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An alternative numerical procedure for simulating the dynamical response of non‐linear elastic rods
Author(s) -
Da Gama Rogério martins Saldanha
Publication year - 1990
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620290109
Subject(s) - piecewise linear function , mathematics , jump , rod , riemann hypothesis , linear elasticity , work (physics) , riemann problem , conservation law , numerical analysis , piecewise , function (biology) , constant (computer programming) , mathematical analysis , linear system , finite element method , computer science , physics , medicine , alternative medicine , pathology , quantum mechanics , evolutionary biology , biology , thermodynamics , programming language
In this paper there is presented an alternative numerical procedure for obtaining approximations to non‐linear conservation laws like those that describe the dynamical behaviour of elastic rods (composed of materials whose stress–strain relation is non‐linear). The above‐mentioned procedure consists of approximating the solution of the Riemann problem (associated with the considered conservation law) by a piecewise constant function (satisfying the jump conditions) and using Glimm's scheme for advancing in time, step by step. The proposed numerical approach eliminates the necessity of solving (in a complete way) the associated Riemann problem, easing and cheapening its computational implementation. This procedure is employed for simulating the dynamical response of an elastic‐non‐linear rod, fixed at its edges, that is left in a non‐equilibrium state. There is presented a comparison between results obtained through a classical procedure and through the procedure proposed in this work.