• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.3
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• pp.339-352
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• 2001

The inverse kinematics problem of Stewart platform is straightforward, but no closed form solution of the forward kinematic problem has been presented. Since we need the real-time forward kinematic solution in MIMO control and the motion monitoring of the platform, it is important to acquire the 6 DOF displacements of the platform from measured lengths of six cylinders in small sampling period. Newton-Raphson method a simple algorithm and good convergence, but it takes too long calculation time. So we reduce 6 nonlinear kinematic equations to 3 polynomials using Nairs method and 3 polynomials to 2 polynomials. Then Newton-Raphson method is used to solve 3 polynomials and 2 polynomials respectively. We investigate operation counts and performance of three methods which come from the equation reduction and Newton-Raphson method, and choose the best method.

• Earthquakes and Structures
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• v.18 no.4
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• pp.481-492
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• 2020

A New hyperbolic shear deformation theory is developed for the bending analysis of softcore and hardcore functionally graded sandwich beams. This theory satisfies the equilibrium conditions at the top and bottom faces of the sandwich beam and does not require the shear correction factor. The governing equations are derived from the principle of virtual work. Sandwich beams have functionally graded skins and two types of homogenous core (softcore and hardcore). The material properties of functionally graded skins are graded through the thickness according to the power-law distribution. The Navier solution is used to obtain the closed form solutions for simply supported FGM sandwich beams. The accuracy and effectiveness of proposed theory are verified by comparison with previous research. A detailed numerical study is carried out to examine the influence of the deflections, stresses, and sandwich beam type on the bending responses of functionally graded sandwich beams.

• Journal of Communications and Networks
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• v.18 no.6
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• pp.873-883
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• 2016

In this paper, we focus on maximizing weighted sum energy efficiency (EE) for a multi-cell multi-user channel. In order to solve this non-convex problem, we first decompose the original problem into a sequence of parallel subproblems which can optimized separately. For each subproblem, a base station employs dirty paper coding to maximize the EE for users within a cell while regulating interference induced to other cells. Since each subproblem can be transformed to a convex multiple-access channel problem, the proposed method provides a closed-form solution for power allocation. Then, based on the derived optimal covariance matrix for each subproblem, a local optimal solution is obtained to maximize the sum EE. Finally, simulation results show that our algorithm based on non-linear precoding achieves about 20 percent performance gains over the conventional linear precoding method.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.6
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• pp.108-113
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• 1999

For cylindrical shells, the closed-form solutions are confined to the specific boundary and/or loading conditions. Though the finite element method is certainly a powerful solution approach for the structural dynamics problems, it has been well known to provide the solution reliable only in the low frequency region due to the inherent high sensitivities of structual and numerical modeling errors. Instead, the spectral element method has been proved to provide accurate dynamic characteristics of a structure even at the ultrasonic frequency region. Since the wave characteristic of a cylindrical shell becomes identical to that fo a flat plate as the frequency increases, an equivalent plate model (EPM) representing the high-frequency dynamic characteristics of the cylindrical shell is introduced herein. The EPM-based spectral element analysis solutions are compared with the known analytical solutions for the cylindrical shells to confirm the validity of the present modeling approach.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.3
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• pp.181-195
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• 2013

This study considers an air and liquid-filled geomembrane tube section resting on a horizontal foundation. All quantities are normalized to obtain geometrically similar solutions in the static equilibrium condition. Analytic solutions are expressed in closed form. The solution for the air or liquid-filled tube section is derived systematically as an extreme case of the air and liquid-filled tube section. The validity of these solutions is confirmed by comparing to previous study, and some results are shown for the characteristic parameters and shapes of air and/or liquid-filled cases. Using the result of present study, one can estimate the shape and characteristic parameters of a tube section without numerical integrations or iterations.

• Structural Engineering and Mechanics
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• v.5 no.1
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• pp.59-68
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• 1997

A two-step method is presented for the optimum design of trusses with available sections under stress and Euler buckling constraints. The shape design of the truss is used as a means to convert the discrete solution into a continuous one. In the first step of the method, a continuous solution is obtained by sizing and shape design using an approximate polynomial expression for the buckling coefficients. In the second step, the member sizes obtained are changed to the nearest available sections and the truss is reconfigured by using the exact values for the buckling coefficients. The optimizer used is based on the sequential quadratic programming and the gradients are evaluated in closed form. The method is illustrated by two numerical examples.

• Structural Engineering and Mechanics
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• v.42 no.3
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• pp.313-334
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• 2012

This paper examines the problem of a penny-shaped crack in a thermoporoelastic body. On the basis of the recently developed general solutions for thermoporoelasticity, appropriate potentials are suggested and the governing equations are solved in view of the similarity to those for pure elasticity. Exact and closed form fundamental solutions are expressed in terms of elementary functions. The singularity behavior is then discussed. The present solutions are compared with those in literature and an excellent agreement is achieved. Numerical calculations are performed to show the influence of the material parameters upon the distribution of the thermoporoelastic field. Due to its ideal property, the present solution is a natural benchmark to various numerical codes and simplified analyses.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.23 no.6
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• pp.715-726
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• 2010

In this paper, a comparative study of metallic and non-metallic stiffened plates under a lateral pressure load is performed using conventional statistically determinate and SQP(Sequential Quadratic Programming) optimisation approaches. Initially, a metallic flat-bar stiffened plate is exemplified from the superstructure of a marine vessel and, subsequently, its structural topology is varied as hat-section stiffened FRP(Fibre Reinforced Plastics) single skin plates and monocoque FRP sandwich plates having a PVC foam core. These proposed structural alternatives are analysed using elastic closed-form solutions and SQP optimisation method under stress and deflection limits obtained from practice to calculate and optimise geometry dimensions and weights. Results obtained from the comparative study provide useful information for marine designers especially at the preliminary design stage where various building materials and structural configurations are dealt with.

• Structural Engineering and Mechanics
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• v.58 no.4
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• pp.719-729
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• 2016

The main objective of the present paper is to study the effect of the yield criterion on the magnitude of the strain rate and plastic work rate intensity factors in axisymmetric flow of isotropic incompressible rigid perfectly plastic material by means of a problem permitting a closed-form solution. The boundary value problem consisting of the axisymmetric deformation of a plastic tube is solved. The outer surface of the tube contracts. The radius of the inner surface does not change. The material of the tube obeys quite a general yield criterion and its associated flow rule. The maximum friction law is assumed at the inner surface of the tube. Therefore, the velocity field is singular near this surface. In particular, the strain rate and plastic work rate intensity factors are derived from the solution. It is shown that the strain rate intensity factor does not depend on the yield criterion but the plastic work rate intensity factor does.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.1
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• pp.78-83
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• 1997

The paper presents the experimental analysis of a Stewart platform-based force-torque senor. The closed-form solution of forward kinematics of the Stewart platform is derived approximately by way of a linearization technique, and the solution is used in the force analysis of the force-torque sensor. An exper- mental studies show that the proposed method including gravity compensation algorithm is valid for Stew- art platform-based force-torque sensors. The performance of the developed force-torque sensor is evaluated in view of accuracy and linearity in measurements.