• Proceedings of the Korean Society for Technology of Plasticity Conference
• /
• 1999.08a
• /
• pp.78-87
• /
• 1999

A mathematical model for the stress free surface profile in Over-Round and Round-Oval grove rolling, which can be used effectively in the calculation of pass area, is presented. The new model has generality, simplicity and accuracy for practical usage. The stress free surface profile of an outgoing stock can be modeled when the maximum spread of it known a priori. The equation for the stress free surface profile is formulated from the linear interpolation of the radius of curvature of an incoming stock and that of roll groove to the axis direction. In developing the analytical model, the effect of rolling temperature and friction between roll and work piece(stock) were not considered since the geometry of roll groove and the incoming work piece were assumed a dominant factor which decides the stress free surface profile of the outgoing stock. A simulation with the analytical model developed also has been carried out to demonstrate the stress free surface profile of the outgoing stock.

• Proceedings of the KSME Conference
• /
• 2000.04b
• /
• pp.771-776
• /
• 2000

Fine grid calculations are reported for the developing turbulent flow in a straight duct and a curved duct of square cross-section with a radius of curvature to hydraulic diameter ratio ${\delta}=R_c/H_H=3.357$ and a bend angle of 180 deg. A sequence of modeling refinements is introduced; the replacement of wall function by a fine mesh across the sublayer and a low Reynolds number second moment closure up to the near wall sublayer in which the non-linear return to isotropy model and the cubic-quasi-isotropy model for the pressure strain are adopted; and the introduction of a multiple source model for the exact dissipation rate equation. Each refinement is shown to lead to an appreciable improvement in the agreement between measurement and computation.

• Steel and Composite Structures
• /
• v.18 no.3
• /
• pp.693-709
• /
• 2015

In this article, nonlinear free vibration behaviour of functionally graded spherical panel is analysed. A nonlinear mathematical model is developed based on higher order shear deformation theory for shallow shell by taking Green-Lagrange type of nonlinear kinematics. The material properties of functionally graded material are assumed to be varying continuously in transverse direction and evaluated using Voigt micromechanical model in conjunction with power-law distribution. The governing equation of the shell panel is obtained using Hamilton's principle and discretised with the help of nonlinear finite element method. The desired responses are evaluated through a direct iterative method. The present model has been validated by comparing the frequency ratio (nonlinear frequency to linear frequency) with those available published literatures. Finally, the effect of geometrical parameters (curvature ratio, thickness ratio, aspect ratio and support condition), power law indices and amplitude of vibration on the frequency ratios of spherical panel have been discussed through numerical experimentations.

• Journal of the Korea institute for structural maintenance and inspection
• /
• v.15 no.1
• /
• pp.77-84
• /
• 2011

This study is to develop nonlinear analysis algorithm for transfer matrix method, which can be applied to continuous beam analysis. Gauss-Lobatto integral rule is adopted and the transfer matrix is derived from stiffness matrix. In the transfer matrix method, the system equation has a constant number of unknowns regardless of number of D.O.F. Therefore, the transfer matrix method has computational efficiencies not only in linear elastic analysis but also in nonlinear analysis. To verify the developed method, the analysis results of several examples are compared with commercial code in moment-curvature, moment-displacement and load-displacement relation.

• Journal of the Korea institute for structural maintenance and inspection
• /
• v.15 no.2
• /
• pp.125-135
• /
• 2011

The latest study for formulation of finite element method and computation techniques has progressed widely. The classical method in the formulation of frame elements for geometrically nonlinear analysis derives the geometric stiffness directly from the governing differential equation for bending with axial force. From the computational viewpoint of this paper, the most common approach is the finite element method. Commonly, the formulation of frame elements for geometrically nonlinear structures is based on appropriate interpolation functions for the transverse and axial displacements of the member. The formulation of flexibility-based elements, on the other hand, is based on interpolation functions for the internal forces. In this paper, a new method is used to suppose that interpolation functions for the displacements from the curvatures is Lagrangian interpolation. This paper derives flexibility matrix from that displacement functions and is considered the application of it. Using the flexibility matrix, this paper apply the program considered geometrically nonlinear analysis to common problems.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.23 no.8
• /
• pp.1063-1071
• /
• 1999

Fine grid calculations are reported for the developing turbulent flow in a curved duct of square cross-section with a radius of curvature to hydraulic diameter ratio ${\delta}=Rc/D_H=3.357 $ and a bend angle of 720 deg. A sequence of modeling refinements is introduced; the replacement of wall function by a fine mesh across the sublayer and a low Reynolds number algebraic second moment closure up to the near wall sublayer in which the non-linear return to isotropy model and the cubic-quasi-isotropy model for the pressure strain are adopted; and the introduction of a multiple source model for the exact dissipation rate equation. Each refinement is shown to lead to an appreciable improvement in the agreement between measurement and computation.

• Structural Engineering and Mechanics
• /
• v.67 no.6
• /
• pp.565-578
• /
• 2018

This research article reported the nonlinear finite solutions of the nonlinear flexural strength and stress behaviour of nano sandwich graded structural shell panel under the combined thermomechanical loading. The nanotube sandwich structural model is derived mathematically using the higher-order displacement polynomial including the full geometrical nonlinear strain-displacement equations via Green-Lagrange relations. The face sheets of the sandwich panel are assumed to be carbon nanotube-reinforced polymer composite with temperature dependent material properties. Additionally, the numerical model included different types of nanotube distribution patterns for the sandwich face sheets for the sake of variable strength. The required equilibrium equation of the graded carbon nanotube sandwich structural panel is derived by minimizing the total potential energy expression. The energy expression is further solved to obtain the deflection values (linear and nonlinear) via the direct iterative method in conjunction with finite element steps. A computer code is prepared (MATLAB environment) based on the current higher-order nonlinear model for the numerical analysis purpose. The stability of the numerical solution and the validity are verified by comparing the published deflection and stress values. Finally, the nonlinear model is utilized to explore the deflection and the stresses of the nanotube-reinforced (volume fraction and distribution patterns of carbon nanotube) sandwich structure (different core to face thickness ratios) for the variable type of structural parameter (thickness ratio, aspect ratio, geometrical configurations, constraints at the edges and curvature ratio) and unlike temperature loading.

• Steel and Composite Structures
• /
• v.33 no.6
• /
• pp.865-875
• /
• 2019

The current article proposed to develop a geometrical model for the analysis and modelling of the uniaxial functionally graded structure using the higher-order displacement kinematics with and without the presence of porosity including the distribution. Additionally, the formulation is capable of modelling three different kinds of grading patterns i.e., Power-law, sigmoid and exponential distribution of the individual constituents through the thickness direction. Also, the model includes the distribution of porosity (even and uneven kind) through the panel thickness. The structural governing equation of the porous graded structure is obtained (Hamilton's principle) and solved mathematically by means of the isoparametric finite element technique. Initially, the linear frequency parameters are obtained for different geometrical configuration via own computer code. The comparison and the corresponding convergence studies are performed for the unidirectional FG structure for the validation purpose. Finally, the impact of different influencing parameters like aspect ratio (O), thickness ratio (S), curvature ratio (R/h), porosity index (λ), type of porosity (even or uneven), power-law exponent (n), boundary condition on the free vibration characteristics are obtained for the FG panel and discussed in details.

• Advances in aircraft and spacecraft science
• /
• v.11 no.1
• /
• pp.55-81
• /
• 2024

This paper presents the exact solutions and closed forms for of nonlinear stability and vibration behaviors of straight and curved beams with nonlinear viscoelastic boundary conditions, for the first time. The mathematical formulations of the beam are expressed based on Euler-Bernoulli beam theory with the von Karman nonlinearity to include the mid-plane stretching. The classical boundary conditions are replaced by nonlinear viscoelastic boundary conditions on both sides, that are presented by three elements (i.e., linear spring, nonlinear spring, and nonlinear damper). The nonlinear integro-differential equation of buckling problem subjected to nonlinear nonhomogeneous boundary conditions is derived and exactly solved to compute nonlinear static response and critical buckling load. The vibration problem is converted to nonlinear eigenvalue problem and solved analytically to calculate the natural frequencies and to predict the corresponding mode shapes. Parametric studies are carried out to depict the effects of nonlinear boundary conditions and amplitude of initial curvature on nonlinear static response and vibration behaviors of curved beam. Numerical results show that the nonlinear boundary conditions have significant effects on the critical buckling load, nonlinear buckling response and natural frequencies of the curved beam. The proposed model can be exploited in analysis of macrosystem (airfoil, flappers and wings) and microsystem (MEMS, nanosensor and nanoactuators).

• Journal of the Korean Geotechnical Society
• /
• v.29 no.10
• /
• pp.39-48
• /
• 2013

This paper presents an equation to depict the penetration behavior during the standard penetration test (SPT) in sandy deposits. An energy balance approach is considered and the driving mechanism of the SPT sampler is conceptually modeled as that of a miniature open-ended steel pipe pile into sands. The equation consists of three sets of input parameters including hyperbolic parameters (m and ${\lambda}$) which are difficult to determine. An iterative technique is thus applied to determine the optimized values of m and ${\lambda}$ using three measured values from a routine SPT data. It is verified from a well-documented record that the simulated penetration curves are in good agreement with the measured ones. At a given depth, the increase in m results in the decrease in ${\lambda}$ and the increase in the curvature of the penetration curve as well as the simulated N-value. Generally, the predicted penetration curve becomes nearly straight for the portion of exceeding the seating drive zone, which is more pronounced as soil density increases. Thus, the simulation method can be applied to extrapolating a prematurely completed test data, i.e., to determining the N value equivalent to a 30 cm penetration. A simple linear equation is considered for obtaining similar results.