PUMA
Istituto di Scienza e Tecnologie dell'Informazione     
Kharenko D., Padovani C., Pagni A., Pasquinelli G., Semin L. Numerical methods for a class of nonlinear hyperbolic problems: a comparative study. Technical report, 2009.
 
 
Abstract
(English)
In this paper we consider the problem of the free longitudinal vibrations of a beam made of a bimodular material, i.e. an elastic material whose in-tension Young's modulus is a fraction of that under compression. After recalling the exact solutions for an ifinite beam and for a beam with fixed ends calculated via the characteristics method, we apply high-resolution methods based on the finite-element approach to solve the nonliner equation of the motion. In particular, we compare the exact solutions with the numerical solutions calculated using the space-time element method, the collocation and least-squares method, as well as TVD and Newmark methods.
Subject Bimodular material
Nonlinear dynamics
Exact solutions
J.2 Physical Sciences and Engineering
35L15 Initial value problems for second-order, hyperbolic equations
35L67 Shocks and singularities
74B20 Nonlinear elasticity
74H05 Explicit solutions
74H15 Numerical approximation of solutions
74S05 Finite element methods
74S20 Finite difference methods


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