A Linearised θ Numerical Scheme for the Vibrations of Inextensible Beams

Autor:	T. K. Papathanasiou
Rok vydání:	2021
Předmět:	Constraint (information theory) Vibration Hermite polynomials Discretization Scheme (mathematics) Applied mathematics Special case Finite element method Quadrature (mathematics) Mathematics
Zdroj:	European Journal of Computational Mechanics.
ISSN:	2642-2050 2642-2085
DOI:	10.13052/ejcm1779-7179.3015
Popis:	A linearised finite element numerical scheme for the vibration of inextensible beams is developed. The proposed scheme is based on the methodology introduced by S. Bartels [15] and satisfies a linearised form of the inextensibility constraint. The time m arching procedure is based on repeated use of the theta-parameter integration quadrature. Three parameters are introduced in total and appropriately selected such that the energy conservation features are improved compared to the Bartels algorithm while the inextensibility constraint is satisfied as accurately as possible. Cubic Hermite polynomials are employed for the spatial discretisation. The Bartels algorithm is retrieved as a special case. Several numerical experiments are presented demonstrating the theoretically predicted enhanced inextensibility mimicking and optimum values of the method parameters are identified.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::71e3c8961afd4d728a132a45e5da8aa9 https://doi.org/10.13052/ejcm1779-7179.3015 Zobrazit plný text záznamu