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By C Guedes Soares; Joško Parunov

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Extra resources for Advanced ship design for pollution prevention : proceedings of the International Workshop "Advanced Ship Design for Pollution Prevention", Split, Croatia, 23-24 November 2009

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Proc. IWWWFB, Plitvice Lakes. Newman, JN. 1994. Wave effects on deformable bodies. Applied Ocean Research 16: 47–59. Pavazza, R. 2005. Torsion of thin-walled beams of open cross-sections with influence of shear. International Journal of Mechanical Sciences 47: 1099–1122. , Matoković, A. 1998. Idealisation of ships with large hatch opening by a thin-walled rod of open section on many elastic supports. Thinwalled Structures 32: 305–325. Pedersen, PT. 1985. Torsional response of container ships. Journal of Ship Research 31: 194–205.

X Bw = EI w ∂ x2 , (4) 3 ∂ ws ∂ wb Q = GAs = − EI b . ∂x ∂x 3 ∂2 ψ t . ∂ x2 f e = k eδ e + meδe , (5) (12) (13) where fe is nodal forces vector, δe is nodal displacements vector, ke is stiffness matrix, and me is mass matrix. , Figure 2. ψ = ψ t + ψ s . (11) 1D FEM procedure for vertical ship hull vibrations is well known in literature. Coupled horizontal and torsional vibrations are a more complex problem. Due to analogy between bending and torsion the same shape functions, represented by Hermitian polynomials, are used.

This allows for keeping exactly the same coupling procedure as for the full FE model. onstrated on typical merchant ships, taking into account their specific loading such as sloshing for FPSOs and LNGs. Once implemented, the method is very robust and can be easily adapted to any commercial FE package. Acknowledgments This paper presents part of the teaching material prepared and used in the scope of the course “Modelling of Environment and Environmental Loads” within the project “Advanced Ship Design for Pollution Prevention (ASDEPP)” that was financed by the European Commission through the Tempus contract JEP-40037-2005.

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