• Advances in concrete construction
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• v.7 no.3
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• pp.151-166
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• 2019

This paper introduces a new efficient analytical method, based on shear deformations obtained with 2D elasticity theory approach, to perform an explicit closed-form solution for calculation the interfacial shear and normal stresses in plated RC beam. The materials of plate, necessary for the reinforcement of the beam, are in general made with fiber reinforced polymers (Carbon or Glass) or steel. The experimental tests showed that at the ends of the plate, high shear and normal stresses are developed, consequently a debonding phenomenon at this position produce a sudden failure of the soffit plate. The interfacial stresses play a significant role in understanding this premature debonding failure of such repaired structures. In order to efficiently model the calculation of the interfacial stresses we have integrated the effect of shear deformations using the equilibrium equations of the elasticity. The approach of this method includes stress-strain and strain-displacement relationships for the adhesive and adherends. The use of the stresses continuity conditions at interfaces between the adhesive and adherents, results pair of second-order and fourth-order coupled ordinary differential equations. The analytical solution for this coupled differential equations give new explicit closed-form solution including shear deformations effects. This new solution is indented for applications of all plated beam. Finally, numerical results obtained with this method are in agreement of the existing solutions and the experimental results.

• Advances in Computational Design
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• v.5 no.1
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• pp.55-89
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• 2020

For the first time, an accurate analytical solution, based on coupled three-dimensional (3D) piezoelasticity equations, is presented for free vibration analysis of the angle-ply elastic and piezoelectric flat laminated panels under arbitrary boundary conditions. The present analytical solution is applicable to composite, sandwich and hybrid panels having arbitrary angle-ply lay-up, material properties, and boundary conditions. The modified Hamiltons principle approach has been applied to derive the weak form of governing equations where stresses, displacements, electric potential, and electric displacement field variables are considered as primary variables. Thereafter, multi-term multi-field extended Kantorovich approach (MMEKM) is employed to transform the governing equation into two sets of algebraic-ordinary differential equations (ODEs), one along in-plane (x) and other along the thickness (z) direction, respectively. These ODEs are solved in closed-form manner, which ensures the same order of accuracy for all the variables (stresses, displacements, and electric variables) by satisfying the boundary and continuity equations in exact manners. A robust algorithm is developed for extracting the natural frequencies and mode shapes. The numerical results are reported for various configurations such as elastic panels, sandwich panels and piezoelectric panels under different sets of boundary conditions. The effect of ply-angle and thickness to span ratio (s) on the dynamic behavior of the panels are also investigated. The presented 3D analytical solution will be helpful in the assessment of various 1D theories and numerical methods.

• Journal of the Korea Institute of Military Science and Technology
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• v.1 no.1
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• pp.211-218
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• 1998

As a part of trajectory modulation to increase system survivability and terminal effectiveness, impact angle control is required in the terminal phase of tactical missile systems. The missile systems are not allowed to have high altitude to reduce probability of detection by sensors of missile defense systems. In this paper, an analytic form of a time-optimal control law is suggested in the case of constrained missile maneuverability and impact angle under the assumption of a zero-lag autopilot. The control law is obtained by establishing optimal missile-target engagement geometry in the vertical plane. Extension of the law for missiles with autopilot response lags requiring a numerical solution is studied by introducing an iterative algorithm for optimal switching time determination of which the initial switching instants are obtained from the analytic solution. Also suggested is a closed-form impact angle control law derived by an energy-optimal approach. The performances of the proposed guidance laws are evaluated by a series of computer runs.

• Korean Management Science Review
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• v.25 no.3
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• pp.1-12
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• 2008

The Swaption is one of the popular Interest rates derivatives. In spite of such a popularity, the swaption pricing formula is hard to derived within the theoretical consistency. Most of swaption pricing model are heavily depending on the simulation technique. We present a new class of swaption model based on the multi-factor HJM levy-mixture model. A key contribution of this paper is to provide a generalized swaption pricing formula encompassing many market stylize facts. We provide an approximated closed form solution of the swaption price using the Gram-Charlier expansion. Specifically, the solution form is similar to the market models, since our approximation is based on the Lognormal distribution. It can be directly compared with the traditional Black's formula when the size of third and fourth moments are not so large. The proposed extended levy model is also expected to be capable of producing the volatility smiles and skewness.

• Structural Engineering and Mechanics
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• v.54 no.4
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• pp.649-664
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• 2015

In this study, the authors present an analytical approach to find the axisymmetric buckling load of two joined isotropic conical shells under axial compression. The problem of two joined conical shells may be considered as the generalized form of joined cylindrical and conical shells with constant or stepped thicknesses. Thickness of each cone is constant; however it may be different from the thickness of the other cone. The boundary conditions are assumed to be simply supported with rigid rings. The governing equations for the conical shells are obtained and solved with an analytical approach. A simple closed-form expression is obtained for the buckling load of two joined truncated conical shells. Results are compared and validated with the numerical results of finite element method. The variation of buckling load with changes in the thickness and semi-vertex angles of the two cones is studied. Finally, application of the results in practical design and range of engineering validity are investigated.

• Earthquakes and Structures
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• v.17 no.3
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• pp.329-336
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• 2019

An efficient shear deformation beam theory is developed for thermo-elastic vibration of FGM beams. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the on the surfaces of the beam without using shear correction factors. The material properties of the FGM beam are assumed to be temperature dependent, and change gradually in the thickness direction. Three cases of temperature distribution in the form of uniformity, linearity, and nonlinearity are considered through the beam thickness. Based on the present refined beam theory, the equations of motion are derived from Hamilton's principle. The closed-form solutions of functionally graded beams are obtained using Navier solution. Numerical results are presented to investigate the effects of temperature distributions, material parameters, thermal moments and slenderness ratios on the natural frequencies. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

• Earthquakes and Structures
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• v.26 no.2
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• pp.163-174
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• 2024

Dynamic equilibrium equations for finite element analysis were derived for the free field one-dimensional shear wave propagation through the horizontally layered soil deposits with the elastic half-space. We expressed Rayleigh's viscous damping consisting of mass and stiffness proportional terms. We considered two cases where damping matrices are defined in the total and relative displacement fields. Two forms of equilibrium equations are presented; one in terms of total motions and the other in terms of relative motions. To evaluate the performance of new equilibrium equations, we conducted two sets of site response analyses and directly compared them with the exact closed-form frequency domain solution. Results show that the base shear force as earthquake load represents the simpler form of equilibrium equation to be used for the finite element method. Conventional finite element procedure using base acceleration as earthquake load predicts exact solution reasonably well even in soil deposits with unrealistically high damping.

• International Journal of Aeronautical and Space Sciences
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• v.18 no.4
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• pp.729-739
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• 2017

The objective of this study was to optimize minimum-energy impulsive spacecraft intercept using genetic algorithms. A mathematical model was established on two-body system based on f and g solution and universal variable to address spacecraft intercept problem for non-coplanar elliptical orbits. This nonlinear problem includes many local optima due to discontinuity and strong nonlinearity. In addition, since it does not provide a closed-form solution, it must be solved using a numerical method. Therefore, the initial guess is that a very sensitive factor is needed to obtain globally optimal values. Genetic algorithms are effective for solving these kinds of optimization problems due to inherent properties of random search algorithms. The main goal of this paper was to find minimum energy solution for orbit transfer problem. The numerical solution using initial values evaluated by the genetic algorithm matched with results of Hohmann transfer. Such optimal solution for unrestricted arbitrary elliptic orbits using universal variables provides flexibility to solve orbit transfer problems.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.541-547
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• 2000

This paper presents the closed-form forward kinematics of the 6-6 Stewart platform of planar base and moving platform. Based on algebraic elimination method and with one extra linear sensor, it first derives an 8th-degree univariate equation and then finds tentative solution sets out of which the actual solution is to be selected. In order to provide more exact solution despite the error between measured sensor value and the theoretical one, a correction method is also used. The overall procedure requires so little computation time that it can be efficiently used for realtime applications. In addition, unlike the iterative schemes e.g. Newton-Raphson, the algorithm does not require initial estimates of solution and is free of the problems that it does not converge to actual solution within limited time. The presented method has been implemented in C language and a numerical example is given to confirm the effectiveness and accuracy of the developed algorithm.

• Structural Engineering and Mechanics
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• v.52 no.4
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• pp.787-813
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• 2014

Starting with Hamilton's variational principle, the governing field equations for the steady state response of thin-walled beams under harmonic forces are derived. The formulation captures shear deformation effects due to bending and warping, translational and rotary inertia effects and as well as torsional flexural coupling effects due to the cross section mono-symmetry. The equations of motion consist of four coupled differential equations in the unknown displacement field variables. A general closed form solution is then developed for the coupled system of equations. The solution is subsequently used to develop a family of shape functions which exactly satisfy the homogeneous form of the governing field equations. A super-convergent finite element is then formulated based on the exact shape functions. Key features of the element developed include its ability to (a) isolate the steady state response component of the response to make the solution amenable to fatigue design, (b) capture coupling effects arising as a result of section mono-symmetry, (c) eliminate spatial discretization arising in commonly used finite elements, (d) avoiding shear locking phenomena, and (e) eliminate the need for time discretization. The results based on the present solution are found to be in excellent agreement with those based on finite element solutions at a small fraction of the computational and modelling cost involved.