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Numerical Integration Procedure (numerical + integration_procedure)

Distribution by Scientific Domains

Engineering	80%

Selected Abstracts

Crack edge element of three-dimensional displacement discontinuity method with boundary division into triangular leaf elements

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2001
H. Li
Abstract In this paper, the existing Displacement Discontinuity Method (DDM) for three-dimensional elastic analysis with boundary discretized into triangular elements, which is purely based on analytical integrals, is extended from the constant element to the square-root crack edge element. In order to evaluate the singular integral when the receiver point falls into the remitter element, i.e., the observed point (x,y) ,,, a part analytical and part numerical integration procedure is adopted effectively. The newly developed codes prove valid in estimating the Stress Intensity Factor (SIF) KI. Furthermore, for the sake of keeping the advantages of high-speed and high-accuracy in developing the numerical system, a novel method to realize pure analytical integration of influence function is found by the aid of symbolic computation technology of Mathematica. Copyright © 2001 John Wiley & Sons, Ltd. [source]

The modeling of realistic chemical vapor infiltration/deposition reactors

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2010
John Ibrahim
Abstract We describe the low Mach number equations as well as a second-order numerical integration procedure that are used to solve a realistic chemical vapor infiltration/chemical vapor deposition (CVI/CVD) problem. The simulation accounts for a homogeneous gas chemical reaction mechanism, a heterogeneous surface reaction mechanism, and an evolving pore structure model. The numerical solution of the model ultimately leads to the solution of a large system of stiff differential algebraic equations that are to be integrated over a long time. An operator splitting algorithm is employed to deal with the stiffness associated with chemical reactions, whereas a projection method is employed to overcome the difficulty arising from having to solve a large coupled system for velocity and pressure fields. Results show that the proposed integration procedure is very efficient for modeling long time CVI/CVD densification processes. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Improved analytical approximation to arbitrary l-state solutions of the Schrödinger equation for the hyperbolical potential

ANNALEN DER PHYSIK, Issue 4 2009
S.M. Ikhdair
Abstract A new approximation scheme to the centrifugal term is proposed to obtain the l =, 0 bound-state solutions of the Schrödinger equation for an exponential-type potential in the framework of the hypergeometric method. The corresponding normalized wave functions are also found in terms of the Jacobi polynomials. To show the accuracy of the new proposed approximation scheme, we calculate the energy eigenvalues numerically for arbitrary quantum numbers n and l with two different values of the potential parameter ,0. Our numerical results are of high accuracy like the other numerical results obtained by using program based on a numerical integration procedure for short-range and long-range potentials. The energy bound-state solutions for the s-wave (l = 0) and ,0 = 1 cases are given. [source]

Compensation of actuator delay and dynamics for real-time hybrid structural simulation

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 1 2008
M. Ahmadizadeh
Abstract Compensation of delay and dynamic response of servo-hydraulic actuators is critical for stability and accuracy of hybrid experimental and numerical simulations of seismic response of structures. In this study, current procedures for compensation of actuator delay are examined and improved procedures are proposed to minimize experimental errors. The new procedures require little or no a priori information about the behavior of the test specimen or the input excitation. First, a simple approach is introduced for rapid online estimation of system delay and actuator command gain, thus capturing the variability of system response through a simulation. Second, an extrapolation procedure for delay compensation, based on the same kinematics equations used in numerical integration procedures is examined. Simulations using the proposed procedures indicate a reduction in high-frequency noise in force measurements that can minimize the excitation of high-frequency modes. To further verify the effectiveness of the compensation procedures, the artificial energy added to a hybrid simulation as a result of actuator tracking errors is measured and used for demonstrating the improved accuracy in the simulations. Copyright © 2007 John Wiley & Sons, Ltd. [source]

An internally consistent integration method for critical state models,

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 3 2005
Randall J. Hickman
Abstract A new procedure to integrate critical state models including Cam,Clay and modified Cam,Clay is proposed here. The proposed procedure makes use of the linearity of the virgin isotropic compression curve and the parallel anisotropic consolidation lines in e,ln p space which are basic features of the formulation of critical state models. Using this algorithm, a unique final stress state may be found as a function of a single unknown for elastoplastic loading. The key equations are given in this article for the Cam,Clay and modified Cam,Clay models. The use of the Newton,Raphson iterative method to minimize residuals and obtain a converged solution is described here. This new algorithm may be applied using the assumptions of linear elasticity or non-linear elasticity within a given loading step. The new algorithm proposed here is internally consistent and has computational advantages over the current numerical integration procedures. Numerical examples are presented to show the performance of the algorithm as compared to other integration algorithms. Published in 2005 by John Wiley & Sons, Ltd. [source]