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

• Transactions of Materials Processing
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• v.11 no.1
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• pp.75-83
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• 2002

Recently, the hydroforming process is widely applied to the automotive industry and rapidly spreaded to other industries. In this paper, An implicit finite element formulation for simulating axisymmetric tube hydroforming processes is performed. In order to describe normal anisotropy of the tube, Hill's non-quadratic yield function is employed. The frictional contact between die and tube and the frictionless contact between tube and fluid are considered using the mesh-normal vectors computed from the finite element mesh of the tube. The complete set of the governing relations comprising equilibrium and interfacial equations is linearized for Newton-Raphson procedure. In order to verify the validity of the developed finite element formulation, the axisymmetric tube bulge test is simulated and the simulation results are compared with experimental measurements. In a simulation of stepped circular tube hydroforming processes, an optimal hydraulic pressure curve is pursued by considering simultaneously internal pressures and axial forces.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.618-621
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• 2001

The proposed lever actuator has no friction and mass balance characteristics in motion, which are adapt to high-speed and high-density optical disk system. This paper discussed about the theoretical analysis of the lever structure. The modeling of the lever actuator is found. Using the Newton's method, the motion of equation is deduced through the constraint equations and equilibrium equations in three directions (focusing, tracking and tilting). From the above analysis, we know that the shape of the hinge is the very important parameter on determining the performance of the lever actuator, and the actuator has the 2nd order system characteristics. And the first resonant frequency in transmissibility is dependent to the rigidity of the lever while the first transmissibility resonance of conventional actuators is dependent to the first natural resonance of those actuators. This means that the lever actuator is more stable to the external vibration.

• The KSFM Journal of Fluid Machinery
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• v.5 no.2 s.15
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• pp.43-49
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• 2002

In this paper, the steady-state performances analysis of a tilting pad gas bearing(TPGB) we analyzed by using finite element method for compressible Reynolds' equation. TPGB is used in a high-expansion-ratio expander running at a speed of 230,000 rpm. In order to solve the nonlinear finite element equations, the Newton-Raphson method is applied. The variations of the loading capacity, friction force and tilting angle of a single pad v.s. eccentricity direction of eccentricity and bearing number are investigated. The condition for the equilibrium of a pad, which is important for safe working of the bearing, is stated. The performances of the three pad bearing such as loading capacity, friction moment are predicted.

• Transactions of Materials Processing
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• v.9 no.6
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• pp.590-597
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• 2000

A finite element formulation lot the simulation of axisymmetric sheet hydroforming is proposed, and an implicit program is coded. In order to describe normal anisotropy of steel sheet, Hill's non-quadratic yield function (Hill, 1979) is employed. Frictional contacts among sheet surface, rigid tool surface, and flexible hydrostatic pressure are considered using mesh normal vectors based on finite element of the sheet. Applied hydraulic pressure is also considered as a function of forming rate and time and treated as an external loading. The complete set of the governing relations comprising equilibrium and interfacial equations is approximately linearized for Newton-Raphson algorithm. In order to verify the validity of the developed finite element formulation, the axisymmetric bulge test is simulated. Simulation results are compared with other FEM results and experimental measurements and showed good agreements. In axisymmetric hydroforming processes of a disk cover, formability changes are observed according to the hydraulic pressure curve changes.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2009.05a
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• pp.172-175
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• 2009

The purpose of this study is to predict the forming limit diagram (FLD) of strain-rate sensitive materials on the basis of the Marciniak and Kuczynski (M-K) theory. The strain-rate effect is taken into consideration in such a way that the stress-strain curves for various strain-rates are inputted into the formulation as point data, not as curve-fitted models such as power function. To solve the nonlinear system of equations derived from the equilibrium and constraints in the groove region and the safe zone, the Newton-Raphson method is used. The theoretical FLDs using four different yield criteria, that are von Mises, Hill (1948), Hill (1979), Logan and Hosford, are compared with the experimental, numerical (FEA) and other theoretical results. A new trial is made where a modified M-K model having n-step grooves is introduced to describe a real localized neck.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.04a
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• pp.9-18
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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 in 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.

• Korean Journal of Soil Science and Fertilizer
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• v.34 no.3
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• pp.213-236
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• 2001

The ionic composition of soil solution is related to a nutrient uptake by plant. Many models for estimating ionic composition of solution have been developed, and most of them have been used for calculating a content of mineral and ionic species in a geochemical point of view. An approximation model considering both cation and anion in soil solution was developed. Variables such as pH, Eh, EC, cations(K, Ca, Mg. Na, Fe, Mn, Al, $NH_4{^+}$), anions(Si, S, P, CY, $NO_3{^-}$, $HCO_3{^-}$ and chemical equilibria of ionic species in soil solution were input into Excel sheet. The activities of soluble ion, ionpairs and complexes of input element were estimated by Newton-Raphson method using conditional equilibrium constant calculated by Davies equation and special models. Equilibrium contents of insoluble minerals and complexes were also calculated.

• Journal of the Korean Geotechnical Society
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• v.29 no.6
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• pp.77-86
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• 2013

Embankments on soft ground experience significant deformation during time-dependent consolidation settlement, as well as an initial undrained settlement. Since infinitesimal strain theory assumes no configuration change and minute strain during deformation, finite strain analysis is required for better prediction of geotechnical problems involving large strain and geometric change induced by imposed loadings. Updated Lagrangian formulation is developed for time-dependent consolidation combining both force equilibrium and mass conservation of fluid, and mechanical constitutive equation is written in Janumann stress rate. Numerical convergence during Newton's iteration in large deformation analysis is improved by Nagtegaal's approach of considering the effect of rotation in mechanical constitutive relationship. Numerical simulations are conducted to discuss numerical reliability and applicability of developed numerical code: deformation of cantilever beam, two-dimensional consolidation. The numerical results show that developed formulation can efficiently describe large deformation problems. Proposed formulation is expected to facilitate the upgrading of a numerical code based on infinitesimal strain theory to that based on finite strain analysis.

• Journal of the Korean Geotechnical Society
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• v.27 no.3
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• pp.75-83
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• 2011

Emerging issues related with fully coupled Thermo-Hydro-Mechanical (THM) behavior of unsaturated soil demand the development of a numerical tool in diverse geo-mechanical and geo-environmental areas. This paper presents general governing equations for coupled THM processes in unsaturated porous media. Coupled partial differential equations are derived from three mass balances equations (solid, water, and air), energy balance equation, and force equilibrium equation. With Galerkin formulation and time integration of these governing equations, finite element code is developed to find nonlinear solution of four main variables (displacement-u, gas pressure-$P_g$), liquid pressure-$P_1$), and temperature-T) using Newton's iterative scheme. Three cases of numerical simulations are conducted and discussed: one-dimensional drainage experiments (u-$P_g-P_1$), thermal consolidation (u-$P_1$-T), and effect of pile on surrounding soil due to surface temperature variation (u-$P_1$-T).