Abstract
Linear structural dynamics is one of the many field problems of engineering that can receive a variational formulation. The classical approach is the kinematical one, and the discretization of the Hamiltonian variational principle in finite elements results from a polynomial approximation of the displacement field inside each separate region. Continuity will be secured through identification of a suitable set of generalized interface displacements, in which case the kinematical elements are said to be conforming. Integrating the kinetic and potential energies of the finite elements leads to lagrangian, or so-called coherent, mass and stiffness matrices.
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Geradin, M., Huck, A., Fraeijs de Veubeke, B. (1972). Structural Dynamics. In: Structural Dynamics. International Centre for Mechanical Sciences, vol 126. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2957-9_1
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DOI: https://doi.org/10.1007/978-3-7091-2957-9_1
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