doi: 10.52899/24141437_2025_04_455
UDK: 629.12.011

Non-Prismatic Beam Finite Elements for Modeling and Calculating Sailing Ship and Yacht Rigging

Кульцеп А. В., Манухин В. А.
Article language:
Citation Link: Kultsep AV, Manukhin VA. Non-Prismatic Beam Finite Elements for Modeling and Calculating Sailing Ship and Yacht Rigging. Transactions of the Saint Petersburg State Marine Technical University. 2025;4(4):455–467. DOI: 10.52899/24141437_2025_04_455 EDN: GFBEGD

Annotation

BACKGROUND: The paper proposes new beam finite elements with variable cross-section for modeling non-prismatic sections of sailing ship and yacht rigging when calculating the overall strength and stability of the mast(s)–standing rigging system. AIM: This work aimed to determine and present explicit expressions for the components of the stiffness and stability matrices of finite elements with and without transverse shear during bending in two principal planes of inertia, tension/compression, and torsion. METHODS: The matrix components are determined by the variational finite element method and are given for the general case, when the moments of inertia and the cross-sectional area of a certain type are approximated by the element length using a quadratic polynomial, and for special cases of bending a beam with a solid circular and annular cross-section, where its varies linearly along the element length. RESULTS: The paper presents the solutions of test problems and a comparison with other known finite elements. The efficiency of the proposed elements for calculating a non-prismatic unrigged mast of a sailing yacht is shown in comparison with similar prismatic elements. CONCLUSION: The developed non-prismatic finite element B4 is included in the FESTA (Finite Element Stability Analysis) program library and can be used to model beam elements of structures with various cross-sections. The element can be used both for modeling and calculating solid and tubular elements of sailboat masts and for modeling non-prismatic frame connections of a set of hulls for ships and vessels. Keywords: finite element; rigging; stiffness matrix; stability matrix; cross-section; unrigged mast; overall strength and stability.

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