• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.1
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• pp.79-90
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• 2005

In this paper we study the numerical solutions of the stochastic differential equations of the form $$du(x,\;t)=f(x,\;t,\;u)dt\;+\;g(x,\;t,\;u)dW(t)\;+\;\sum\limits_{|q|\leq2m}\;A_q(x,\;t)D^qu(x,\;t)dt$$ where $0\;{\leq}\;t\;{\leq}\;T,\;x\;{\in}\;R^{\nu}$, ($R^{nu}$ is the $\nu$-dimensional Euclidean space). Here $u\;{\in}\;R^n$, W(t) is an n-dimensional Brownian motion, $$f\;:\;R^{n+\nu+1}\;{\rightarrow}\;R^n,\;g\;:\;R^{n+\nu+1}\;{\rightarrow}\;R^{n{\times}n},$$, and $$A_q\;:\;R^{\nu}\;{\times}\;[0,\;T]\;{\rightarrow}\;R^{n{\times}n}$$ where ($A_q,\;|\;q\;|{\leq}\;2m$) is a family of square matrices whose elements are sufficiently smooth functions on $R^{\nu}\;{\times}\;[0,\;T]\;and\;D^q\;=\;D^{q_1}_1_{\ldots}_{\ldots}D^{q_{\nu}}_{\nu},\;D_i\;=\;{\frac{\partial}{\partial_{x_i}}}$.

• Structural Engineering and Mechanics
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• v.58 no.5
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• pp.847-868
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• 2016

In this study, the free vibration analysis of axially moving beams is investigated according to Reddy-Bickford beam theory (RBT) by using dynamic stiffness method (DSM) and differential transform method (DTM). First of all, the governing differential equations of motion in free vibration are derived by using Hamilton's principle. The nondimensionalised multiplication factors for axial speed and axial tensile force are used to investigate their effects on natural frequencies. The natural frequencies are calculated by solving differential equations using analytical method (ANM). After the ANM solution, the governing equations of motion of axially moving Reddy-Bickford beams are solved by using DTM which is based on Finite Taylor Series. Besides DTM, DSM is used to obtain natural frequencies of moving Reddy-Bickford beams. DSM solution is performed via Wittrick-Williams algorithm. For different boundary conditions, the first three natural frequencies that calculated by using DTM and DSM are tabulated in tables and are compared with the results of ANM where a very good proximity is observed. The first three mode shapes and normalised bending moment diagrams are presented in figures.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.4
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• pp.427-436
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• 2000

This study presents the nonlinear responses of a hinged-clamped beam under broadband random excitation. By using Galerkin's method the governing equation is reduced to a system or nonautonomous nonlinear ordinary differential equations. The Fokker-Planck equation is used to generate a general first-order differential equation in the joint moments of response coordinates. Gaussian and non-Gaussian closure schemes are used to close the infinite coupled moment equations. The closed equations are then solved for response statistics in terms of system and excitation parameters. The case of two mode interaction is considered in order to compare it with the case of three mode interaction. Monte Carlo simulation is used for numerical verification.

• Journal of the Korea Concrete Institute
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• v.14 no.6
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• pp.1010-1021
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• 2002

The current ACI design code does not take into account the contribution of concrete for the torsional moment of reinforced concrete(RC) beams subjected to pure torsion. This code is not capable of evaluating the inter-effects between concrete and torsional reinforcement on the torsional resistance of the RC beams. Some test results indicated that the current ACI code was not successful in predicting the observed torsional moment of the RC beams with reasonable accuracy. The research reported in this paper provides an evaluation equation to predict the torsional moment of the RC beams subjected to pure torsion. The proposed equation is derived from the equilibrium as well as compatibility equations of the truss model for the cracked RC beams. Comparisons between the observed and calculated torsional moments of the 66 tested beams, showed reasonable agreement.

• Steel and Composite Structures
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• v.34 no.1
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• pp.107-122
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• 2020

Moment resisting stub columns (MRSCs) have increasingly adopted in special moment-resisting frame (SMF) systems in steel building structures, especially in Asian countries. The MRSCs typically provide a lower deformation capacity compared to shear-panel stub columns, a limited post-yield stiffness, and severe strength degradation as adopting slender webs. A new MRSC design with cored configuration, consisting of a core-segment and two side-segments using different steel grades, has been proposed in the study to improve the demerits mentioned above. Several full-scale components of the cored MRSC were experimentally investigated focusing on the hysteretic performance of plastic hinges at the ends. The effects of the depths of the core-segment and the adopted reduced column section details on the hysteretic behavior of the components were examined. The measured hysteretic responses verified that the cored MRSC enabled to provide early yielding, great ductility and energy dissipation, enhanced post-yield stiffness and limited strength degradation due to local buckling of flanges. A parametric study upon the dimensions of the cored MRSC was then conducted using numerical discrete model validated by the measured responses. Finally, a set of model equations were established based on the results of the parametric analysis to accurately estimate strength backbone curves of the cored MRSCs under increasing-amplitude cyclic loadings.

• Journal of the Korean GEO-environmental Society
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• v.22 no.1
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• pp.5-12
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• 2021

Owing to economically efficient and easy installation, bucket foundation is a promising solution for offshore wind turbines. This paper aims at finding the behavior of suction caissons and soil surrounding the foundation by using three-dimensional finite element analysis. Under various loading conditions, a wide range of foundation geometries installed in dense and medium dense sandy soil was considered to evaluate ultimate horizontal load and overturning moment capacity. The results show that the rotation and displacement of the bucket due to monotonic loading are largely dependent on the foundation geometry, soil density and load eccentricity. Normalized diagrams and equations for the ultimate horizontal load and overturning moment capacities are presented that are useful tool for the preliminary design of such foundation type.

• Structural Engineering and Mechanics
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• v.85 no.5
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• pp.679-691
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• 2023

Many codes allow designers to use the bending moment diagram computed by elastic analysis and modify it by a certain amount of moment redistribution (MR) to account for plastic behaviour of continuous beams. However, several researchers indicated that the MR at the ultimate limit state (𝛽_u) for some beams deviate significantly from the specified values of various codes. This paper examines the applicability of the provisions on 𝛽_u in ACI 318-19 and Eurocode 2 through numerical investigations and comprehensively explores the influencing factors. The results show that some parameters not considered in those codes influence 𝛽_u to a certain extent, where the ratio of tensile reinforcement ratio at intermediate support to tensile reinforcement ratio at midspan (𝜌_s1/𝜌_s2) and load type are crucial parameters to consider. The specific combination of these two parameters may make the codes overestimate or significantly underestimate the 𝛽_u. On the other hand, the yield state of both critical sections is found to have an important influence on the influence degree of each parameter on 𝛽_u. The yield conditions are investigated, and an empirical judgment equation is proposed. In addition, the influence laws of the critical parameters on 𝛽_u have been further proved by theoretical derivation. Finally, due to 𝜀_t is found to have a better linear correlation with 𝛽_u than x_u/d, equations as a function of 𝜀_t for predicting the 𝛽_u of continuous beams under the two loads are proposed, respectively.

• Structural Engineering and Mechanics
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• v.91 no.6
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• pp.643-656
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• 2024

The prediction of the moment rotation behavior of semi-rigid connections has been the subject of extensive research. However, to improve the accuracy of these predictions, there is a growing interest in employing machine learning algorithms. This paper investigates the effectiveness of using Multi-gene genetic programming (MGGP) to predict the moment-rotation behavior of flush-end plate connections compared to that of artificial neural networks (ANN) and previous studies. It aims to automate the process of determining the most suitable equations to accurately describe the behavior of these types of connections. Experimental data was used to train ANN and MGGP. The performance of the models was assessed by comparing the values of coefficient of determination (R²), maximum absolute error (MAE), and root-mean-square error (RMSE). The results showed that MGGP produced more accurate, reliable, and general predictions compared to ANN and previous studies with an R² exceeding 0.99, an RMSE of 6.97, and an MAE of 38.68, highlighting its advantages over other models. The use of MGGP can lead to better modeling and more precise predictions in structural design. Additionally, an experimentally-based regression analysis was conducted to obtain the rotational capacity of FECs. A new equation was proposed and compared to previous ones, showing significant improvement in accuracy with an R² score of 0.738, an RMSE of 0.014, and an MAE of 0.024.

• Transactions of the Korean Society of Automotive Engineers
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• v.2 no.1
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• pp.9-25
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• 1994

In the present study, the Reynolds-averaged Navier-Stokes equations, together with the equations of the $k-{\varepsilon}$ model of turbulence, were solved numerically in a general body-fitted coordinate system for three-dimensional turbulent flows around the six basic shapes of the magnetically levitated train(MAGLEV). The numerical computations were conducted on the MAGLEV model configurations to provide information on shapes of this type very near the elevated track at a constant Reynolds number of $1.48{\times}10^{6}$ based on the body length. The coordinate system was generated by numerically solving a set of Poisson equations. The convective transport equations were discretized using the finite-analytic scheme which employed analytic solutions of the locally-linearized equations. A time marching algorithm was employed to enable future extensions to be made to handle unsteady and fully-elliptic problems. The pressure-velocity coupling was treated with the SIMPLER-algorithm. Of particular interests were wall effect by the elevated track on the aerodynamic forces and flow characteristics of the six models calculated. The results indicated that the half-circle configuration with extended sides and with smooth curvature of sides was desirable because of the low aerodynamic forces and pitching moment. And it was found that the separation bubble was occured at wake region in near the elevated track.

• Journal of Advanced Marine Engineering and Technology
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• v.40 no.3
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• pp.235-239
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• 2016

The capsizing speed of an unstable vessel with a lost restoring moment can be understood as a unique response to an accident situation, and is naturally affected by such parameters as moment of inertia, metacentric height, and transverse damping coefficient of the hull in the case of free roll motion. Additionally, it is supposed that the analysis of capsize accidents can be further simplified when a vessel's leaning velocity is shown to be quite low. Therefore, capsize accidents with low leaning speeds are desirably categorized in view of rescuing strategies, as opposed to fast capsize accidents, since the attitude of the declining hull can be properly estimated, which allows rescuers to have more time for helping accident cases. This study focuses on deriving some analytical equations based on the roll decay ratio parameter, which describes how a hull under a low-speed capsize is related to the situational hull characteristics. The suggested equations are applied to a particular ship to disclose the analytical responses from the model ship. It was confirmed that the results show the general characteristics of slow capsizing ships.