A simplified geometric stiffness in stability analysis of thin-walled structures by the finite element method

ABSTRACTVibration analysis of a thin-walled structure can be performed with a consistent mass matrix determined by the shape functions of all degrees of freedom (d.o.f.) used for construction of conventional stiffness matrix, or with a lumped mass matrix. In similar way stability of a structure can be analysed with consistent geometric stiffness matrix or geometric stiffness matrix with lumped buckling load, related only to the rotational d.o.f. Recently, the simplified mass matrix is constructed employing shape functions of in-plane displacements for plate deflection. In this paper the same approach is used for construction of simplified geometric stiffness matrix. Beam element, and triangular and rectangular plate element are considered. Application of the new geometric stiffness is illustrated in the case of simply supported beam and square plate. The same problems are solved with consistent and lumped geometric stiffness matrix, and the obtained results are compared with the analytical solution. Also, a combination of simplified and lumped geometric stiffness matrix is analysed in order to increase accuracy of stability analysis

A new finite element formulation for vibration analysis of thick plates

A new procedure for determining properties of thick plate finite elements, based on the modified Mindlin theory for moderately thick plate, is presented. Bending deflection is used as a potential function for the definition of total (bending and shear) deflection and angles of cross-section rotations. As a result of the introduced interdependence among displacements, the shear locking problem, present and solved in known finite element formulations, is avoided. Natural vibration analysis of rectangular plate, utilizing the proposed four-node quadrilateral finite element, shows higher accuracy than the sophisticated finite elements incorporated in some commercial software. In addition, the relation between thick and thin finite element properties is established, and compared with those in relevant literature

Approximate natural vibration analysis of rectangular plates with openings using assumed mode method

ABSTRACTNatural vibration analysis of plates with openings of different shape represents an important issue in naval architecture and ocean engineering applications. In this paper, a procedure for vibration analysis of plates with openings and arbitrary edge constraints is presented. It is based on the assumed mode method, where natural frequencies and modes are determined by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange's equations of motion. The presented solution represents an extension of a procedure for natural vibration analysis of rectangular plates without openings, which has been recently presented in the literature. The effect of an opening is taken into account in an intuitive way, i.e. by subtracting its energy from the total plate energy without opening. Illustrative numerical examples include dynamic analysis of rectangular plates with rectangular, elliptic, circular as well as oval openings with various plate thicknesses and different combinations of boundary conditions. The results are compared with those obtained by the finite element method (FEM) as well as those available in the relevant literature, and very good agreement is achieved

Hydroelastic response of 19000 TEU class ultra large container ship with novel mobile deckhouse for maximizing cargo capacity

This paper is related to structural design evaluation of 19,000 TEU ultra large container ship, dealing with hydroelastic response, i.e. springing and whipping. It illustrates application of direct calculation tools and methodologies to both fatigue and ultimate strength assessment, simultaneously taking into account ship motions and her elastic deformations. Methodology for springing and whipping assessment within so called WhiSp notation is elaborated in details, and in order to evaluate innovative container ship design with increased loading capacity, a series of independent hydroelastic computations for container ship with mobile deckhouse and conventional one are performed with the same calculation setup. Fully coupled 3D FEM – 3D BEM model is applied, while the ultimate bending capacity of hull girder is determined by means of MARS software. Beside comparative analysis of representative quantities for considered ships, relative influence of hydroelasticity on ship response is addressed

Quasi-static response of a 19000 TEU class ultra large container ship with a novel mobile deckhouse for maximizing cargo capacity

Modern sea transportation is characterized by ever larger container ships, which require direct calculation procedures and numerical tools to achieve their reliable structural design. There are different attempts to increase the ship loading capacity, as for instance a container ship with a novel mobile deckhouse enabling her to carry additional number of containers, and at the same time changing basic structural properties of the ship. This paper is related to structural design evaluation of a 19,000 TEU ultra large container ship with novel mobile deckhouse for maximizing cargo capacity, particularly relying on quasi-static approach. The ship structural design is evaluated both for fatigue and extreme loads, where conventional container ship of same particulars is used as a reference. Independent analyses of new and conventional design indicate that conventional container ship shows somewhat better performance from viewpoint of fatigue, while global extreme loading is at the same level

A SHEAR LOCKING-FREE BEAM FINITE ELEMENT BASED ON THE MODIFIED TIMOSHENKO BEAM THEORY

An outline of the Timoshenko beam theory is presented. Two differential equations of motion in terms of deflection and cross-section rotation are comprised in one equation and analytical expressions for displacements and sectional forces are given. Two different displacement fields are recognized, i.e. flexural and axial shear, and a modified beam theory with extension is worked out. Flexural and axial shear locking-free beam finite elements are developed. Reliability of the finite elements is demonstrated with numerical examples for a simply supported, clamped and free beam by comparing the obtained results with analytical solutions

Influence of Different Restoring Stiffness Formulations on Hydroelastic Response of Large Container Ships

Pronounced flexibility of modern container ships can cause falling into resonance with the encounter frequencies of ordinary sea spectrum causing consequently the occurrence of springing. In order to adequately capture such physical phenomena, hydroelasticity methodology for ship structure design has to be applied including the proper definition of the restoring stiffness, being one of the main hydroelastic analysis components. This paper deals with three current restoring stiffness formulations – the consistent one with distributed mass, the consistent one with lumped masses, and the complete one. Formulation of the restoring stiffness via the finite element method is developed as a very useful approach for practical utilization of the hydroelasticity methodology. The validity of the new developed approach is checked on the case of a regular barge. The hydroelasticity of one real life container ship is evaluated and the influence of different restoring stiffness formulations is considered

Application of 1D FEM & 3D BEM Hydroelastic Model for Stress Concentration Assessment in Large Container Ships

Ultra Large Container Ships (ULCS) have relatively lower torsional stiffness and higher speed, compared to the other merchant ships. Due to their specifi c design and operational characteristics, natural frequencies of ULCS can fall into the range of encounter frequencies of ocean wave. So, their structural design should be based on hydroelastic analysis. In this paper an outline of an earlier developed hydroelastic model, comprised of a sophisticated beam structural model and a 3D panel hydrodynamic model, is given. The sophisticated beam model includes shear infl uence on both bending and torsion, contribution of transverse bulkheads to hull stiffness as well as an appropriate modelling procedure of relatively short engine room structure. The model represents a reliable numerical tool for determination of ship global hydroelastic response in frequency domain, by the modal superposition method and here a possibility of its extension for stress concentrations assessment, as a prerogative for fatigue damage calculation, is shown. The procedure is illustrated within the numerical example which includes complete hydroelastic analysis of an 11400 TEU container ship. The transfer functions of sectional forces are determined and compared to the rigid body response. Further on, modal displacements at selected cross-sections are calculated, and then they are spread to the fore and aft contour of a fi ne 3D FEM substructure model. Finally, the stress concentrations in the considered structural detail are obtained. The validation of the sophisticated beam model is done by correlation analysis with the dry natural vibration response of the fi ne mesh 3D FEM model. Global and local hydroelastic responses are compared with those calculated by the fully coupled 3D FEM + 3D BEM hydroelastic model and acceptable agreement is obtained