• Journal of Korean Association for Spatial Structures
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• v.4 no.3 s.13
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• pp.103-109
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• 2004

The lowest load when the equilibrium condition becomes to be unstable is defined as the buckling load. The primary objective of this paper is to be analyse stability boundaries for star dome under combined loads and is to investigate the iteration diagram under the independent loading parameter. In numerical procedure of the geometrically nonlinear problems, Arc Length Method and Newton-Raphson iteration method is used to find accurate critical point(bifurcation point and limit point). In this paper independent loading vector is combined as proportional value and star dome was used as numerical analysis model to find stability boundary among load parameters and many other models as multi-star dome and arch were studied. Through this study we can find the type of buckling mode and the value of buckling load.

• Computational Structural Engineering
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• v.9 no.3
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• pp.209-216
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• 1996

The primary objective of this paper is to grasp many characteristics of buckling behavior of latticed spherical domes under various conditions. The Arc-Length Method proposed by E.Riks is used for the computation and evaluation of geometrically nonlinear fundamental equilibrium paths and bifurcation points. And the direction of the path after the bifurcation point is decided by means of Hosono's concept. Three different nonlinear stiffness matrices of the Slope-Deflection Method are derived for the system with rigid nodes and results of the numerical analysis are examined in regard to geometrical parameters such as slenderness ratio, half-open angle, boundary conditions, and various loading types. But in case of analytical model 2 (rigid node), the post-buckling path could not be surveyed because of Newton-Raphson iteration process being diversed on the critical point since many eigenvalues become zero simultaneously.

• Computational Structural Engineering
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• v.11 no.1
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• pp.217-226
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• 1998

The purpose of this study is to develop a technique for the shape analysis of plane truss structures under prescribed displacement modes. The shape analysis is performed based on the existence theorem of the solution and the Moore-Penrose generalized inverse matrix. In this paper, the homologous deformation of structures was proposed as prescribed displacement modes, the shape of the structure is determined from these various modes and applied loads. In general, the shape analysis is a kind of inverse problem different from stress analysis, and the governing equation becomes nonlinear. In this regard, Newton-Raphson method was used to solve the nonlinear equation. Three different shape models are investigated as numerical examples to show the accuracy and the effectiveness of the proposed method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.9
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• pp.1384-1390
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• 2001

This paper deals with the forward kinematics of the 6-6 Stewart platform of planar base and moving platform using one extra linear sensor. Based on algebraic elimination method, 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 theoretic alone, a correction method is also used in this paper. The overall procedure requires so little computation time that it can be efficiently used for real-time applications. In addition, unlike the iterative scheme 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.8 no.3
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• pp.233-242
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• 1999

In the present study, the elasto-plastic analysis of prismatic plate structures subjected to pure bending is carried out using the finite strip method. The end cross-sections of the structure are assumed to remain plane during deformation, and the compatibility along corner lines is ensured by choosing proper displacement functions. The effects of both the initial geometrical imperfections and residual stresses due to fabrication are included in the combined geometrically and materially nonlinear simulation. The von-Mises yield criterion and the Prandtl-Reuss flow theory of plasticity are applied in modelling the elasto-plastic behavior of material. Newton-Raphson iterations are carried out as the rotation of the end cross sections of the structure is increased step by step. The parameter representing the overall axial strain of structure is adjusted constantly during the iteration process in order to eliminate the resulting overall axial force on any cross-section of the structure in correspondence with the assumption of zero axial force in pure bending. Several numerical examples are presented to validate the present method and to investigate the effects of some material and geometrical parameters.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.6 no.2
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• pp.1-15
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• 1986

The algorithm Proposed utilizes the two-levels technique. In the first level which consists of two phases, the cross-sectional area of the truss member is optimized by transforming the nonlinear problem into SUMT, and solving SUMT utilizing the modified Newton-Rahson method. In the second level, the geometric shape is optimized utilizing the unindirectional search technique of the Powell method which make it possible to minimize only the objective function. The algorithm Proposed in this study is numerically tested for several truss structures with various shapes, loading conditions and design criteria, and compared with the results of the other algorithms to examine its applicability and stability. The numerical comparisons show that the two-Levels algorithm Proposed in this study is safely applicable to any design criteria, and the convergency rate is relathely fast and stable compared with other iteration methods for the geometric optimization of truss structures.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.3
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• pp.933-944
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• 1996

In this paper, two new techniques, the pattern filling and the refined flow field regeneration, based on the finite element method and Eulerian mesh advancement approach have been developed to analyze incompressible viscous flow with free surfaces. The gorerning equation for flow analysis is Navier-Stokes equation including inertia and gravity effects. The penalty and Newton-Raphson methods are used effectively for finite element formulation. The flow front surface and the volume inflow rate are calculated using the pattern filling technique to select an adequate pattern among five filling patterns at each quadrilateral control volume. By the refined flow field regeneration technique, the new flow field which renders better prediction in flow surface shape is generated and the velocity field at the flow front part is calculated more exactly. Using the new thchniques to be developed, the dam-breaking problem has been analyzed to predict flow phenomenon of fluid and the predicted front positions versus time have been compared with the reported experimental result.

• Proceedings of the KIEE Conference
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• 1996.07a
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• pp.139-141
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• 1996

The switched reluctance motors(SRM) are simple and robust in structure. Because the wide range of power and speed, their application field is increasing. In order to design the motors and to evaluate the performance of them properly, an accurate study about the analysis of motor characteristics is required. In this paper, for the analysis of SRM characteristics, the finite element method which is based on the solution of combined equations both the electromagnetic field equations and the circuit equations of stator is adopted. The analysis model is to he assumed two-dimensional and the nonlinear property of magnetic materials is considered by Newton-Raphson method. To verify the usefulness of the proposed algorithm, commercial SRM is chosen and simulated. The computed torques obtained by Maxwell Stress Tensor are compared with the experimental data and it is found that they are in good agreement. By applying the proposed algorithm to two cases, currents of stator and torques at every angular positions of rotor are obtained step by step. Comparing them, one can recognize that torque ripple of SRM can he improved by controlling the switching sequences of driving circuits.

• Macromolecular Research
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• v.11 no.6
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• pp.399-409
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• 2003

The first esterification reactor in the continuous polymerization of poly(ethylene terephthalate) has been analyzed by solving the material balances for the two-phase system with respect to the solubility of terephthalic acid. The Newton-Raphson method was used to solve the material balance equations instead of the Simplex method that is frequently used for finding a minimum point of a residual rather than a solution of an equation. A solution for the material balance equations, with the constraint of non-zero liquid phase fraction, could not be obtained with the solubility data of Yamada et al., but could be obtained with solubilities over a minimum value that is larger than their data. Thus, the solubility data of Yamada et al. are considered to be too small. On the other hand, the solubility data of Baranova and Kremer are so large that they gave a solution with the liquid phase only. Based on our results, several typical solubility curves satisfying the constraint of a non-zero liquid phase fraction are suggested in this study; we studied the reaction characteristics of the system using these curves. A higher temperature and a lower pressure are preferred for reducing the content of diethylene glycol.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.18 no.2
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• pp.23-28
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• 2004

In EIT, various image reconstruction algorithms have been used in order to compute the internal resistivity distribution of the unknown object with its electric potential data at the boundary. Mathematically the EIT image reconstruction algorithm is a nonlinear ill-posed inverse problem. In this paper, a SPSA approach is proposed for the solution of the EIT image reconstruction. Results of numerical experiments of EIT solved by the SPSA approach are presented and compared to that obtained by the modified Newton-Raphson(mNR) method.