• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1157-1169
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• 2010

This paper presents the analytical solution of the fractional Fokker-Planck equation by Adomian decomposition method. By using initial conditions, the explicit solution of the equation has been presented in the closed form and then the numerical solution has been represented graphically. Two different approaches have been presented in order to show the application of the present technique. The present method performs extremely well in terms of efficiency and simplicity.

• Journal of Mechanical Science and Technology
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• v.19 no.11
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• pp.2016-2024
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• 2005

In this work, a mixed beam approach that combines both the stiffness and the flexibility methods has been performed to analyze the coupled composite blades with closed, two-cell cross-sections. The Reissner's semi-complementary energy functional is used to derive the beam force-displacement relations. Only the membrane part of the shell wall is taken into account to make the analysis simple and also to deliver a clear picture of the mixed method. All the cross section stiffness coefficients as well as the distribution of shear across the section are evaluated in a closed-form through the beam formulation. The theory is validated against experimental test data, detailed finite element analysis results, and other analytical results for coupled composite blades with a two-cell airfoil section. Despite the simple kinematic model adopted in the theory, an accuracy comparable to that of two-dimensional finite element analysis has been obtained for cases considered in this study.

• Journal of the Korean Society for Advanced Composite Structures
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• v.5 no.2
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• pp.1-8
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• 2014

Fiber reinforced polymeric plastic (FRP) materials have many advantages over conventional structural materials, i.e., high specific strength and stiffness, high corrosion resistance, right weight, etc. Among the various manufacturing methods, pultrusion process is one of the best choices for the mass production of structural plastic members. Since the major reinforcing fibers are placed along the axial direction of the member, this material is usually considered as an orthotropic material. However, pultruded FRP (PFRP) structural members have low modulus of elasticity and are composed of orthotropic thin plate components the members are prone to buckle. Therefore, stability is an important issue in the design of the pultruded FRP structural members. Many researchers have conducted related studies to publish the design method of FRP structures and recently, referred to the previous researches, pre-standard for LRFD of pultruded FRP structures is presented. In this paper, the accuracy and suitability of design equation for the local buckling strength of pultruded FRP I-shape compression members presented by ASCE are estimated. In the estimation, we compared the results obtained by design equation, closed-form solution, and experiments conducted by previous researches.

• Journal of the Institute of Electronics and Information Engineers
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• v.51 no.11
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• pp.33-39
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• 2014

We propose an optimal number of transmit antennas which maximizes energy-efficiency (EE) in multi-user massive multiple-input multiple-output (MIMO) downlink system with the maximal ratio transmission (MRT) precoding. With full channel state information at the transmitter (CSIT), we find a closed form solution by partial differential function with proper approximations using average channel gain, independence of individual channels, and average path loss. With limited feedback, we get a solution numerically by the bisection with approximations in the same manner, and analyze an effect of feedback bits on the optimal number of transmit antennas. Simulation results show that the optimal numbers of transmit antenna getting from proposed closed form solution and exhaustive search are nearly same.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2005.04a
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• pp.187-190
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• 2005

A simple beam model based on a mixed method is proposed for the analysis of thin-walled composite blades with a two-cell airfoil section. A semi-complementary energy functional is used to obtain the beam force-displacement relations. The theory accounts for the effects of elastic couplings, shell wall thickness, warping, and warping restraint. All the kinematic relations as well as the cross-section stiffnesses are evaluated in a closed-form through the current beam formulation. The theory has been applied to two-cell composite blades with extension-torsion couplings and fairly good correlation has been observed in comparison with a detailed analysis and other literature.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.2
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• pp.277-284
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• 1993

Interfacial surface crack perpendicular to the surface, which is imbedded into bonded quarter planes under single anti-plane shear load is analyzed. The problem is formulated using Mellin transform, form which single Wiener-Hopf equation is derived. By solving the equation stress intensity factor is obtained in closed form. This solution can be used as a Green's function to generate the solutions of other problems with the same geometry but of different loading conditions.

• Structural Engineering and Mechanics
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• v.42 no.6
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• pp.761-781
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• 2012

The collapse of structures due to snow loads on roofs occurs frequently for steel structures and rarely for reinforced concrete structures. Since the most significant difference between these structures is related to their ability to handle dead loads, dead loads are believed to play an important part in the collapse of structures by snow loads. As such, the effect of dead loads on displacements and stress couples produced by live loads is presented for plates with different edge conditions. The governing equation of plates that takes into account the effect of dead loads is formulated by means of Hamilton's principle. The existence and effect of dead loads are proven by numerical calculations based on the Galerkin method. In addition, a closed-form solution for simply supported plates is proposed by solving, in approximate terms, the governing equation that includes the effect of dead loads, and this solution is then examined. The effect of dead loads on static live loads can be explained explicitly by means of this closed-form solution. A method that reflects the effects of dead loads on live loads is presented as an example. The present study investigates an additional factor in lightweight roof structural elements, which should be considered due to their recent development.

• Structural Engineering and Mechanics
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• v.44 no.5
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• pp.681-704
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• 2012

The dynamic response of Euler-Bernoulli beams to resonant harmonic moving loads is analysed. The non-dimensional form of the motion equation of a beam crossed by a moving harmonic load is solved through a perturbation technique based on a two-scale temporal expansion, which permits a straightforward interpretation of the analytical solution. The dynamic response is expressed through a harmonic function slowly modulated in time, and the maximum dynamic response is identified with the maximum of the slow-varying amplitude. In case of ideal Euler-Bernoulli beams with elastic rotational springs at the support points, starting from analytical expressions for eigenfunctions, closed form solutions for the time-history of the dynamic response and for its maximum value are provided. Two dynamic factors are discussed: the Dynamic Amplification Factor, function of the non-dimensional speed parameter and of the structural damping ratio, and the Transition Deamplification Factor, function of the sole ratio between the two non-dimensional parameters. The influence of the involved parameters on the dynamic amplification is discussed within a general framework. The proposed procedure appears effective also in assessing the maximum response of real bridges characterized by numerically-estimated mode shapes, without requiring burdensome step-by-step dynamic analyses.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.8
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• pp.1883-1897
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• 1993

Interactive computer-aided analysis of mechanical systems has recently been undergoing an evolution due to highly efficient computer graphics. The industrial implementation of state-of-the-art analytical developments in mechanisms has been facilitated by computer-aided design packages because these rigid-body mechanism analysis programs dramatically reduce the time required for linkage design. This paper proposes a component modular approach to computeraided kinematic motion analysis for general planar multiloop mechanisms. Most multiloop mechanisms can be decomposed into serveral components. The kinematic properties (position, velocity, and acceleration) of every node can then be determined from the kinematic analysis of the corresponding component modules by a closed-form solution procedure. In this paper, 8 types of modules are defined and formulations for kinematic analysis of the component modules are derived. Then a computer-aided kinematic analysis program is developed using the proposed approach and the solution procedure of an example shows the effectiveness and accuracy on the approach.

• Composites Research
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• v.16 no.5
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• pp.28-38
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• 2003

In this study, the analytical investigation of orthotropic rectangular plate is presented. The loaded edges are assumed to be simply supported and the unloaded edges could have elastically restrained boundary conditions including the extreme boundary condition such as simple, fixed, and free. Using the closed-form solutions, the buckling analyses of orthotropic plate with arbitrary boundary conditions are performed. Based on the data obtained by conducting numerical analysis, the simplified form of equation for finding the buckling coefficient of plate with elastically restrained boundary conditions at the unloaded edges is suggested as a function of aspect ratio, elastic restraint. and material properties of the plate. The results of buckling analyses by closed-form solution and simplified form of solution are compared for various orthotropic material properties. It is confirmed that the difference of results is less than 1.5%.