• Structural Engineering and Mechanics
• /
• v.60 no.1
• /
• pp.149-162
• /
• 2016

Structure-dependent integration methods seem promising for structural dynamics applications since they can integrate unconditional stability and explicit formulation together, which can enable the integration methods to save many computational efforts when compared to an implicit method. A newly developed structure-dependent integration method can inherit such numerical properties. However, an unusual overshooting behavior might be experienced as it is used to compute a forced vibration response. The root cause of this inaccuracy is thoroughly explored herein. In addition, a scheme is proposed to modify this family method to overcome this unusual overshooting behavior. In fact, two improved formulations are proposed by adjusting the difference equations. As a result, it is verified that the two improved formulations of the integration methods can effectively overcome the difficulty arising from the inaccurate integration of the steady-state response of a high frequency mode.

• Transactions on Electrical and Electronic Materials
• /
• v.17 no.6
• /
• pp.369-374
• /
• 2016

This paper presents a design procedure of an integrated inductor with a magnetic core for power converters. This procedure considerably reduces design time and effort. The proposed design procedure is verified by the development of an inductor model dedicated to the monolithic integration of DC-DC converters for portable applications. The numerical simulation based on the FEM (finite elements method) shows that 3D modeling of the integrated inductor allows better estimation of the electrical parameters of the desired inductor. The optimization of the electrical parameter values is based on the numerical analysis of the influence of the geometric parameters on the electrical characteristics of the inductor. Using the VHDL-AMS language, implementation of the integrated inductor in a micro Buck converter demonstrate that simulation results present a very promising approach for the monolithic integration of DC-DC converters.

• Earthquakes and Structures
• /
• v.14 no.1
• /
• pp.45-53
• /
• 2018

A family of the structure-dependent methods seems very promising for time integration since it can simultaneously have desired numerical properties, such as unconditional stability, second-order accuracy, explicit formulation and numerical dissipation. However, an unusual overshoot, which is essentially different from that found by Goudreau and Taylor in the transient response, has been experienced in the steady-state response of a high frequency mode. The root cause of this unusual overshoot is analytically explored and then a remedy is successfully developed to eliminate it. As a result, an improved formulation of this family method can be achieved.

• Proceedings of the KSME Conference
• /
• 2004.11a
• /
• pp.453-458
• /
• 2004

This study proposes a new two-level condensation scheme for the construction of a reduced system. In the first step, the candidate area is selected for the construction of the reduced system by energy estimation in element-level. In the second step, primary degrees of freedom are selected by sequential elimination from the candidate degrees of freedom linked to the selected elements. Numerical examples demonstrate that the proposed method saves the computational cost effectively and provides a reduced system which predicts the eigenvalues accurately. Moreover, the well-constructed reduced system can present the reliable behavior of the structure under arbitrary dynamic loads comparing to that of global system. Time integration in a reduced system can save the computing time remarkably. Through a few numerical examples, the efficiency and reliability of the proposed scheme are verified.

• Structural Engineering and Mechanics
• /
• v.28 no.5
• /
• pp.587-601
• /
• 2008

In this study, a numerical procedure based on the finite element method for materially and geometrically nonlinear analysis of reinforced and prestressed concrete slender columns with arbitrary section subjected to combined biaxial bending and axial load is developed. In order to overcome the low computer efficiency of the conventional section integration method in which the reinforced concrete section is divided into a large number of small areas, an efficient section integration method is used to determine the section tangent stiffness. In this method, the arbitrary shaped cross section is divided into several concrete trapezoids according to boundary vertices, and the contribution of each trapezoid to section stiffness is determined by integrating directly the trapezoid. The space frame flexural theory is utilized to derive the element tangent stiffness matrix. The nonlinear full-range member response is traced by an updated normal plane arc-length solution method. The analytical results agree well with the experimental ones.

• Structural Engineering and Mechanics
• /
• v.5 no.3
• /
• pp.283-295
• /
• 1997

This paper presents a high precision integration method for the dynamic response analysis of structures with holonomic constraints. A detail recursive scheme suitable for algebraic and differential equations (ADEs) which incorporates generalized forces is established. The matrix exponential involved in the scheme is calculated precisely using $2^N$ algorithm. The Taylor expansions of the nonlinear term concerned with state variables of the structure and the generalized constraint forces of the ADEs are derived and consequently, their particular integrals are obtained. The accuracy and effectiveness of the present method is demonstrated by two numerical examples, a plane truss with circular slot at its tip point and a slewing flexible cantilever beam which is currently interesting in optimal control of robot manipulators.

• Journal of the Korea Institute of Military Science and Technology
• /
• v.14 no.3
• /
• pp.532-537
• /
• 2011

This paper describes the development of SPH(Smooth Particle Hydrodynamics) scheme and integration into the multi-material shock physics code(ExLO) for the purpose of the application to the extreme large deformation problems. SPH numerical scheme has been extended into the fluid dynamics and the high-speed impact events, such as space structure protection against space debris and meteorite catering. Like other hydrocodes, SPH scheme also solves the conservation equations with the constitutive equation including equation of state. The benchmark problem, Taylor-Impact test, was simulated and the predictions show good agreements with both the published numerical data and experimental data. Currently, the contact treatment between materials is under development.

• Structural Engineering and Mechanics
• /
• v.3 no.2
• /
• pp.145-162
• /
• 1995

A damped trapezoidal rule method for numerical time-integration is presented, and its application in analyses of dynamic response of damped structures is discussed. It is shown that the damped trapezoidal rule method has features that make it an attractive approach for applications in dynamic analyses of structures. Accuracy and stability analyses are developed for the damped single-degree-of-freedom systems. Error analyses are also performed for the Newmark beta method and compared with the damped trapezoidal rule method as a basis for discussion of the relative merits of the proposed method. The procedure is fully explicit and easy to implement. However, since the method is an explicit method, it is conditionally stable. The methodology is applied to several example problems to illustrate its strengths, limitations and inherent simplicity.

• Structural Engineering and Mechanics
• /
• v.55 no.4
• /
• pp.885-900
• /
• 2015

This paper introduces Romberg-Richardson's method as one of the numerical integration tools for computation of stress intensity factor in a pre-cracked specimen subjected to a complex stress field across the crack faces. Also, the computation of stress intensity factor for various stress fields using existing three methods: average stress over interval method, piecewise linear stress method, piecewise quadratic method are modified by using Richardson extrapolation method. The direct integration method is used as reference for constant and linear stress distribution across the crack faces while Gauss-Chebyshev method is used as reference for nonlinear distribution of stress across the crack faces in order to obtain the stress intensity factor. It is found that modified methods (average stress over intervals-Richardson method, piecewise linear stress-Richardson method, piecewise quadratic-Richardson method) yield more accurate results after a few numbers of iterations than those obtained using these methods in their original form. Romberg-Richardson's method is proven to be more efficient and accurate than Gauss-Chebyshev method for complex stress field.

• The KIPS Transactions:PartA
• /
• v.11A no.5
• /
• pp.401-406
• /
• 2004

Among many algorithms for the integration problems in which one wants to compute the approximation to the definite integral in the average case setting, we study the average case errors of numerical integration rules using interpolation. In particular, we choose the composite Newton-Cotes quadratures and the function values at equally spaced sample points on the given interval as information. We compute the average case error of composite Newton-Cotes quadratures and show that it is minimal(modulo a multiplicative constant).