# Quadratic form of strain energy

1. Jun 10, 2013

### boeing_737

Hi,

I have some confusion about strain energy. When using Lagrange's equations to derive the EOM of vibrating structures, the strain energy is written as :

U = $q^{T}$K$q$ ; ($q$ is the vector of generalized coordinates, and K is the stiffness matrix). Writing it in this form makes it easy to obtain $\partial U/ \partial q$ used in Lagrange's equations.

My question is, is the quadratic form of strain energy only valid for linear elastic deformation? Can we write such a quadratic form when we have geometric nonlinearities in the problem (beam undergoing large deformations for example)?

Thanks
yogesh