• Magazine of the Korean Society of Agricultural Engineers
• /
• v.36 no.1
• /
• pp.54-62
• /
• 1994

The expanding technique of the Stochastic Finite Element Method(SFEM) is proposed in this paper for adapting direct integration methods in stochastical dynamic analysis of structures. Grafting the direct integration methods and the SFEM together, one can deal with nonlinear structures and nonstationary process problems without any restriction. The stochastical central diffrence and stochastic Houbolt methods are introduced to show the expanding technique, and their adaptabilities are discussed. Results computed by the proposed method (the Stochastic Finite Element Method in Dynamics: SFEMD) for two degree-of-free- dom system are compared with those obtained by Monte Carlo Simulation.

• 한국기계연구소 소보
• /
• s.18
• /
• pp.55-66
• /
• 1988

Many direct integration methods are used for numerical analyses of dynamic motion. In these methods, the governing equations of a dynamic system are integrated successively using a step-by-step numerical integration procedure. Time derivatives in the equations are generally approximated using difference formulas involving one or more increments of the time. Time increment has closely relationship with the accuracy of the motion analysis. In this paper, a 4th order Houbolt direct integration method is derived. For a spring-mass system, the motion of the system are analyzed from the 3rd order Houbolt and the 4th order Houbolt approaches respectively. Finally the paper proposes the optimal time-increment based on the accuracy of numerical analyses.

• Structural Engineering and Mechanics
• /
• v.13 no.5
• /
• pp.569-589
• /
• 2002

In performing the dynamic analysis, the step size used in a step-by-step integration method might be much smaller than that required by the accuracy consideration in order to capture the rapid chances of dynamic loading or to eliminate the linearization errors. It was first found by Chen and Robinson that these difficulties might be overcome by integrating the equations of motion with respect to time once. A further study of this technique is conducted herein. This include the theoretical evaluation and comparison of the capability to capture the rapid changes of dynamic loading if using the constant average acceleration method and its integral form and the exploration of the superiority of the time integration to reduce the linearization error. In addition, its advantage in the solution of the impact problems or the wave propagation problems is also numerically demonstrated. It seems that this time integration technique can be applicable to all the currently available direct integration methods.

• Proceedings of the Earthquake Engineering Society of Korea Conference
• /
• 1999.10a
• /
• pp.155-161
• /
• 1999

Many direct integration methods have been developed for dynamic analysis of structures, In order to compare each other methods and give guideline for selecting a time increment the amplification matrix is constructed according to algorithm of each method and stability and accuracy analysis is done. Four story shear building under external excitations is analyzed by each method and the RMS errors of displacements of top floor and compared with each other.

• Structural Engineering and Mechanics
• /
• v.64 no.4
• /
• pp.495-504
• /
• 2017

This paper proposes a new direct numerical integration algorithm for solving equation of motion in structural dynamics problems with nonlinear stiffness. The new implicit method's degree of accuracy is higher than that of existing methods due to the higher order of the acceleration. Two parameters are defined, leading to a new family of unconditionally stable methods, which helps to take greater time steps in integration and eliminate concerns about the duration of solving. The method developed can be utilized for a number of solid plane finite elements, examples of which are given to compare the proposed method with existing ones. The results indicate the superiority of the proposed method.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.7 no.3
• /
• pp.241-248
• /
• 1987

The theoretical backgrounds of the several methods were surveyed and reviewed to fin out the adequate one to determine equivalent modal damping values in solving the dynamic problem of soil-structure interaction by mode superposition method. Furthermore the rigorous damping matrix of equation of motion was obtained through component mode synthesis technique and used in direct integration of the equation. The analytical results by direct integration method were compared with those of mode superposition approach using the various sets of equivalent modal damping values calculated by the methods to be reviewed. Two types of superstructures and four kinds of subsurface conditions were considered and combined to make soil-structure coupled models. It was realized that dissipating energy method gives the equivalent modal damping values which lead the most similar results to direct integration ones. In case of fixed base, the responses of all methods except stiffness weighted approach are almost equal to those of direct integration method.

• 유체기계공업학회:학술대회논문집
• /
• 2002.12a
• /
• pp.370-377
• /
• 2002

Generally, the system of calculation for the multi-path ultrasonic flow meters can be divided into two methods by how to get the mean velocity, namely, weighting and direct method. Weighting-method derive the mean velocity through modeling in theoretical velocity profile. Direct-method derive the mean velocity though actual flow distribution. The system of calculation varies with maker's transducer configuration and integration method. Each system has merits and demerits. This paper describes the system of integration that calculates line velocity over cross-section of the circular pipe. Flow rate mr discussed in this paper is a difference between theoretical flow rate and integrated flow rate according to values of Reynolds number in symmetric flow field or theoretical flow rate and integrated flow rate according to rotated model in asymmetric flow field.

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
• /
• 1992.08a
• /
• pp.146-149
• /
• 1992

The dynamic inelastic analysis is now often performed for the safe structural design against the seismic events or explosions. Several powerful methods of dynamic inelastic analysis such as direct intergration methods and modal superposition methods were developed with the development of computers during the last three decades. This type of analysis generally adopts the step-by-step time-integration procedure and gives a complete time history of the evolution of the structure.(omitted)

• 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.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1993.04a
• /
• pp.37-44
• /
• 1993

There are a lot of linear dynamic analysis methods for complex structures. Each method has advantages and shortcomings. Method of dynamic analysis for complex structure is selected considering characteristics of dynamic loading, computer facility available number of degree of freedem and accuracy of results. It is a main point of view to get economical results rather then accurate ones for analysis of general complex structures, Mode superposition method and direct integration method are generally used. However, the characteristics of load is not considered in mode superpositon method, the personal computer cannot be used in direct integration methods. To over-come these shortcomings, the component mode method incorporating Ritz algorithm updated is proposed to solve economically dynamic behavior of the structures. The purpose of study is a formulation of algorithm, and computer programing suitable for dynamic analysis of the complex structure in personal computer environment.