Plate Forces and Moments Blog Post pdf

Transcription

1 Plate Forces and Moments Blog Post pdf Author: Surya Batchu Senior Stress Engineer Founder, STRESS EBOOK LLC. 1 P a g e

2 Plate Forces and Moments - Intro: You may have heard these terms related to plate forces and moments: Membrane loads Transverse shear loads Bending moments These terms refer to the plate forces and moments (plate/shell elements or laminate elements). But primarily, we will be focusing on FEM application. Plate elements are the most commonly used finite elements to model sheet metal or plate type structures. In case of laminates or sandwich panels, their finite element formulation is also based on the same basic plate theory. Except in laminates, different plies or layers with different material properties, orientations and other characteristics are accounted for. Here is a good link that goes into a lot of detail on the mechanics laminates: Basic Mechanics of Laminates The same link is also available on our Engineering Resources page along with many other useful links, so check those out too. But in this post, we will focus on the FEM analysis output file and the plate forces and moments written to the output file. So it behooves us to understand the plate forces and moments and how to interpret them. Plate Forces and Moments Schematics: The following figure illustrates the membrane loads and transverse shear loads on a plate/shell/laminate element. By 'membrane' loads, we mean these loads are acting in the plane of the element. By 'transverse' loads, we mean these loads are acting out of the plane of the element. Axial loads NX and NY are shown according to the right hand 2 P a g e

3 screw rule convention. NXY is the in plane shear load. QX and QY are transverse shear loads. All the loads have the units of lb/in (element edge length) in English units. Plate Forces and Moments: Membrane and Transverse Shear Loads These loads include applied loads (nodal, inertial, pressure etc.), and loads from the adjoining elements. The schematic shown above is a free body diagram of this element. All the forces balance each other for static equilibrium. It is also important to note that all these loads are written out to the analysis output file at the mid-plane or Surface-0 of the elements as 'running' (load per unit edge length) loads. 3 P a g e

4 There are also grid point forces that can be written out using the "GPFORCE" case control card's print option in nastran. These loads are nodal loads that satisfy the grid point force balance from all elements connected to that node. Similarly, we also have the plate element bending and twisting moments. These moments are shown in the schematic below. Plate Forces and Moments: Bending and Twisting Moments In the figure above, we can see the various bending (MX and MY) and twisting (MXY) moments. The same balancing and units (lb-in/in) principles apply to these moments as well. MX and MY try to bend the plate, while MXY tries to twist the plate. 4 P a g e

5 Finite Element Analysis - Element Forces: So how can we make sense of these loads and moments in a practical sense? The best way to do that is to experiment with a sample test model. To keep it simple, we will focus on the element forces. Let us build a simple 0.063" thick 4.0"x4.0" square plate made from 2024-T3 aluminum alloy. An element size of 0.5" is used creating all square elements. The model is shown below with thickness turned on. Plate Forces and Moments: Sample Model Setup The three nodes at the left side are fixed, the three nodes at the right are loaded as shown. This is a thin plate so it does not take much load to bend it. 5 P a g e

6 The sequence of steps is as follows: Run this model (SOL 101) Make sure GPFORCE and FORCE "(PRINT)" options are turned on in the case control of the input deck Select an element somewhere in the middle Display its freebody nodal loads Sum the nodal loads along element axes at the two nodes on either side of the element Then divide the total load on either side of the element with the edge length between the two nodes Thus, we get the 'running' loads NX NY NXY QX and QY We then compare these numbers to what is written out to the output file at the center of the selected element PHEW! That was a of steps. But don't worry, the figure below shows the freebody display of element ID 29. Below that we see what is written out to the output file after all the steps above are done. Finite Element Analysis Online Course Element 29 Freebody Loads: The figure below displays the freebody loads on element ID 29. This element was chosen due its location being close to the center of the plate. The idea is to look at a far field element from load and constraint locations. 6 P a g e

7 Plate Forces and Moments: Element FBD Considering element ID 29, we can see that the X load at nodes 50 and 59 balance those at nodes 45 and P a g e

8 Any Element Edge Length = 0.5" At nodes 50/59: Total X Load = lb lb = lb NX = /0.5 = lb/in At nodes 46/45: Total X Load = lb lb = lb NX = /0.5 = lb/in So NX is balanced on either side. Same calculations apply to all the other forces. Element 29 Output File Force and Moment Values: Now we need to check and see if these force values are reported at the center of this element in the output file. The figure below shows the plate forces and moments for element ID 29. Plate Forces and Moments: Output File 8 P a g e

9 We can see in the figure above that the FX or NX value matches with the calculations from the element 29 freebody display we saw earlier. The moments may have similar calculations, but I might do that part in a later post, haven't figured that one out yet. So there you have it. If you have any comments on this make sure you let me know, comment... 9 P a g e