Efficient formulation of a two-dimensional geometrically exact Bernoulli beam

Abstract: In this talk, I will focus on a two-dimensional geometrically exact formulation of a Bernoulli beam. The formulation is based on the integrated form of equilibrium equations, which are combined with the kinematic equations and generalized material equations, leading to a set of three first-order differential equations. These equations are then discretized by finite differences and the boundary value problem is converted into an initial value problem using a technique inspired by the shooting method. The accuracy of the numerical approximation is conveniently increased by refining the integration scheme on the element level while the number of global degrees of freedom is kept constant, which leads to high computational efficiency. The element has been implemented into an open-source finite element code. I will show a favorable comparison with standard beam elements formulated in the finite-strain framework and with analytical solutions. Several extensions of the proposed approach, including curved initial geometry, follower pressure load, and beam-to-beam contact will be also discussed. This is joint work with M. Jirásek and E. La Malfa Ribolla.

REFERENCES

[1] Jirásek, M.,La Malfa Ribolla, E., and Horák, M. Efficient finite difference formulation of a ge-ometrically nonlinear beam element. International Journal for Numerical Methods in Engineering,(2021) 122:7013–7053.

[2] Horák, M., La Malfa Ribolla, E., and Jirásek, M. Efficient formulation of a two-noded geometrically exact curved beam element. International Journal for Numerical Methods in Engineering, (2022), accepted for publication.

MathematicsPhysics

Audience: researchers in the topic

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Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor).

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