• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.11
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• pp.165-170
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• 2013

When we build up a 3D model from the given 2D images, linear algorithms are often used to reduce computational cost or for initialization of nonlinear algorithms. However, contemporary linear algorithms have apparently linear structures, but virtually they are implemented using SVD. The SVD is also implemented using numerical analysis algorithms that need initialization. Moreover, solutions using SVD are more difficult to analyze than closed-form solutions. To avoid from such inconvenient numerical analysis algorithms of the contemporary methods and for convenient analysis of solutions, this paper proposes a convenient linear method that produces a closed-form solution.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.4
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• pp.496-505
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• 2007

This paper proposes closed-form plastic limit load solutions for elbows under in-plane bending, via three-dimensional (3-D), small strain FE limit analyses using elastic-perfectly plastic materials. A wide range of elbow and thinning geometries are considered. For systematic analyses of the effect of the axial thinning length on limit loads, two limiting cases are considered; a sufficiently long wall thinning, and the circumferential part-through surface crack. Closed-form plastic limit load solutions for wall thinning with intermediate longitudinal extents are then obtained from these two limiting cases. The effect of the axial extent of wall thinning on plastic limit loads for elbows is highlighted by comparing that for straight pipes. Although the proposed solutions are developed for the case when wall thinning exists in the center of elbows, it is also shown that they can be applied to the case when wall thinning exists anywhere within the elbow.

• Structural Engineering and Mechanics
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• v.3 no.1
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• pp.61-74
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• 1995

A linearly tapered, doubly symmetric thin-walled closed member, such as power-transmission towers and tourist towers, are often characterized by local variation in mass and/or rigidity, due to additional mass and rigidity. On the preliminary stage of design the closed-form solution is more effective than the finite element method. In order to propose approximate solutions, the discontinuous and local variation in mass and/or rigidity is treated continuously by means of a usable function proposed by Takabatake(1988, 1991, 1993). Thus, a simplified analytical method and approximate solutions for the free and forced transverse vibrations in linear elasticity are demonstrated in general by means of the Galerkin method. The solutions proposed here are examined from the results obtained using the Galerkin method and Wilson-${\theta}$ method and from the results obtained using NASTRAN.

• Journal of Mechanical Science and Technology
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• v.19 no.spc1
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• pp.237-254
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• 2005

The vast mechanical systems could be classified as closed loop system, open loop system and open & closed (switching) system. In the closed loop system, the kinematics and dynamics of 3-D mechanisms will be reviewed and closed form solutions using the direction cosine matrix method and reflection transformation method will be introduced. In the open loop system, kinematic & dynamic analysis methods regarding the redundant system which has more degrees of freedom in joint space than those of task space are reviewed and discussed. Finally, switching system which changes its phase between closed and open loop motion is investigated with the principle of dynamical balance. Among switching systems, the human gait in biomechanics and humanoid in robotics are presented.

• 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.22 no.2
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• pp.197-222
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• 2006

In this paper, the non-linear time-dependent closed-form, discrete and combined solutions for the post-elastic response of a geometrically and physically non-linear suspended cable to a uniformly distributed load considering the creep effects, are presented. The time-dependent closed-form method for the particularly straightforward determination of a vertical uniformly distributed load applied over the entire span of a cable and the accompanying deflection at time t corresponding to the elastic limit and/or to the elastic region, post-elastic and failure range of a suspended cable is described. The actual stress-strain properties of steel cables as well as creep of cables and their rheological characteristics are considered. In this solution, applying the Irvine's theory, the direct use of experimental data, such as the actual stress-strain and strain-time properties of high-strength steel cables, is implemented. The results obtained by the closed-form solution, i.e., a load corresponding to the elastic limit, post-elastic and failure range at time t, enable the direct use in the discrete non-linear time-dependent post-elastic analysis of a suspended cable. This initial value of load is necessary for the non-linear time-dependent elastic and post-elastic discrete analysis, concerning incremental and iterative solution strategies with tangent modulus concept. At each time step, the suspended cable is analyzed under the applied load and imposed deformations originated due to creep. This combined time-dependent approach, based on the closed-form solution and on the FEM, allows a prediction of the required load that occurs in the post-elastic region. The application of the described methods and derived equations is illustrated by numerical examples.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.525-529
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• 2004

A novel translational 3-dof parallel mechanism is proposed and analyzed. The mechanism consists of three RRPS serial subchains and an additional passive 3-dof type serial subchain. Three RRPS serial subchains alone may form a structure of the 6-DOF Stewart Platform mechanism. However, in the proposed mechanism, an additional passive serial subchain acts as constraints to restrict the output motion of the mechanism in 3-DOF translational space. The closed form position solutions of the proposed mechanism and its first-order kinematic model are derived. Then its workspace size and kinematic characteristics are examined via kinematic isotropic index.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.520-524
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• 2004

In this work, a novel spherical 3-dof parallel mechanism is proposed and analyzed. The mechanism consists of three RRPS serial subchains and an additional passive 3-dof type serial subchain. Three RRPS serial subchains alone may form a structure of 6-DOF Stewart Platform mechanism. However, in the proposed mechanism, an additional passive serial subchain acts as constraints to restrict the output motion of the mechanism within 3-DOF spherical space. The closed form solutions of position analysis of the proposed mechanism and its first-order kinematic model are derived. Then its workspace size and kinematic characteristics are examined via kinematic isotropic index.

• 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.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.505-512
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• 2017

In this paper, we explain how the exact closed-form solutions of the classical problems of viscous fluid flow over a heated stretching plate and shrinking sheet can be obtained by a reliable method.