Numerical High-Order Model for the Nonlinear Elastic Computation of Helical Structures | Zendy

Fatima Boussaoui | Zendy; Hassane Lahmam | Zendy; Bouazza Braikat | Zendy

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Numerical High-Order Model for the Nonlinear Elastic Computation of Helical Structures

Author(s) -

Fatima Boussaoui,

Hassane Lahmam,

Bouazza Braikat

Publication year - 2021

Publication title -

modelling and simulation in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.264

H-Index - 20

eISSN - 1687-5591

pISSN - 1687-5605

DOI - 10.1155/2021/6655909

Subject(s) - curvilinear coordinates , discretization , nonlinear system , computation , finite element method , tangent , mathematics , linearization , context (archaeology) , newton's method , iterative method , kinematics , mathematical analysis , algorithm , geometry , classical mechanics , structural engineering , physics , paleontology , quantum mechanics , engineering , biology

In this work, we propose a high-order algorithm based on the asymptotic numerical method (ANM) for the nonlinear elastic computation of helical structures without neglecting any nonlinear term. The nonlinearity considered in the following study will be a geometric type, and the kinematics adopted in this numerical modeling takes into account the hypotheses of Timoshenko and de Saint-Venant. The finite element used in the discretization of the middle line of this structure is curvilinear with twelve degrees of freedom. Using a simple example, we show the efficiency of the algorithm which was carried out in this context and which resides in the reduction of the number of inversions of the tangent matrix compared to the incremental iterative algorithm of Newton-Raphson.

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