FEM-Beam elements question


I am writing a program to do a real time finite element analysis for the behavior of a wire(of infinitely small diameter) as it comes in contact with an object.(basically a wire moving inside a rigid tube.The wire will deflect if it touches the tube).

Can I model this wire as a mesh of beam elements arbitrarily oriented in space?If yes, I want to know how to fix the coordinate frames for each element in order to find the transformation matrix.

Any help is greatly appreciated.

many thanks, SB

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You could, but you'd want to use much smaller moments of interia than you'd calculate for a beam. It's a wire and has little resistance to bending.

Each element coordinate system is based on the location of its nodes in the undeformed state (small deformations). The beam x axis is defined from one node to the other. One way to do the other axes is to use a vector (v) that orients the beam's section properties. Y or Z could be found from the cross product of x and v. That's a general way and how Nastran works.

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Jeff Finlayson

Thank you Jeff,

The one doubt I have now is this:

Once these coordinate frames are attached to the beam elements,can the transformation matrix between the local and the global(say the screen coordinate system) be given by a diagonal matrix comprising of the Direction Cosines corresponding to the 2 systems?specifically,

if the direction cosine matrix,

lambda = [ l1 m1 n1 l2 m2 n2 l3 m3 n3]

where l1 is the cosine of the angle between the global X and local x m1 is cosine of the angle between the global X and local y n1 is cosine of the angle between the global X and local z ..and so on.

Since for a beam element arbitrarily oriented in space, the element stiffness matrix will be of size 12 by 12 corresponding to the six DOF at each node, the Transformation matrix should also be of size 12 by 12.

therefore,Transformation matrrix,

T=[lambda 0 0 0 lambda 0 0 0 lambda]

Is this form of transformation matrix between the local and global systems correct?

thanks, suraj

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