Equivalent shell element for passenger ship structural design

Research output: ThesisDoctoral ThesisCollection of Articles


Predicting the global and local static and vibration response of a modern passenger ship is a challenging task, with major reliability and economic consequences if something goes wrong. Therefore, an accurate but computationally light calculation method is already needed in the early design phases when most of the important decisions are made. Currently, the ship's global response is investigated using a coarse mesh global Finite Element (FE) model, in which the mesh size equals the web-frame spacing. Girders are modelled with off-set beam elements and stiffeners together with plating using equivalent elements. Since the available equivalent elements do not or only partly consider the bending properties of the stiffened panel, the local response needs to be analysed separately using time-consuming sub-modelling technique. The objective of this thesis is to overcome the named limitations by introducing a more advanced equivalent element technique. The stiffened panel can be considered as a three-layer laminate shell element, where the first layer represents the plate, the second layer the stiffener web and the third layer the stiffener flange. The element follows Equivalent Single Layer (ESL) First-order Shear Deformation Theory (FSDT). It includes membrane, membrane-bending, bending, and out-of-plane shear stiffness, the constitutive properties of which are found through a homogenisation process. This enables significant computational savings in design and further in the optimisation problem, as layer-wise formulation enables stiffened panel scantlings to be changed without remeshing the model, as well as accurate assessment of the stresses. However, for certain local engineering problems, this simplification is limited, since due to homogenisation process the local plate bending between the stiffeners is neglected. In static analysis the superposition principle can be used to fix the homogenised mean stress field with local oscillations resulting from the periodic structure. In vibration analysis, due to interaction of modes, more advanced correction is needed. For smaller panel-level problems, a single-degree-of-freedom spring-mass system-based solution is presented. For a larger structure, in which bulkheads, pillars, and girders are included, a kinetic and strain energy-based method is presented. The ranges of validity of the equivalent element with and without the additional local corrections have been defined and discussed. The case studies presented in this thesis focused on passenger ship structures, but the element can also be utilised for other ship types or large complex structures where fine mesh analysis is not justified.
Translated title of the contributionEquivalent shell element for passenger ship structural design
Original languageEnglish
QualificationDoctor's degree
Awarding Institution
  • Aalto University
  • Romanoff, Jani, Supervising Professor
  • Remes, Heikki, Thesis Advisor
Print ISBNs978-952-64-0531-5
Electronic ISBNs978-952-64-0532-2
Publication statusPublished - 2021
MoE publication typeG5 Doctoral dissertation (article)


  • equivalent element
  • equivalent single layer (ESL) theory
  • homogenisation
  • passenger ship
  • structural design
  • global finite element model
  • stiffened panel
  • static response
  • vibration response


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