ISSN:
0029-5981
Keywords:
conserving algorithms
;
non-linear dynamics
;
non-linear rods
;
dissipative algorithms
;
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
The long-term dynamic response of non-linear geometrically exact rods under-going finite extension, shear and bending, accompanied by large overall motions, is addressed in detail. The central objective is the design of unconditionally stable time-stepping algorithms which exactly preserve fundamental constants of the motion such as the total linear momentum, the total angular momentum and, for the Hamiltonian case, the total energy. This objective is accomplished in two steps. First, a class of algorithms is introduced which conserves linear and angular momentum. This result holds independently of the definition of the algorithmic stress resultants. Second, an algorithmic counterpart of the elastic constitutive equations is developed such that the law of conservation of total energy is exactly preserved. Conventional schemes exhibiting no numerical dissipation, symplectic algorithms in particular, are shown to lead to unstable solutions when the high frequencies are not resolved. Compared to conventional schemes there is little, if any, additional computational cost involved in the proposed class of energy-momentum methods. The excellent performance of the new algorithm in comparison to other standard schemes is demonstrated in several numerical simulations.
Additional Material:
15 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620380903
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