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I don't really understand your problem. Maybe you've solved it already? Do you mean, why does that integral give only a small displacement result even though the text books say you should use it? In that case I think it's only small-displacement if you use a 1D stress scalar, which isn't really...

I'm not entirely clear on this, but I don't think you should ever be calculating F_int from F_int = Ke * u. Isn't it that the 'u' is the displacement at the end of the iteration, but you don't know that when you're forming the element matrices. So instead you use F_int = Integral (Bt * sigma) dV...

Thanks Reitzel The ANSYS theory manual shows that the stress stiffness matrix for 3-D solid elements is the same in all directions regardless of the direction of the stress. This suggests the stiffening happens equally in all directions. Perhaps it's an approximation because it will always be...

Most descriptions tell us that a tensile stress in one direction stiffens a structure against deflection in other directions. But does it also stiffen against further deformation in the same direction? Some testing with FEA software says yes - vibration modes in the direction of the stress...

Look at this series of lectures and the notes that are with them. It's given by the author of ADINA and derives and explains exactly this problem in quite a lot of detail. It can also help if you have his book "Finite Element Procedures" by Bathe...

I haven't used Staad Pro but for general debugging: Does it converge towards the correct value when you refine the mesh? If so then just refine until it doesn't change much. Does the deformed shape look correct - ie shows that the ends are clamped not pinned, etc? Are the reaction forces...

I've used a method that uses an additional 50-100% of the memory of the matrix itself. The matrix is sparse and each finite element is added to it one by one. You'll need to define the sparsity pattern before using it. You can do that with a initial dummy "assembly" run which just builds a data...