• Steel and Composite Structures
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• v.38 no.1
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• pp.33-45
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• 2021

The Runge-Kutta method of 6th-order has been employed in this paper to analyze the flow of Casson nanofluid along permeable exponentially stretching cylinder. The modeled PDEs are changed into nonlinear ODEs through appropriate nonlinear transformations. The aim of the paper is to investigate the effects of different parameters such as Casson fluid parameter, slip parameter, suction parameter, Prandtl number, Lewis number, Brownian motion parameter, and thermophoresis parameter, with the variation of mass concentration profile. Numerical results are attained using a renowned numerical scheme shooting technique and for the authenticity of present methodlogy, the results are verified with earlier open text.

• Structural Engineering and Mechanics
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• v.83 no.5
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• pp.681-692
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• 2022

The vibrational response of the two bones in a Volleyball player's arm under ball impact is conducted. The two bones in hand, Ulna and Radius, are modeled as two cylindrical shells. The formulations associated with the shells' vibration are obtained using the energy method. Then, the results are extracted with the aid of the two-dimensional form of DQM in conjunction with Runge-Kutta. The results are validated by means of a published paper. Lastly, the role of parameters in determining vibrational frequency as well as deflection is explored through parametric studies. It was shown that the impactor speed and the time of the impact could be essential factors in determining the vibration behavior of the bones. This work can be used in the further investigation of the behavior of bones and physiological structures.

• Computers and Concrete
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• v.30 no.5
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• pp.369-375
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• 2022

Current exertion reports the numerical analysis of boundary layer slip flow of Casson Nano fluid along a permeable cylinder that is stretching in exponential manner. The modeled PDEs are changed into nonlinear ODEs through appropriate nonlinear transformations. Numerical results are attained using a renowned numerical scheme shooting method with Runge-Kutta procedure of 6^th-order. Influential role of relevant parameters like Reynolds, suction, Casson fluid and slip parameters on velocity profile is investigated. The effect of influence of slip parameter γ on temperature profile is seen through graph. To ensure the authenticity of numerical procedure, outcomes of some special cases of present work are compared with published work and strong agreement is noticed.

• Steel and Composite Structures
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• v.49 no.3
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• pp.281-291
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• 2023

Due to the fact that the nonlinear low-velocity impact response of graphene platelets reinforced metal foams (GPLRMF) doubly curved shells have not been investigated in the existing works, this paper aims to solve this issue. Using Reddy's high-order shear deformation theory (HSDT), the nonlinear governing equations of GPLRMF doubly curved shells are obtained by Euler-Lagrange method, discretized by Galerkin principle, and solved by the fourth-order Runge-Kutta method to obtain the impact force and central deflection. The nonlinear Hertz contact law is applied to determine the contact force. Finally, the impacts of graphene platelets (GPLs) distribution pattern, porosity distribution form, porosity coefficient, damping coefficient, impact parameters (radius and initial velocity), GPLs weight fraction, pre-stressing force and different shell types on the low-velocity impact curves are analyzed. It can be found that, among the four shell structures, the impact resistance of spherical shell is the best, while that of cylindrical shell is the worst.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.31 no.3B
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• pp.293-303
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• 2011

An efficient diagonalized approximate factorization algorithm (DAF) is developed for the solution of three-dimensional incompressible viscous flows. The pressure-based, artificial compressibility (AC) method is used for calculating steady incompressible Navier-Stokes equations. The AC form of the governing equations is discretized in space using a second-order-accurate finite volume method. The present DAF method is applied to derive a second-order accurate splitting of the discrete system of equations. The primary objective of this study is to investigate the computational efficiency of the present DAF method. The solutions of the DAF method are evaluated relative to those of well-known four-stage Runge-Kutta (RK4) method for fully developed and developing laminar flows in curved square ducts and a laminar flow in a cavity. While converged solutions obtained by DAF and RK4 methods on the same computational meshes are essentially identical because of employing the same discrete schemes in space, both algorithms shows significant discrepancy in the computing efficiency. The results reveal that the DAF method requires substantially at least two times less computational time than RK4 to solve all applied flow fields. The increase in computational efficiency of the DAF methods is achieved with no increase in computational resources and coding complexity.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.31 no.2
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• pp.87-95
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• 2018

This paper introduces a new explicit spectral element method for the simulation of SH-waves in semi-infinite domains. To simulate the wave motion in unbounded domains, it is necessary to reduce the infinite extent to a finite computational domain of interest. To prevent the wave reflection from the trunctated boundaries, perfectly matched layer(PML) wave-absorbing boundary is introduced. The forward problem for simulating SH-waves in PML-truncated domains can be formulated as second-order PDEs. The second-order semi-discrete form of the governing PDEs is constructed by using a mixed spectral elements with Legendre-gauss-Lobatto quadrature method, which results in a diagonalized mass matrix. Then the second-order semi-discrete form is transformed to a first-order, whose solutions are calculated by the fourth-order Runge-Kutta method. Numerical examples showed that solutions of SH-wave in the two-dimensional analysis domain resulted in stable and accurate, and reflections from truncated boundaries could be reduced by using PML boundaries. Elastic wave propagation analysis using explicit time integration method may be apt for solving larger domain problems such as three-dimensional elastic wave problem more efficiently.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.6 no.4
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• pp.413-420
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• 1994

Dynamics of the river plume is a very complicated non-linear problem with the free boundary changing in time and space. Mixing with the ambient water through the boundary makes the problem more complicated. In this paper we reduced 3-dimensional problem into 1-dimensional one by using the integral analysis method. Basic equations have been integrated over the lateral and vertical variations. For these integrations we adopted the well-established assumption that the flow-axis component of plume velocity and the density difference of the plume with the ambient water have Gaussian distributions in directions which are perpendicular to the flow-axis of the plume. We also used the result of our previous study on the lateral spreading velocity of the plume derived under the same assumption. And entrainment was included as a mixing process. The resultant 1-dimensional equations were solved by Runge-Kutta numerical method. Consequently, comparatively easy method of numerical analysis is presented for the 3-dimensional river plume. The method can also be used for the analysis of the thermal plume of cooling water of power plants.

• Journal of Surface Science and Engineering
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• v.41 no.5
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• pp.205-213
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• 2008

A 3D particle code is developed to analyze electron behavior in a planar magnetron sputtering cathode either in balanced or unbalanced configuration. Three types of collisions are included; electron - neutral elastic, excitation to a metastable state and ionization. Flight path is calculated by a 4-th order Runge-Kutta method with a time step of 10 ps. Effects of electron starting position, magnetic field intensity and configuration were analyzed. For a more efficient and accurate modeling, multithreading technique is considered for multicore CPU computers. Under an assumption of cold ion approach, target erosion profiles are predicted for a flat target surface.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2008.04a
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• pp.380-385
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• 2008

3 DOFs model for the collision analysis of a bridge super-structure and a super-structure of the navigating vessels were proposed and analyzed. The collision event between the super-structure of vessel and the super-structure of bridge are different from the normal collision event that collided at sub-structure of bridge. Because of its moment arm, the stability force of vessel could affect to the collision behaviors. To consider this effect, 3 DOFs model including two translation DOFs and one rotational DOF were introduced. The restoration forces of the collision system were considered as nonlinear springs. The equations of motion were derived if form of differential equations and numerically solved by 4th order Runge-Kutta method. The accuracy and the feasibility of this model were verified by the numerical example with parameter of moment arm length.

• Wind and Structures
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• v.23 no.5
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• pp.421-447
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• 2016

Wind-induced and earthquake-induced excitations on tall structures can be effectively controlled by Tuned Liquid Damper (TLD). This work presents a numerical simulation procedure to study the performance of tuned liquid tank- structure system through ${\sigma}$-transformation based fluid-structure coupled solver. For this, a 'C' based computational code is developed. Structural equations are coupled with fluid equations in order to achieve the transfer of sloshing forces to structure for damping. Structural equations are solved by fourth order Runge-Kutta method while fluid equations are solved using finite difference based sigma transformed algorithm. Code is validated with previously published results. The minimum displacement of structure is observed when the resonance condition of the coupled system is satisfied through proper tuning of TLD. Since real-time excitations are random in nature, the performance study of TLD under random excitation is also carried out in which the Bretschneider spectrum is used to generate the random input wave.