• Ocean Systems Engineering
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• v.11 no.1
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• pp.59-81
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• 2021

The nonlinear formulation using the principle of virtual work-energy for free vibration of a large-sag extensible catenary riser in two dimensions is presented in this paper. A support at one end is hinged and the other is a free-sliding roller in the horizontal direction. The catenary riser has a large-sag configuration in the static equilibrium state and is assumed to displace with large amplitude to the motion state. The total virtual work of the catenary riser system involves the virtual strain energy due to bending, the virtual strain energy due to axial deformation, the virtual work done by the effective weight, and the inertia forces. The nonlinear equations of motion for two-dimensional free vibration in the Cartesian coordinate system is developed based on the difference between the Euler's equations in the static state and the displaced state. The linear and nonlinear stiffness matrices of the catenary riser are obtained and the eigenvalue problem is solved using the Galerkin finite element procedure. The natural frequencies and mode shapes are obtained. The results are validated with regard to the reference research addressing the accuracy and efficiency of the proposed nonlinear formulation. The numerical results for free vibration and the effect of the nonlinear behavior for catenary riser are presented.

• Structural Engineering and Mechanics
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• v.23 no.3
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• pp.217-232
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• 2006

A crack model for the fracture in concrete based on meshless method is proposed in this paper. The cracks in concrete are classified into micro-cracks or macro-cracks respectively according to their widths, and different numerical approaches are adopted for them. The micro-cracks are represented with smeared crack approach whilst the macro-cracks are represented with discrete cracks that are made up with additional nodes and boundaries. The widely used meshless method, Element-free Galerkin method, is adopted instead of finite element method to model the concrete, so that the discrete crack approach is easier to be implemented with the convenience of arranging node distribution in the meshless method. Rotating-Crack-Model is proved to be preferred over Fixed-Crack-Model for the smeared cracks of this composite crack model due to its better performance on mesh bias. Numerical examples show that this composite crack model can take advantage of the positive characteristics in the smeared and discrete approaches, and overcome some of their disadvantages.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.11
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• pp.2705-2712
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• 2000

In meshless methods some techniques to impose essential boundary conditions have been developed since the approximations do not satisfy Kronecker delta properties at nodal points. In this study, new scheme for imposing essential boundary conditions is developed. Weight functions are modified by multiplying with auxiliary weight functions and the resulting shape functions satisfy Kronecker delta property on the bound ary nodes. In addition, the resulting shape functions possess and interpolation features on the boundary segments where essential boundary conditions are prescribed. Therefore the essential boundary conditions can be exactly satisfied with the new method. More importantly, the impositions of essential boundary conditions using the present method is relatively easy as in finite element method. Numerical examples show that the method also retains high convergence rate comparable to Lagrange multiplier method.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.1
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• pp.43-57
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• 1999

The fluid flow and heat transfer in a thin liquid film are investigated numerically. The flow Is assumed to be two-dimensional laminar and surface tension is considered. The most important characteristics of this flow is the existence of a hydraulic jump through which the flow undergoes very sharp and discontinuous change. Arbitrary Lagrangian-Eulerian(ALE) method is used to describe moving free boundary and a modified SIMPLE algorithm based on streamline upwind Petrov-Galerkin(SUPG) finite element method is used for time marching iterative solution. The numerical results obtained by solving unsteady full Navier-Stokes equations are presented for planar and radial flows subject to constant wall temperature or constant wall heat flux, and compared with available experimental data. It Is discussed systematically how the inlet Reynolds and Froude numbers and surface tension affect the formation of a hydraulic jump. In particular, the effect of temperature dependent fluid properties is also discussed.

• Structural Engineering and Mechanics
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• v.61 no.2
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• pp.193-207
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• 2017

In this study, the vibration of an electrostatically actuated micro cantilever beam is analyzed in which a viscoelastic layer covers a portion of the micro beam length. This proposed model is considered as the main element of mass and pollutant micro sensors. The nonlinear motion equation is extracted by means of Hamilton principle, considering nonlinear shortening effect for Euler-Bernoulli beam. The non-linear effects of electrostatic excitation, geometry and inertia have been taken into account. The viscoelastic model is assumed as Kelvin-Voigt model. The motion equation is discretized by Galerkin approach. The linear free vibration mode shapes of non-uniform micro beam i.e. the linear mode shape of the system by considering the geometric and inertia effects of viscoelastic layer, have been employed as comparison function in the process of the motion equation discretization. The discretized equation of motion is solved by the use of multiple scale method of perturbation theory and the results are compared with the results of numerical Runge-Kutta approach. The frequency response variations for different lengths and thicknesses of the viscoelastic layer have been founded. The results indicate that if a constant volume of viscoelastic layer is to be deposited on the micro beam for mass or gas sensor applications, then a modified configuration may be found by using the analysis of this paper.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.209-212
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• 2002

Since Berkhoff proposed the mild-slope equation in 1972, it has widely been used for calculation of shallow water wave transformation. Recently, it was extended to give an extended mild-slope equation, which includes the bottom slope squared term and bottom curvature term so as to be capable of modeling wave transformation on rapidly varying topography. These equations were derived by integrating the Laplace equation vertically. In the present study, we develop a finite element model to solve the Laplace equation directly while keeping the same computational efficiency as the mild-slope equation. This model assumes the vertical variation of wave potential as a cosine hyperbolic function as done in the derivation of the mild-slope equation, and the Galerkin method is used to discretize . The computational domain was discretized with proper finite elements, while the radiation condition at infinity was treated by introducing the concept of an infinite element. The upper boundary condition can be either free surface or a solid structure. The applicability of the developed model was verified through example analyses of two-dimensional wave reflection and transmission. .

• Structural Engineering and Mechanics
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• v.7 no.2
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• pp.181-202
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• 1999

Dynamic response of axisymmetric arbitrary laminated composite cylindrical shell of finite length, using three-dimensional elasticity equations are studied. The shell is simply supported at both ends. The highly coupled partial differential equations are reduced to ordinary differential equations (ODE) with variable coefficients by means of trigonometric function expansion in axial direction. For cylindrical shell under dynamic load, the resulting differential equations are solved by Galerkin finite element method, In this solution, the continuity conditions between any two layer is satisfied. It is found that the difference between elasticity solution (ES) and higher order shear deformation theory (HSD) become higher for a symmetric laminations than their unsymmetric counterpart. That is due to the effect of bending-streching coupling. It is also found that due to the discontinuity of inplane stresses at the interface of the laminate, the slope of transverse normal and shear stresses aren't continuous across the interface. For free vibration analysis, through dividing each layer into thin laminas, the variable coefficients in ODE become constants and the resulting equations can be solved exactly. It is shown that the natural frequency of symmetric angle-ply are generally higher than their antisymmetric counterpart. Also the results are in good agreement with similar results found in literatures.

• Transactions of the Korean Society of Automotive Engineers
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• v.15 no.2
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• pp.101-108
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• 2007

This paper presents an efficient meshless method for analyzing cracked piezoelectric structures subjected to mechanical and electrical loading. The method employs an element free Galerkin (EFG) formulation and an enriched basic function as well as special shape functions that contain discontinuous derivatives. Based on the moving least squares (MLS) interpolation approach, The EFG method is one of the promising methods for dealing with problems involving progressive crack growth. Since the method is meshless and no element connectivity data are needed, the burdensome remeshing procedure required in the conventional finite element method (FEM) is avoided. The numerical results show that the proposed method yields an accurate near-tip stress field in an infinite piezoelectric plate containing an interior hole. Another example is to study a ceramic multilayer actuator. The proposed model was found to be accurate in the simulation of stress and electric field concentrations due to the abrupt end of an internal electrode.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.11
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• pp.1538-1551
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• 1997

Kinetic energy conservation for fixed and moving grids is examined in time-accurate finite element computation of fully unsteady inviscid flows. As numerical algorithms, fractional step method (FSM) and modified SIMPLE are used. To simulate the flow in moving grid system, arbitrary Lagrangian-Eulerian (ALE) method is adopted. In the present study, the energy conserving time integration rule for finite element algorithm is proposed and discussed schematically. It is shown that the discretization by Crank-Nicolson in time and Galerkin (central difference) in space must be used to ensure energy conservation. The developed code has been tested for a standing vortex in fixed or moving grid system, sloshing in a tank and propagation of a solitary wave, and has been shown to be a completely energy conserving algorithm.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1999.04a
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• pp.321-326
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• 1999

In this study, fatigue crack propagation problem of plate under multi-axial loading is mainly considered To analyze this special problem, recently developed technique called EFGM(Element-Free Galerkin Method), one of the Meshfree Methods, and general fatigue crack growth raw herein Paris law are used Using the Implemented scheme, paths of fatigue cracks by constant-amplitude load fluctuation and multiple-crack growth behavior are examined. The failure mechanism of steel plate due to crack propagation is studied. As a result, an algorithm that treats multiple fatigue crack problems is proposed. A numerical example shows that the prediction of growing paths can be achieved successfully and efficiently by proposed algorithm.