A Nonlinear Elastic Beam System with Inelastic Contact Constraints

A Nonlinear Elastic Beam System with Inelastic Contact Constraints Abstract. In this paper we study freely propagating inertial, i.e., unforced, waves, in an elastic beam constrained so that all motion takes place above and on a flat, rigid support surface, subject to a gravitational force and a compressive longitudinal load. Contact between the beam and the support surface is assumed to be completely inelastic. A nonlinear beam model is used, incorporating a quartic extension of the familiar quadratic potential energy functional for the standard Euler—Bernoulli model. After briefly reviewing the rationale for the model and some of its properties, as developed in earlier articles, we present existence and uniqueness results for the constrained system obtained with the use of a ``penalty function'' approach involving the addition of a ``uni-directional friction'' dissipative term, active only when the constraint is violated, to the unconstrained system. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

A Nonlinear Elastic Beam System with Inelastic Contact Constraints

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Copyright © Inc. by 2002 Springer-Verlag New York
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
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