• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.677-693
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• 2018

In this work, we generalize a family of optimal eighth order weighted-Newton methods to Banach spaces and study its local convergence to approximate a locally-unique solution of a system of nonlinear equations. The convergence in this study is shown under hypotheses only on the first derivative. Our analysis avoids the usual Taylor expansions requiring higher order derivatives but uses generalized Lipschitz-type conditions only on the first derivative. Moreover, our new approach provides computable radius of convergence as well as error bounds on the distances involved and estimates on the uniqueness of the solution based on some functions appearing in these generalized conditions. Such estimates are not provided in the approaches using Taylor expansions of higher order derivatives which may not exist or may be very expensive or impossible to compute. The convergence order is computed using computational order of convergence or approximate computational order of convergence which do not require usage of higher derivatives. This technique can be applied to any iterative method using Taylor expansions involving high order derivatives. The study of the local convergence based on Lipschitz constants is important because it provides the degree of difficulty for choosing initial points. In this sense the applicability of the method is expanded. Finally, numerical examples are provided to verify the theoretical results and to show the convergence behavior.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.539-544
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• 1991

In order to verify robot motions for a desired work, it is necessary to visualize it on a computer screen. This paper presents a simulation algorithm for robot manipulator motion. Kinematic description is based on the Denavit- Hartenberg link representation. In order to be applied to various types of the robot manipulator, inverse kinematics make use of the Newton-Raphson iterative method with the least squares method. Joint variables are interpolated by the lowest polynomial segment satisfying acceleration continuity. The robot motions are generated and then animated on a computer screen in the form of skeleton type.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.144-150
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• 2000

In this paper, we introduce a modified six-degrees-of-freedom parallel-link manipulator, which will be applied to the human vibration experiments. We analyze the inverse kinematics and workspace of this manipulator and comprehend the characteristics of kinematics analyzed. Additionally, solutions of forward kinematics are obtained through the iterative Newton-Raphson method known as one of the most used numerical analysis. Finally, dynamic equation of the manipulator is derived in closed form through the Newton-Euler approach, which will be used for the development of control software.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.6
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• pp.1445-1451
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• 1994

To calculate the wave pressure acting on coastal structures under the design wave condition, it is often necessary to numerically reproduce the big standing wave profiles close to wave breaking condition. For this, the governing equation and all nonlinear terms occurring in boundary conditions should be effectively considered in the numerical wave profile. In particular, the velocity square term in the free surface boundary condition is very important. A boundary element method is applied here to calculate the standing wave profile with the velocity square term fully treated by Newton iterative method. In order to check the validity of the method, the numerical wave profiles are compared to ones calculated by the perturbation method, the Fourier approximation method and the hydraulic experiment.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.4 no.5
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• pp.11-14
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• 1981

This study intends to decide the economic sample size based on the cost of sampling Inspection for destructive testing. The marginal percent defective is used as the lot tolerance percent defective (LTPD), and the Newton's iterative method is adopted to calculate the optimum sample size(n), given by the consumer's risk($\beta$ - risk) and the acceptance number(c).

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.99-110
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• 2000

This paper is devoted to the parallelism of a numerical matrix eigenvalue problem. The eigenproblem arises in a variety of applications, including engineering, statistics, and economics. Especially we try to approach the industrial techniques from mathematical modeling. This paper has developed a parallel algorithm to find all eigenvalues. It is contributed to solve a specific practical problem, a vibration problem in the industry. Also we compare the runtime between the serial algorithm and the parallel algorithm for the given problems.

• Journal of the Korean Society of Combustion
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• v.3 no.1
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• pp.21-29
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• 1998

Mathematical modeling of combustion characteristics in HVOF thermal spray processes was carried out on the basis of equilibrium chemistry. The main objective of this work was the development of a computation code which allows to determine chemical composition of combustion products, adiabatic flame temperature, thermodynamic and transport properties. The free energy minimization method was employed with the descent Newton-Raphson technique for numerical solution of systems of nonlinear thermochemical equations. Adiabatic flame temperature was calculated by using a Newton#s iterative method incorporating the computation module of chemical composition. The performance of this code was verified by comparing computational results with data obtained by ChemKin code and in the literature. Comparisons between the calculated and measured flame temperatures showed a deviation less than 2%. It was observed that adiabatic flame temperature augments with increase in combustion pressure; the influence was significant in the region of low pressure but becomes weaker and weaker with increase in pressure. Relationships of adiabatic flame temperature, dissociation ratio and combustion pressure were also analyzed.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.10
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• pp.2543-2554
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• 1993

In this paper, the kinematic and dynamic analyses of spatial complex kinematic chain are studied. Through the new method both using the set of identification numbers and applying the DenavitHartenberg link representation method to the spatial complex kinematic chain, the kinematic configuration of the chain is represented. Some link in the part of closed chain being fictitiously cutted, the complex kinematic chain is transformed to the branched chain. The kinematic constraint equations are derived from the constraint conditions which the cutted sections of the link have to satisfy. And the joint variables being partitioned in the independent joint variables and the dependent joint variables, the dependent variables are calculated from the independent variables by using the Newton-Raphson iterative method and the pseudoinverse matrix. The equations of motion are derived under the independent joint variables by using the principle of virtual work. Algorithms for dynamic analysis are presented and simulations are done to verify accuracy and efficiency of the algorithms.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.335-342
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• 2002

A continuum-based design sensitivity analysis (DSA) method fur non-shape problems is developed for geometrically nonlinear elastic structures. The non-shape problem is characterized by the design variables that are not associated with the domain of system like sizing, material property, loading, and so on. Total Lagrangian formulation with the Green-Lagrange strain and the second Piola-Kirchhoff stress is employed to describe the geometrically nonlinear structures. The spatial domain is discretized using the 4-node isoparametric plane stress/strain elements. The resulting nonlinear system is solved using the Newton-Raphson iterative method. To take advantage of the derived analytical sensitivity In topology optimization, a fast and efficient design sensitivity analysis method, adjoint variable method, is employed and the material property of each element is selected as non-shape design variable. Combining the design sensitivity analysis method and a gradient-based design optimization algorithm, an automated design optimization method is developed. The comparison of the analytical sensitivity with the finite difference results shows excellent agreement. Also application to the topology design optimization problem suggests a very good insight for the layout design.

• Steel and Composite Structures
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• v.32 no.3
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• pp.293-304
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• 2019

In the present paper, the element free Galerkin (EFG) method is developed for geometrically nonlinear analysis of deep beams considering small scale effect. To interpret the behavior of structure at the nano scale, the higher-order gradient elasticity nonlocal theory is taken into account. The radial point interpolation method with high order of continuity is used to construct the shape functions. The nonlinear equation of motion is derived using the principle of the minimization of total potential energy based on total Lagrangian approach. The Newmark method with the small time steps is used to solve the time dependent equations. At each time step, the iterative Newton-Raphson technique is applied to minimize the residential forces caused by the nonlinearity of the equations. The effects of nonlocal parameter and aspect ratio on stiffness and dynamic parameters are discussed by numerical examples. This paper furnishes a ground to develop the EFG method for large deformation analysis of structures considering small scale effects.