An unconditionally stable time integration for the dynamics of elastic beams and shells in finite motions

An unconditionally stable time integration for the dynamics of elastic beams and shells in finite motions

Domenico MAGISANO, Leonardo LEONETTI,Giovanni GARCEA

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Abstract. This work presents a numerical framework for long dynamic simulations of structures made of multiple thin shells undergoing large deformations. The C1-continuity requirement of the Kirchhoff-Love theory is met in the interior of patches by cubic NURBS approximation functions with membrane locking avoided by patch-wise reduced integration. A simple penalty approach for coupling adjacent patches, applicable also to non-smooth interfaces and non-matching discretization is adopted to impose translational and rotational continuity. A time-stepping scheme is proposed to achieve energy conservation and unconditional stability for general nonlinear strain measures and penalty coupling terms, like the nonlinear rotational one for thin shells. The method is a modified mid-point rule with the internal forces evaluated using the average value of the stress at the step end-points and an integral mean of the strain-displacement tangent operator over the step computed by time integration points.

Keywords
Nonlinear Dynamics, Large Deformation, Stability, Kirchhoff-Love

Published online 3/17/2022, 6 pages
Copyright © 2023 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: Domenico MAGISANO, Leonardo LEONETTI,Giovanni GARCEA, An unconditionally stable time integration for the dynamics of elastic beams and shells in finite motions, Materials Research Proceedings, Vol. 26, pp 257-262, 2023

DOI: https://doi.org/10.21741/9781644902431-42

The article was published as article 42 of the book Theoretical and Applied Mechanics

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

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