Drilling freedom |
| The formulation for the Quad8 and Tri6 plate elements only includes 5 degrees of freedom at each of the nodes. This is normal practice in conventional plate shell theory (refer to Timoshenko's "Theory of Plates and Shells"). The finite element method in general includes a full six degrees of freedom for each node (DX, DY, DZ, RX, RY, RZ). |
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| Thus the 5 dof plate element formulations do not provide any stiffness in one direction - rotation about the axis normal to the plate. This is called the drilling freedom. It has been found that this degree of freedom is redundant in formulating equations that describe the behaviour of general plate shell structures. Thus it is simply omitted from the classical formulations to reduce the complexity of the problem. Unfortunately this creates problems with numerical analysis. |
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| In order to solve this problem we must use a procedure to suppress these singularities. Strand7 checks each of the nodes in the model to ensure that they have stiffness in each of the 6 global directions. If a node is found that has zero stiffness (actually less than some user set threshold) Strand7 then determines whether this is in a direction normal to a plate or some other direction. If the singularity is in some other direction then Strand7 assumes that the problem is far more serious and terminates the solution. If the singularity is normal to a plate it is assumed to be a drilling freedom singularity. Strand7 then adds a small amount of stiffness to the matrix to avoid the singularity and to allow the solution to proceed. The amount of stiffness added is small and not sufficient to influence the results of the analysis. It can be controlled by the user via the default solver options. Normally the default values will be sufficient for most problems. |
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