuselage pressurization and depressurization happens multiple times through out the aircraft’s service life may also be important from a skin-stringer joint fatigue analysis perspective.

I hope this post adds value to your time and I hope you learned something new. If you find problems with this post, or if you have any feedback, I’d love to hear from you.

Feel free to comment below the post.

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Surya Batchu
Surya Batchu

Surya Batchu is the founder of Stress Ebook LLC. A senior stress engineer specializing in aerospace stress analysis and finite element analysis, Surya has close to two decades of real world aerospace industry experience. He shares his expertise with you on this blog and the website via paid courses, so you can benefit from it and get ahead in your own career.