A novel explicit three-sub-step time integration method for wave propagation problems

A novel explicit three-sub-step time integration method is proposed. From linear analysis, it is designed to have at least second-order accuracy, tunable stability interval, tunable algorithmic dissipation and no overshooting behaviour. A distinctive feature is that the size of its stability interval can be adjusted to control the properties of the method. With the largest stability interval, the new method has better amplitude accuracy and smaller dispersion error for wave propagation problems, compared with some existing second-order explicit methods, and as the stability interval narrows, it shows improved period accuracy and stronger algorithmic dissipation. By selecting an appropriate stability interval, the proposed method can achieve properties better than or close to existing second-order methods, and by increasing or reducing the stability interval, it can be used with higher efficiency or stronger dissipation. The new method is applied to solve some illustrative wave propagation examples, and its numerical performance is compared with those of several widely used explicit methods.

Seismic Performance of RC Column Using Fiber Hinge Concept with Time Integration Method

Recent seismic events showed the importance of understanding the structural performance of RC column that can be predicted numerically. The accuracy of column performance depends on type of the analysis and representation of seismic effect. Therefore, in this paper a nonlinear time history analysis has been performed to assess the seismic performance of bridge column using fiber hinge concept with time integration method using sap2000 software. A long bridge RC column is utilized and subjected to seismic excitation. The column has been divided into different size and numbers of fiber to assess the accuracy of the analysis and time consuming to analyze each case of fiber hinges. In addition, this paper used three-time integration methods, Newmark, Hilber-Hughes-Taylor, and Chung & Hulbert to predict the most suitable method to be used in column seismic analysis. The time history displacement and base shear in addition to moment rotation of the column are the most important factors to evaluate the column seismic performance. The analysis results demonstrated that the most suitable time integration method is Hilber-Hughes-Taylor for such type of the analysis since it gives more stable base shear result than other two methods. Furthermore, the results indicated that the accuracy of seismic performance increased by number of fibers incremental. Moreover, the number of steel fibers should be equal to the number of bars with same area and location. The unconfined and confined concrete should be divided into small areas to get accurate prediction of column seismic performance.

Performance of a Three-Substep Time Integration Method on Structural Nonlinear Seismic Analysis

In this work, a study of a three substeps’ implicit time integration method called the Wen method for nonlinear finite element analysis is conducted. The calculation procedure of the Wen method for nonlinear analysis is proposed. The basic algorithmic property analysis shows that the Wen method has good performance on numerical dissipation, amplitude decay, and period elongation. Three nonlinear dynamic problems are analyzed by the Wen method and other competitive methods. The result comparison indicates that the Wen method is feasible and efficient in the calculation of nonlinear dynamic problems. Theoretical analysis and numerical simulation illustrate that the Wen method has desirable solution accuracy and can be a good candidate for nonlinear dynamic problems.

Approximation of Non-Linear Rotor Dynamic Resonance Behavior of Vertically Aligned Hydro-Units Guided by Tilting-Pad Bearings

Dynamic analyses of vertical hydro power plant rotors require the consideration of the non-linear bearing characteristics. This study investigates the vibrational behavior of a typical vertical machine using a time integration method that considers non-linear bearing forces. Thereby, the influence of support stiffness and unbalance magnitude is examined. The results show a rising influence of unbalance on resonance speed with increasing support stiffness. Furthermore, simulations reveal that the shaft orbit in the bearing is nearly circular for typical design constellations. This property is applied to derive a novel approximation procedure enabling the examination of non-linear resonance behavior, using linear rotor dynamic theory. The procedure considers the dynamic film pressure for determining the pad position. In addition, it is time-efficient compared to a time integration method, especially at high amplitudes when damping becomes small.

Impact of difference between explicit and implicit second-order time integration schemes on isotropic/anisotropic steady incompressible turbulence field

This study presents the impact of the difference between the implicit and explicit time integration methods on a steady turbulent flow field. In contrast to the explicit time integration method, the implicit time integration method may produce significant kinetic energy conservation error because the widely used spatial difference method for discretizing the governing equations is explicit with respect to time. In this study, the second-order Crank-Nicolson method is used as the implicit time integration method, and the fourth-order Runge-Kutta, second-order Runge-Kutta and second-order Adams-Bashforth methods are used as explicit time integration methods. In the present study, both isotropic and anisotropic steady turbulent fields are analyzed with two values of the Reynolds number. The turbulent kinetic energy in the steady turbulent field is hardly affected by the kinetic energy conservation error. The rms values of static pressure fluctuation are significantly sensitive to the kinetic energy conservation error. These results are examined by varying the time increment value. These results are also discussed by visualizing the large scale turbulent vortex structure.

Finite-Element Modeling of Time-Domain Controlled-Source Electromagnetic Survey with Weighted Laguerre Polynomials

To facilitate the modeling of time-domain controlled-source electromagnetic survey, we propose an efficient finite-element method with weighted Laguerre polynomials, which shows a much lower computational complexity than conventional time integration methods. The proposed method allows sampling the field at arbitrary time steps and also its accuracy is determined by the number of polynomials, instead of the time sampling interval. Analysis is given regarding the optimization of the polynomial number to be used and the criterion of selecting the time scale factor. Two numerical examples in marine and land survey environments are included to demonstrate the superiority of the proposed method over the existing backward Euler time integration method. The proposed method is expected to facilitate the modeling of transient electromagnetic surveys in the geophysical regime.

NUMERICAL DIFFERENTIATION OF BEND FORMS OF THE LONG ELASTIC RODS

The technique of numerical differentiation of the bend forms of long elastic rods is presented. This technique is based on search for new bend forms of the rod by solving the equations of oscillations with using the time integration method and the polynomial spline-functions that are being described the current bend form. In it, the spline-functions are found by current bend form approximation where each of the found functions is responsible to certain point of rod elastic line and describes the position of nearby points. Using the described approximation technique with subsequent numerical differentiation, the dependences of the derivatives on an arbitrary bend form of the rod with a length that is equal to 100 m are shown. To confirm the reliability, the results of numerical differentiation of the bend forms of the elastic rods described by given functions are presented and the numerical results obtained using the proposed method are compared with the results of analytical differentiation of the original functions. The graphs of values derivatives dependence to rod length are drawn and tables with numerical values of differentiation results are shown. It is concluded that the considered technique of numerical differentiation of rods bend forms allows to do the research of dynamics of rod systems. It gives the exact result of differentiation, provides the continuity and smoothness of all four derivatives functions of spline that are being described the bend form with considerable length. Described technique was realized in a computer program with graphic user interface. Program allows to monitor for dynamics of the oscillatory motion of the modeled system in real-time by calculating and drawing the current band forms of the rotating rod during the oscillation.