reduction of stiffness matrix when spring fixity is involved
reduction of stiffness matrix when spring fixity is involved
(OP)
hi, I have a vertical cantilever beam which is having spring fixities in all 6 dofs (at the base)... there is a load in vertical and in lateral direction at the free end.... after developing the stiffness matrix, how do i do prepare the reduced K matrix - basically, how do i solve for the displacements/rotations in this case..thanks for any help on this






RE: reduction of stiffness matrix when spring fixity is involved
RE: reduction of stiffness matrix when spring fixity is involved
RE: reduction of stiffness matrix when spring fixity is involved
RE: reduction of stiffness matrix when spring fixity is involved
RE: reduction of stiffness matrix when spring fixity is involved
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: reduction of stiffness matrix when spring fixity is involved
if the structure was a cantilever fixed at base, my reduced K matrix would be of size 6x6, now in this case, where I have springs in 6dof. how do I get to reduced matrix.. if I consider the base fixed and calculate the reactions, based on the stiffness of springs, I can get the displacements at the base (due the reactions I calculated assuming encastre fixity).. so how do I move from here... thanks for your guidance
RE: reduction of stiffness matrix when spring fixity is involved
RE: reduction of stiffness matrix when spring fixity is involved
RE: reduction of stiffness matrix when spring fixity is involved
RE: reduction of stiffness matrix when spring fixity is involved
If my original understanding still applies, then the global stiffness matrix you create by ignoring all external restraints is 12x12. Each row and column represents one of the structure's 12 overall degrees of freedom. Each one of the 12 terms along the matrix's leading diagonal represents the stiffness "experienced by" one of the degrees of freedom if all the other degrees of freedom were rigidly clamped. Hence the effect of a spring support at that degree of freedom can be modelled merely by adding the numerical value of the spring's stiffness to that term on the leading diagonal. What you are doing, in effect, is treating each spring as a very simple member (so simple it has a 1x1 member stiffness matrix), then merging that simple member stiffness matrix into the global stiffness matrix.
This is really basic stuff. So basic it is actually quite hard to describe.
If you have any follow-up queries I will not be able to field them, as I am going away for a fortnight to one of those increasingly rare places that do not have ready internet access.
RE: reduction of stiffness matrix when spring fixity is involved
Yes, that is what I suggested, but reading the recent posts from Denial, I agree with his point that if you want to model separate springs for each freedom, with no interaction, then it will be simpler to just add the relevant stiffness to each element of the leading diagonal for the base node.
One other suggestion is that while you are experimenting with these things it is much easier to work in 2D, and when you have worked out a procedure it is fairly straightforward to extend it to 3D.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: reduction of stiffness matrix when spring fixity is involved
thanks IDS (Civil/Environmental) too
RE: reduction of stiffness matrix when spring fixity is involved
Jason McKee
proud R&D Manager of
Cross Section Analysis & Design
Software for the structural design of cross sections
Moment Curvature Analysis
Interaction Diagrams
Reifnorcement Design etc.
RE: reduction of stiffness matrix when spring fixity is involved
RE: reduction of stiffness matrix when spring fixity is involved
I am writing a nonlinear program with spring supports using the method you described. It all works except the spring support displacement adds to itself with each iteration.
For example if I have a simple column supporting 1 kip and the base of the column has a support stiffness of 1 kip/in, then I'll get the following displacements at the base of the column...
1st iteration: 1 in
2nd iteration: 2 in
3rd iteration: 3 in, etc.
I'm trying to figure out where the error would be and thought you might have an idea based on your responses. Any idea?
RE: reduction of stiffness matrix when spring fixity is involved
RE: reduction of stiffness matrix when spring fixity is involved
Thanks anyways!
RE: reduction of stiffness matrix when spring fixity is involved
thread727-416155: Incorporating moment-rotation springs to 1D FEA
BA
RE: reduction of stiffness matrix when spring fixity is involved
(Many a time I have had the same experience as you seem to have had here. The mere act of attempting to describe a problem in sufficient detail for another person to understand it shines a new light on it for me.)