Compliance matrix

[kodam2]

Hello all, Sorry if my question is too basic, but anyway i have to clear out. What is compliance matrix ?. How it is related with with hookes law (F=Kx)?. Thanks in advance.
Kodam

 

[rb1957]

compliance is the reciporal of stiffness ...
F=kx, x=CF ... C=1/k.

i've used this for determining bolt loads. the same applies to FE, except in matrix form, i guess [C]=inv[k]

 

[trajmarina]

Compliance matrix is inverted stiffnes matrix (here K)

 

[prost]

Hooke's law is an intermediary. To derive the finite element equations Ku=f, you start with the principle of virtual work. You may recall that principle from your strength of materials classes. The principle of virtual work relates the virtual strain energy stored up in a body to the virtual work of the applied external forces. In the virtual strain energy part of the equation, therefore, you have a bunch of stresses and strains. Since your ultimate goal is an equation relating the displacements 'u' to some forcing function 'f', if you are using Hooke's law to describe the relationship between strains and stresses, you then go into the integrals that form the principal of virtual work statement and start substituting the Hooke's law strains for the stresses in this strain energy part of the equation. You know the definitions of the strains in terms of displacement derivatives, so you swap out the strains for the displacement derivatives. A few manipulations of the virtual strain energy integral (sometimes using Green's theorem I recall) and voila, you have the K*u in the Ku=f relationship. 'K' is the stiffness matrix and 1/K is the compliance, as already has been pointed out.

 

[kodam2]

Thanks a ton to u guys. As far as i have learned K plays a important role to find the body the u. But when, why and where one needs to use/derive compliance matrix ?. Because its just inversion of K. Thanks again.

kodam2

 

[prost]

From a FE perspective, if you derive the compliance matrix directly, all you would have to do is multiply this compliance matrix by the force vector and get the displacements directly. Never seen anybody do this, so I take it is not possible to derive the compliance matrix directly. It surely would save a ton of computing time, though!

Sometimes people in the literature seem to prefer to think of a compliance rather than a stiffness; I have found no justification for this other than personal choice.

 

[kodam2]

Thanks prost!. I got clear now.

regards,
kodam2

 

[Qshake]

Often the compliance is useful when doing experimental work as you don't often measure force but rather strain. As a result you've now experimentally got the displacment and need to translate to force or stress, hence the need for compliance.

Regards,
Qshake

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[kodam2]

Thanks! Qshake.

kodam2