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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 = [itex]q^{T}[/itex]K[itex]q[/itex] ; ([itex]q[/itex] is the vector of generalized coordinates, andKis the stiffness matrix). Writing it in this form makes it easy to obtain [itex]\partial U/ \partial q[/itex] 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

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# Quadratic form of strain energy

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