Browsing by Author "Avi, Eero"

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Coarse mesh finite element model for cruise ship global and local vibration analysis
(2021-09) Avi, Eero; Laakso, Aleksi; Romanoff, Jani; Remes, Heikki; Lillemäe-Avi, Ingrit
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
This paper presents a practical procedure for creating finite element (FE) model for vibration analysis of cruise ships. The most preferable FE modelling approaches are studied and discussed through case studies of common ship structures, which cover the range from low to high frequencies. The application of homogenized equivalent single layer (ESL) theory based equivalent element for stiffened panel is extended to local forced vibration analysis, where inertia induced interaction between plate and stiffener occurs. Modal method is used with an energy-based correction for accounting the plate-stiffener interaction into modal properties. Case study results reveal that mesh density of one 4-node element per web frame spacing is suitable for global FE-model when vibration analysis is limited to global hull girder modes. For such modes it is sufficient to only include the membrane stiffness of stiffened panels. For investigating the response at higher frequencies, bending properties of stiffened panel should be included and mesh density should be at least two elements per web frame spacing. Then forced vibration analysis can be performed with an excellent accuracy up to frequencies about one third of the local plate natural frequencies between the stiffeners. Beyond that, the influence of the local plate vibration becomes more significant in panel vibration, making the ESL-theory based element limited. With the applied correction method, the validity of the ESL-model can be extended to approximately two thirds of the local plate natural frequency.
Correction of local deformations in free vibration analysis of ship deck structures by equivalent single layer elements
(2019-10-01) Laakso, Aleksi; Avi, Eero; Romanoff, Jani
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Equivalent single layer (ESL) elements provide an easy and computationally effective way to model stiffened plates in finite element analysis of ship structures. Secondary stiffeners are incorporated into the plate or shell formulation. In the free vibration analysis, these elements ignore inertia induced local deformation of plating between the secondary stiffeners. Oscillating motion causes inertia induced body load that locally deforms the plate. This local deformation may have a significant effect on the global modal frequencies of a deck structure. This paper presents a method for correcting ESL modal frequencies by modifying generalised mass and stiffness of the modes. The modification is based on the kinetic and strain energies of the local deformations. Energy components are derived from local consideration of plate in cylindrical bending under enforced support vibration. The method is validated in a case study of ship deck structure against shell mesh results, and good agreement is found.
Equivalent shell element for passenger ship structural design
(2021) Avi, Eero
School of Engineering | Doctoral dissertation (article-based)
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.
Equivalent shell element for ship structural design
(2012) Avi, Eero
School of Engineering | Master's thesis
This thesis presents an equivalent shell element for assessing the ship global and local static and vibration response in early design phases. The stiffened plate is considered as a three layer laminate element, where the first layer represents the plate, the second layer the stiffener web and the third the stiffener flange. The layers are described as 2D iso- and orthotropic materials, where the elasticity matrices are found by applying the Rule of Mixtures. The element includes the extension, membrane-bending coupling, bending and additionally also shear stiffness, which follows the Reissner-Mindlin plate theory for anisotropic homogenous shells. The developed shell formulation has been implemented in commercial FE software FEMAP with NX Nastran and demonstrated in three study cases: stiffened plate, passenger ship cabin area and boxlike ship. The results were validated by comparison with those obtained from 3D fine mesh analysis. All studies show that with reasonable mesh density the laminate element can be used to obtain the static and vibration response of global and local ship structure. Four 4-noded elements per vibration shape have been found to be an optimal size to evaluate eigenvalues with less than 10 % error, which fulfils the industry requirements. Compared to other available equivalent elements, the present laminate element can also predict the normal and shear stresses in stiffener web and flange.
Free vibration by length-scale separation and inertia-induced interaction -application to large thin-walled structures
(2023) Laakso, Aleksi; Romanoff, Jani; Niemela, Ari; Remes, Heikki; Avi, Eero
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
This paper analyses free vibration of interacting length-scales of 3D-thin-walled structures by combination of Finite Elements Method and analytical calculation of strain and kinetic energies. Equivalent single layer elements with structurally homogenized mass and stiffness enable significantly reduced computational cost. Analytical equations are used to re-introduce effects of inertia-induced deformations of the local length-scale that are restrained by the kinematic of homogenized equivalent single layer elements. The method is validated against fine mesh Finite Element Analysis in a case study representing typical 3D-structure seen in cruise ships. The method achieves excellent accuracy for the 10 first natural modes.
Modeling of ship’s side shell openings in global finite element models
(2017-09-25) Kaldoja, Martin
Insinööritieteiden korkeakoulu | Master's thesis
This thesis presents and investigates two common techniques of modeling large periodic side shell openings in global finite element models for evaluation of passenger ship hull girder static response in early design phase. The first technique is based on homogenization of side shell structure and modeling side shell openings with homogenized orthotropic material using 4-noded and 8-noded shell elements. Second technique is direct modeling of side shell openings using coarse mesh, where cost of simplification to geometry and mesh size is studied. The proposed techniques are validated with respect to 3D fine mesh analysis in two cases. First, periodic side shell model is studied for evaluation of correct in plane response under uniform axial and shear loading. Second, the techniques are investigated in a box-like ship under 4-point bending load. Accuracy of both techniques is evaluated by means of hull girder deflection, longitudinal deck forces and side shell vertical shear forces. In addition, the performance in border of periodic grid and at areas of high strain gradients is investigated. The results indicate that equivalent orthotropic modeling of both central and offset openings gives accurate global deflection and longitudinal bending response in a simple model where strain gradients are small. When significant strain gradients are introduced e.g. where internal longitudinal bulkheads are discontinuous, the deflection and longitudinal bending response accuracies are compromised. Local response of orthotropic model is less accurate and especially compromised at edges of periodic grid and areas of high strain gradient. Additional local errors arise due to micropolar behavior of offset openings, where the equivalence is only achieved in forces but not in moments due to application of classical theory of elasticity. No significant difference in response is observed whether 4- or 8-noded elements are applied. For coarse mesh modeling a sensitivity analysis is performed taking account effect of simplification of structure and mesh size. A reasonable compromise between modeling effort, computational cost and accuracy is found at 4x4 elements per opening. Despite being stiffer in uniformly loaded periodic side shell model, the accuracy of coarse mesh modeling is shown to be reliable in application to box-like ship, where performance is not significantly affected by strain gradients and boundary effects.
Optimisation of passenger ship structures in concept design stage
(2019-10-03) Raikunen, Joni; Avi, Eero; Remes, Heikki; Romanoff, Jani; Lillemäe-Avi, Ingrit; Niemelä, Ari
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
This paper presents an optimization method for concept design state of passenger ship with focus on utilisation of efficient Finite Element Modelling, evolutionary optimisation algorithm and indirect constraint relaxation. The response is analysed using 3D coarse mesh global finite element (FE) model, where stiffened panels are modelled using equivalent single layer (ESL) elements and the primary stiffeners are modelled with offset beam elements. The simplifications on stiffened panels and beams enable exploration of design space without changing the FE-mesh. The strength is defined based on classification society rules. Local stress peaks are allowed to exceed the rule-based strength limits, i.e. stress constraints are relaxed indirectly. Instead of increasing the allowed stress levels, the amount of material exceeding strength criteria is utilised. Optimization is based on Particle Swarm Optimization (PSO) algorithm with objective to reduce steel weight. The results show that stress relaxation has significant effect on the obtained total mass.
Optimization approach for passenger ship structures using Finite Element Method
(2015-06-08) Raikunen, Joni
Insinööritieteiden korkeakoulu | Master's thesis
Modern passenger ships have introduced new structural challenges and lightweight solutions, which require accurate calculation methods in early design stages. This thesis presents a rational based design method for passenger ship structures, which consists of three phases: response analysis, strength evaluation and structural optimization. Presented approach handles complex optimization problems flexible, with high accuracy and in reasonable time frame. It allows treating different structural mem-bers individually by selecting whether it is optimized and which constraints are evaluated. The response was analyzed by using 3D coarse mesh Finite Element (FE) model, where stiffened panels are modeled using equivalent shell elements, based on Equivalent Single Layer theory. Due to element layer-wise formulation it is possible to change panel scantlings directly from the material properties, without re-meshing the model. Primary stiffeners are modeled with offset beam elements. The load and strength was calculated using DNV classification society rules. Local strength problems were identified and left out from the strength evaluation. Optimization was carried out using Particle Swarm Optimization (PSO) algorithm and the optimization process was incorporated into a Matlab-code. The method was applied for two case studies: a box-like ship and a RoPax vessel, while objective was to reduce steel weight. Optimized parameters were plate thick-ness, stiffener size and spacing. T-girders were optimized in the box ship, but were left out from RoPax ship case. In both case studies the mass saving from evaluated areas was significant, 28 % in box ship and 11.4 % in RoPax vessel. Also the load carrying mechanism of RoPax vessel changed. Scantlings of decks and side shell were reduced and longitudinal bulkheads and T-girders became more effective. The approach can be extended by including additional objective functions e.g. center of gravity and cost. T-girders of passenger ship are usually designed according to vibration limits, which could be included as an additional constraint. Future work can be also carried out by including additional loading conditions.