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More on Gap Elements
Use of Gap Beam Elements in Contact Problems

Much analysis is carried out on structures that are made from a number of separate components. These components may be attached by bolting, spot welding etc or they may simply be held in contact by gravity. When the load is applied, the contact area may change and this could have a significant effect on the solution. Examples of structures where contact behaviour is important are, bolted joints, footings/foundations, pressure switches and the launching of newly constructed bridges.

The contact between two surfaces can be modelled in STRAUS using the compression only beam gap element. This element is a beam element that can carry compression loads only. If the beam is placed into tension by the applied loads then it is removed from the analysis. In the case where there is friction between the surfaces the friction gap element can be used.

When building the model the components that are to be in contact are modelled individually and the contact surfaces separated by a small gap. The components are joined together by beam elements connected across the gap between the components. Obviously this takes some planning to ensure that nodes are located in the same locations on adjacent components. This is essential as the gap beams should be normal to the surface of the component. The size of the gap between the two components should normally be as small as practical.

Contact Model of a Concrete Tunnel Subjected to Hydrostatic Pressure

The area where most users go wrong is in setting up the properties for the gap beam elements. The properties for the compression only gap beams should ensure that these elements carry compressive axial force only.

The properties are set in such a way that the beams cannot carry shear or bending forces. This means that the only properties required are the modulus (E) and the area (A). The modulus is normally set equal to the modulus of the components to which the beam is attached. The area should be chosen so that the cross sectional area of the gap elements is equal to the average area supported by each gap beam i.e. area = total contact area / number of gap beam elements. A way of verifying the selected area is to go into the graphical editor and display the beam elements using the section type. Although the beam is not input as a standard section it will be shown as a rod with the appropriate diameter corresponding to the chosen area. If the area is about right the standard sections will be seen to tile the surface of the components. It should be immediately obvious if the total area of the gap elements is equal to the area of contact surface being supported.

The actual values chosen for the properties of the gap beams are not so important. It is however important to ensure that the stiffness of the gap beams is about equal to the stiffness of the components they separate. If this is not done then difficulties may be encountered with convergence or the matrix may become singular for no apparent reason. In fact singular matrices are responsible for about 50% of the support calls we take on gap problems. Many users assume that a really stiff beam is what is required and input a modulus of 1E20 or some ridiculously large area. This can cause the matrices to become illconditioned and the result is a singular matrix at some point in the solution. If you follow the above guidelines you will have no problems in this regard.

A common problem with the use of gap elements occurs when users assign values for I11, I22 and J in the properties for the gap elements. The moment of inertia (I) gives the gap elements bending stiffness and hence some friction like resistance is generated between the two contact surfaces. However this is not a friction force since the magnitude is independent of the normal contact force. If you must include friction between the surfaces then use the friction gap beam in STRAUS. Don’t try to do this with a non-zero moment of inertia (I).

The effect of J is to give the gap beams some torsional stiffness. This has little physical meaning but can cause some computational difficulty. When a gap beam is used to separate two surfaces that have been modelled with plate elements a nonzero value of J can generate a singularity. The most commonly used plate element, the QUAD4, does not have any mechanism to carry torsional loads normal to the surface. (ie the element only has 5 dof only at each node). Problems of this type are avoided by setting J = 0.

For more information please contact us by e-mail: hsh@iperv.it