• Structural Engineering and Mechanics
• /
• v.36 no.5
• /
• pp.529-544
• /
• 2010

Nonlinear equations of structures are generally solved numerically by the iterative solution of linear equations. However, this iterative procedure diverges when the tangent stiffness is ill-conditioned which occurs near limit points. In other words, a major challenge with simple iterative methods is failure caused by a singular or near singular Jacobian matrix. In this paper, using the Newton-Raphson algorithm based on Davidenko's equations, the iterations can traverse the limit point without difficulty. It is argued that the propose algorithm may be both more computationally efficient and more robust compared to the other algorithm when tracing path through severe nonlinearities such as those associated with structural collapse. Two frames are analyzed using the proposed algorithm and the results are compared with the previous methods. The ability of the proposed method, particularly for tracing the limit points, is demonstrated by those numerical examples.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.7 no.3
• /
• pp.141-154
• /
• 1987

The algorithm proposed utilizes the tow-levels technique. In the first level which consists of teeatment only the applied load and design stress as the random variables whose parent distribution has the normal distribution, the cross-sectional areas of the truss members such that the their probabilities of failure have the preseribed failure probabilites are optimized by transforming the nonlinear problem into SUMT, and solving it utilizing modified Newton-Raphson method. In the second level, the geometric shape of truss structure is optimized by utilizing the unidirectional search technique of Powell method which makes it possible to minimize only the objective function. The algorithm proposed is numerically tested for the several truss structures with various shapes and loading conditions. The numerical analysis shows that the rate of decreasing the weight of truss structures is dependent on the prescribed failure probability of the each member of truss structure and the covariance of the applied load and design stress.

• Computational Structural Engineering
• /
• v.9 no.2
• /
• pp.121-131
• /
• 1996

This work proposes an optimality criteria applicable to the optimum design of plane frames subject to multiple behavioral constraints on member stresses and lateral displacements of nodes and also to side constraints on design variables. The method makes use of a first order approximation for both deflection and stress constraints instead of the zero order approximation based on the concept of FSD (fully stressed design). A redesign algorithm is derived from a mathematically rigorous method which uses the Newton-Raphson method to solve the system of nonlinear constraint equations and reduces the design space whenever minimum size restrictions become active. When applied to worked examples it proved more accurate and efficient, and it is often found that optimum designs are not fully stressed designs. This fact suggests that this rigorous method is worth what it claims for complicated computing and thus had better replace the crude stress ratio algorithm adopted by the majority of optimality criteria approaches. This is particularly true as long as we enjoy ever-increasing computing power at negligible costs.

• Proceedings of the Korean Society for Technology of Plasticity Conference
• /
• 2007.05a
• /
• pp.272-275
• /
• 2007

This paper is concerned with modified integration algorithm on the strain-space for rate and temperature dependent elasto-plastic constitutive relations in order to obtain more accurate results in numerical implementation. The proposed algorithm is integrated analytically using integration by part and chain rule and then is applied to the 2-stage Lobatto IIIA with second-order accuracy. It has advantage that is able to consider the convective stress rates on the yield surface of the strain-space. Also this paper is carried out the iteration procedure using the Newton-Raphson method to enforce consistency at the end of the step. And the performance of the proposed algorithm for rate and temperature dependent constitutive relation is illustrated by means of analysis of adiabatic shear bands.

• Proceedings of the Korean Statistical Society Conference
• /
• 2005.11a
• /
• pp.181-186
• /
• 2005

Many data sets obtained from surveys or medical trials often include missing observations. When these data sets are analyzed, it is general to use only complete cases. However, it is possible to have big biases or involve inefficiency. In this paper, we consider a method for estimating parameters in logistic linear models involving non-ignorable missing data mechanism. A binomial response and normal exploratory model for the missing data are used. We fit the model using the EM algorithm. The E-step is derived by Metropolis-hastings algorithm to generate a sample for missing data and Monte-carlo technique, and the M-step is by Newton-Raphson to maximize likelihood function. Asymptotic variances of the MLE's are derived and the standard error and estimates of parameters are compared.

• The Transactions of the Korean Institute of Electrical Engineers A
• /
• v.54 no.6
• /
• pp.267-273
• /
• 2005

This paper proposes a line-to-ground fault location algorithm for underground cable system. A feature of the proposed method is a new algorithm based on the analytic research which has not been tried until now. The proposed method firstly makes voltage and current equations using analysis of distributed parameter circuit for each of cores and sheathes respectively, and then establishes an equation of the fault distance according to the analysis of the fault conditions. Finally the solution of this equation is calculated by Newton-Raphson iteration method. The effectiveness of this proposed algorithm has been proven through PSCAD/EMTDC(Ver. 4.1) simulations.

• Journal of Electrical Engineering and Technology
• /
• v.7 no.4
• /
• pp.493-500
• /
• 2012

In this paper the performance of meta-heuristics algorithms such as GA (Genetic Algorithm), DE (Differential Evolution), PSO (Particle Swarm Optimization) and SA (Simulated Annealing) for the problem of TTC enhancement using FACTS devices are compared. In addition to that in the assessment procedure of TTC two novel techniques are proposed. First the optimization algorithm which is used for TTC enhancement is simultaneously used for assessment of TTC. Second the power flow is done using Broyden - Shamanski method with Sherman - Morrison formula (BSS). The proposed approach is tested on WSCC 9 bus, IEEE 118 bus test systems and the results are compared with the conventional Repeated Power Flow (RPF) using Newton Raphson (NR) method which indicates that the proposed method provides better TTC enhancement and computational efficacy than the conventional procedure.

• Structural Engineering and Mechanics
• /
• v.33 no.1
• /
• pp.15-30
• /
• 2009

In this study, the nonlinear vibrations of stepped beams having different boundary conditions were investigated. The equations of motions were obtained by using Hamilton's principle and made non dimensional. The stretching effect induced non-linear terms to the equations. Natural frequencies are calculated for different boundary conditions, stepped ratios and stepped locations by Newton-Raphson Method. The corresponding nonlinear correction coefficients are also calculated for the fundamental mode. At the second part, an alternative method is produced for the analysis. The calculated natural frequencies and nonlinear corrections are used for training an artificial neural network (ANN) program which has a multi-layer, feed-forward, back-propagation algorithm. The results of the algorithm produce errors less than 2.5% for linear case and 10.12% for nonlinear case. The errors are much lower for most cases except clamped-clamped end condition. By employing the ANN algorithm, the natural frequencies and nonlinear corrections are easily calculated by little errors, and the computational time is drastically reduced compared with the conventional numerical techniques.

• Journal of Institute of Control, Robotics and Systems
• /
• v.2 no.2
• /
• pp.121-126
• /
• 1996

The hydrodynamic coefficients estimation (HCE) is important to design the autopilot and to predict the maneuverability of an underwater vehicle. In this paper, a system identification is proposed for an HCE of an underwater vehicle. First, we attempt to design the HCE algorithm which is insensitive to initial conditions and has good convergence, and which enables the estimation of the coefficents by using measured displacements only. Second, the sensor and measurement system which gauges the data from the full scale trials is constructed and the data smoothing algorithm is also designed to filter the noise due to irregular fluid flow without changing the data characteristics itself. Lastly the hydrodynamic coefficients are estimated by applying the measured data of full scale trials to the developed algorithm, and the estimated coefficients are verified by full scale trials.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.24 no.1 s.173
• /
• pp.225-231
• /
• 2000

Dimensional synthesis of planar and spatial mechanisms mostly requires solution-finding, procedure for a system of polynomial equations. In case the system is nonlinear, numerical techniques like Newton-Raphson are often used. But there are no logical ways for finding all possible solutions in such iterative methods. In this paper, algebraic elimination is used to get all solutions for the synthesis of 5-SS spatial mechanism with seven prescribed positions. The proposed algorithm is more suitable for computer implementation and takes less time than existing one. Two numerical examples are given to demonstrate the implemented algorithm.