• International Journal of Naval Architecture and Ocean Engineering
• /
• v.6 no.4
• /
• pp.1000-1013
• /
• 2014

This paper presents some of the efforts by the authors towards numerical prediction of springing of ships. A time-domain Higher Order Boundary Element Method (HOBEM) based on cubic shape function is first presented to solve a complete second-order problem in terms of wave steepness and ship motions in a consistent manner. In order to avoid high order derivatives on the body surfaces, e.g. mj-terms, a new formulation of the Boundary Value Problem in a body-fixed coordinate system has been proposed instead of traditional formulation in inertial coordinate system. The local steady flow effects on the unsteady waves are taken into account. Double-body flow is used as the basis flow which is an appropriate approximation for ships with moderate forward speed. This numerical model was used to estimate the complete second order wave excitation of springing of a displacement ship at constant forward speeds.

• Structural Engineering and Mechanics
• /
• v.34 no.6
• /
• pp.703-718
• /
• 2010

In classical higher-order discontinuous boundary element formulation for two-dimensional elastostatics, interpolation functions for different boundary variables (i.e., boundary displacements and tractions) are assumed to be the same. However, there is a derivational relationship between these variables. This paper presents a boundary element formulation, called Mixed Boundary Element Formulation, for two dimensional elastostatic problems in which above mentioned relationship is taking into account. The formulations are performed by using discontinuous first and second-order mixed boundary elements. Based on the formulations presented in this study, two computer softwares are developed and verified through some example problems. The results show that the present formulation is credible.

• Journal of Ocean Engineering and Technology
• /
• v.31 no.3
• /
• pp.189-195
• /
• 2017

A three-dimensional higher order boundary element method based on the B-spline is presented. The method accurately models piecewise continuous bodies and induced velocity potentials using B-spline tensor product representations, and it is capable of obtaining accurate pointwise values for the potential and its derivatives, especially in the trailing edge and tip region of the lift generating body, which may be difficult or impossible to evaluate with constant panel methods. In addition, we implement a wake roll-up and examine the tip vortex formation in the near wake region. The results are compared with existing numerical results and the results of experiments performed out at the cavitation tunnel of Chungnam National University.

• Journal of applied mathematics & informatics
• /
• v.26 no.5_6
• /
• pp.1057-1069
• /
• 2008

We consider singularly perturbed Boundary Value Problems (BVPs) for third and fourth order Ordinary Differential Equations(ODEs) of convection-diffusion type with discontinuous source term and a small positive parameter multiplying the highest derivative. Because of the type of Boundary Conditions(BCs) imposed on these equations these problems can be transformed into weakly coupled systems. In this system, the first equation does not have the small parameter but the second contains it. In this paper a computational method named as 'An asymptotic finite element method' for solving these systems is presented. In this method we first find an zero order asymptotic approximation to the solution and then the system is decoupled by replacing the first component of the solution by this approximation in the second equation. Then the second equation is independently solved by a fitted mesh Finite Element Method (FEM). Numerical experiments support our theoritical results.

• Structural Engineering and Mechanics
• /
• v.73 no.1
• /
• pp.97-108
• /
• 2020

This study presents a 4 node, 11 DOF/node plate element based on higher order shear deformation theory for lamina composite plates. The theory accounts for parabolic distribution of the transverse shear strain through the thickness of the plate. Differential field equations of composite plates are obtained from energy methods using virtual work principle. Differential field equations of composite plates are obtained from energy methods using virtual work principle. These equations were transformed into the operator form and then transformed into functions with geometric and dynamic boundary conditions with the help of the Gâteaux differential method, after determining that they provide the potential condition. Boundary conditions were determined by performing variational operations. By using the mixed finite element method, plate element named HOPLT44 was developed. After coding in FORTRAN computer program, finite element matrices were transformed into system matrices and various analyzes were performed. The current results are verified with those results obtained in the previous work and the new results are presented in tables and graphs.

• Advances in nano research
• /
• v.15 no.5
• /
• pp.411-422
• /
• 2023

In the present study, the axial vibration of the nanorods is investigated in the framework of the doublet mechanics theory. The equations of motion and boundary conditions of nanorods are derived by applying the Hamilton principle. A finite element method is developed to obtain the vibration frequencies of nanorods for different boundary conditions. A two-noded higher order rod finite element is used to solve the vibration problem. The natural frequencies of nanorods obtained with the present finite element analysis are validated by comparing the results of classical doublet mechanics and nonlocal strain gradient theories. The effects of rod length, mode number and boundary conditions on the axial vibration frequencies of nanorods are examined in detail. Mode shapes of the nanorods are presented for the different boundary conditions. It is shown that the doublet mechanics model can be used for the dynamic analysis of nanotubes, and the presented finite element formulation can be used for mechanical problems of rods with unavailable analytical solutions. These new results can also be used as references for the future studies.

• Structural Engineering and Mechanics
• /
• v.69 no.4
• /
• pp.427-437
• /
• 2019

In this study, an alternative solution procedure presented by using variational methods for analysis of shear deformable functionally graded material (FGM) beams with mixed formulation. By using the advantages of $G{\hat{a}}teaux$ differential approaches, a refined complex general functional and boundary conditions which comprises seven independent variables such as displacement, rotation, bending moment and higher-order bending moment, shear force and higher-order shear force, is derived for general thick-thin FGM beams via shear deformation beam theories. The mixed-finite element method (FEM) is employed to obtain a beam element which have a 2-nodes and total fourteen degrees-of-freedoms. A computer program is written to execute the analyses for the present study. The numerical results of analyses obtained for different boundary conditions are presented and compared with results available in the literature.

• Steel and Composite Structures
• /
• v.28 no.6
• /
• pp.655-670
• /
• 2018

A coupled method, that combines the Ritz method and the finite element (FE) method, is proposed to solve the vibration problem of rectangular thin and thick plates with general boundary conditions. The eigenvalue partial differential equation(s) of the plate is (are) first reduced to a set of eigenvalue ordinary differential equations by the application of the Ritz method. The resulting eigenvalue differential equations are then reduced to an eigenvalue algebraic equation system using the finite element method. The natural boundary conditions of the plate problem including the free edge and free corner boundary conditions are also implemented in a simple and accurate manner. Various boundary conditions including simply supported, clamped and free boundary conditions are considered. Comparisons with existing numerical and analytical solutions show that the proposed mixed method can produce highly accurate results for the problems considered using a small number of Ritz terms and finite elements. The proposed mixed Ritz-FE formulation is also compared with the mixed FE-Ritz formulation which has been recently proposed by the present author and his co-author. It is found that the proposed mixed Ritz-FE formulation is more efficient than the mixed FE-Ritz formulation for free vibration analysis of rectangular plates with Levy-type boundary conditions.

• Steel and Composite Structures
• /
• v.28 no.5
• /
• pp.629-639
• /
• 2018

In this paper, the vibroacoustic responses of baffled laminated composite sandwich flat panel structure under the influence of harmonic excitation are studied numerically using a novel higher-order coupled finite-boundary element model. A numerical scheme for the vibrating plate has been developed in the frame work of the higher-order mid-plane kinematics and the eigen frequencies are obtained by employing suitable finite element steps. The acoustic responses are then computed by solving the Helmholtz wave equation using boundary element method coupled with the structural finite elements. The proposed scheme has been implemented via an own MATLAB base code to compute the desired responses. The validity of the present model is established from the conformance of the current natural frequencies and the radiated sound power with the available benchmark solutions. The model is further utilized to scrutinize the influence of core-to-face thickness ratio, modular ratio, lamination scheme and the support condition on the sound radiation characteristics of the vibrating sandwich flats panel. It can be concluded that the present scheme is not only accurate but also efficient and simple in providing solutions of the coupled vibroacoustic response of laminated composite sandwich plates.

• Journal of Ocean Engineering and Technology
• /
• v.33 no.1
• /
• pp.17-25
• /
• 2019

A numerical method is suggested for evaluating the singular integral of curved panels in the higher-order boundary element method. Two-step mapping procedures that are significantly related to the physical properties of singular behaviors were developed and illustrated. As a result, the singular behaviors were significantly alleviated, and the efficiency and robustness of the present method for tangentially and axially deformed elements were proven. However, inaccuracies and numerical instabilities of twisted elements were discovered as a result of nonlinearities.