Abstract
The polar model of an elastic Timoshenko beam undergoing large displacements is investigated in detail. Special emphasis is given to the problems involved in the evaluation of the tangent stiffness to provide a complete answer to the question of whether or not tangent stiffness is tensorial and symmetric.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Spivak, M. (1979): A comprehensive introduction to differential geometry. Vols. I-V. Publish or Perish, Wilmington, DE
Marsden, J. E., Hughes, T.J.R. (1983): Mathematical foundations of elasticity. Prentice-Hall, Englewood Cliffs, NJ
Simo, J.C.: A finite strain beam formulation. The three-dimensional-dynamic problem. I. Comput. Meth. Appl. Mech. Engrg. 49, 55–70
Simo, J.C., Vu-Quoc, L. (1986): A three-dimensional finite-strain rod model. II. Computational aspects. Comput. Meth. Appl. Mech. Engrg. 58, 79–116
Simo, J.C., Vu-Quoc, L. (1988): On the dynamics in space of rods undergoing large motions—a geometrically exact approach. Comput. Meth. Appl. Mech. Engrg. 66, 125–161
Abraham, R., Marsden, J.E., Ratiu, T. (1988): Manifolds, tensor analysis, and applications. 2nd edition. Springer, New York
Simo, J.C. (1992): The (symmetric) Hessian for geometrically nonlinear models in solid mechanics: intrinsic definition and geometric interpretation. Comput. Meth.Appl. Mech. Engrg. 96, 189–200
Petersen, P. (1998): Riemannian geometry. Springer, New York
Romano, G. (2002-2003): Scienza delle costruzioni. Tomi I-II. Hevelius, Benevento
Romano, G., Diaco, M., Romano, A., Sellitto, C. (2003): When and why a nonsymmetric tangent stiffness may occur. 16th AIMETA Congress of Theoretical and Applied Mechanics. Ferrara, Italy, Sept. 9–12, 2003
Romano, G., Diaco, M., Sellitto, C. (2004): Tangent stiffness of elastic continua on manifolds. In: Romano, G., Rionero, S. (eds.): Recent trends in the applications of mathematics to mechanics. Springer, Berlin, pp. 155–184
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Italia
About this paper
Cite this paper
Diaco, M., Romano, A., Sellitto, C. (2005). Tangent stiffness of a Timoshenko beam undergoing large displacements. In: Rionero, S., Romano, G. (eds) Trends and Applications of Mathematics to Mechanics. Springer, Milano . https://doi.org/10.1007/88-470-0354-7_6
Download citation
DOI: https://doi.org/10.1007/88-470-0354-7_6
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-0269-2
Online ISBN: 978-88-470-0354-5
eBook Packages: EngineeringEngineering (R0)