Response time and accuracy of digital integrators as functions of the Stieltjes numerical integration formulas

Cybernetics ◽  
1972 ◽  
Vol 4 (6) ◽  
pp. 25-30
Author(s):  
A. V. Kalyaev
Keyword(s):  
Response Time ◽  
Numerical Integration ◽  
Integration Formulas ◽  
Digital Integrators

scholarly journals Impact of Energy Slope Averaging Methods on Numerical Solution of 1D Steady Gradually Varied Flow

2015 ◽  
Vol 62 (3-4) ◽  
pp. 101-119 ◽  
Author(s):  
Wojciech Artichowicz ◽  
Dzmitry Prybytak
Keyword(s):  
Numerical Methods ◽  
Numerical Solution ◽  
Numerical Integration ◽  
Cross Sections ◽  
Flow Model ◽  
One Dimensional ◽  
Averaging Methods ◽  
Integration Formulas ◽  
Different Types ◽  
The One

AbstractIn this paper, energy slope averaging in the one-dimensional steady gradually varied flow model is considered. For this purpose, different methods of averaging the energy slope between cross-sections are used. The most popular are arithmetic, geometric, harmonic and hydraulic means. However, from the formal viewpoint, the application of different averaging formulas results in different numerical integration formulas. This study examines the basic properties of numerical methods resulting from different types of averaging.

scholarly journals Two approaches for automating analysis of electromagnetic processes in non-linear circuits with valves

2019 ◽  
Vol 139 ◽  
pp. 01085 ◽  
Author(s):  
Khushnud Sapaev ◽  
Shukhrat Umarov
Keyword(s):  
Numerical Integration ◽  
Linear Approximation ◽  
Piecewise Linear ◽  
Piecewise Linear Approximation ◽  
Equivalent Circuits ◽  
Electric Circuits ◽  
Electromagnetic Processes ◽  
Integration Formulas ◽  
Analytical Formulas ◽  
Analytical Expressions

This article analyses and compares two approaches related to automating modeling of valve electric circuits with piecewise linear approximation of valve characteristics. The first approach is based on operator equivalent circuits’ analytical formulas and on analytical expressions programming which describe equivalent circuits on each conduction interval of valve elements. The second approach provides implementation of a system for modeling valve converters based on implicit numerical integration formulas.

scholarly journals A Discussion of Low Order Numerical Integration Formulas for Rigid and Flexible Multibody Dynamics

2007 ◽  
Author(s):  
Naresh Khude ◽  
Laurent O. Jay ◽  
Andrei Schaffer ◽  
Dan Negrut
Keyword(s):  
Numerical Integration ◽  
Multibody Dynamics ◽  
Numerical Experiments ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Dynamics Simulation ◽  
Stability And Convergence ◽  
Integration Formulas ◽  
Theoretical Results ◽  
Low Order

The premise of this work is that real-life mechanical systems limit the use of high order integration formulas due to the presence in the associated models of friction and contact/impact elements. In such cases producing a numerical solution necessarily relies on low order integration formulas. The resulting algorithms are generally robust and expeditious; their major drawback remains that they typically require small integration step-sizes in order to meet a user prescribed accuracy. This paper looks at three low order numerical integration formulas: Newmark, HHT, and BDF of order two. These formulas are used in two contexts. A first set of three methods is obtained by considering a direct index-3 discretization approach that solves for the equations of motion and imposes the position kinematic constraints. The second batch of three additional methods draws on the HHT and BDF integration formulas and considers in addition to the equations of motion both the position and velocity kinematic constraint equations. The first objective of this paper is to review the theoretical results available in the literature regarding the stability and convergence properties of these low order methods when applied in the context of multibody dynamics simulation. When no theoretical results are available, numerical experiments are carried out to gauge order behavior. The second objective is to perform a set of numerical experiments to compare these six methods in terms of several metrics: (a) efficiency, (b) velocity constraint drift, and (c) energy preservation. A set of simple mechanical systems is used for this purpose: a double pendulum, a slider crank with rigid bodies, and a slider crank with a flexible body represented in the floating frame of reference formulation.

Using Microplane Material Model for Concrete in Soft Missile Impact Analysis

2010 ◽  
Author(s):  
Jukka Ka¨hko¨nen ◽  
Pentti Varpasuo
Keyword(s):  
Numerical Integration ◽  
Impact Analysis ◽  
Constitutive Relations ◽  
Material Model ◽  
Medium Size ◽  
Test Case ◽  
Nonlinear Phenomena ◽  
Integration Formulas ◽  
The Impact ◽  
Concrete Model

The paper describes basis of a microplane concrete material model which was implemented in a commercial FE -code using user subroutine interface. The material model is called M4. The motivation for this implementation was a need for a concrete model which would perform well in a soft missile impact analysis. Numerical integration over the surface of a unit sphere is crucial to microplane material models. We tested our microplane implementation using several numerical integration formulas presented in literature. The two fairly simple test cases described in this paper revealed clearly the numerical anisotropy induced by the integration formulations. The impact problem was a medium size, medium velocity soft missile impact test case from an international research program. We compared our implementation of M4 model to a tensorial based damage plasticity concrete model and found out that the results were almost identical. However, the numerical results did not agree well with the measurements in this test case. We concluded this disagreement might be consequence of nonlinear phenomena beyond material constitutive relations.

Numerical implementation of the microplane constitutive model for shape memory alloys

2017 ◽  
Vol 233 (6) ◽  
pp. 1117-1133 ◽  
Author(s):  
MR Karamooz-Ravari ◽  
B Shahriari
Keyword(s):  
Shape Memory Alloy ◽  
Constitutive Model ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Numerical Integration ◽  
Biological Properties ◽  
Industrial Applications ◽  
Stress Increment ◽  
Integration Formulas

With the advent of shape memory alloys, several industrial applications were proposed due to their superior mechanical and biological properties. Since the fabrication and characterization of shape memory alloy devices is challenging and expensive, it is necessary to simulate their thermomechanical responses before fabrication. To do so, a powerful constitutive model capable of simulation of the important features of these materials is necessary. To be able to simulate a shape memory alloy device, it is vital to implement a suitable constitutive model in such a way to be used in finite element models. In this paper, an existing constitutive model based on microplane theory is numerically implemented and the effects of stress increment, different numerical integration formulas, and loading direction on the thermomechanical response of shape memory alloy is investigated through superelastic and shape memory proportional and nonproportional loadings. The obtained results show that the stress increment may have significant effect on the results if the forward Euler scheme is utilized. In addition, for the case of numerical integration over the surface of a unit hemisphere, 61 points integration formula without orthogonal symmetry provides the best results while 21 orthogonally symmetric one is the most inaccurate one. Also, the orthogonally symmetric numerical integration formulas predict the isotropic material response while those without orthogonal symmetry predict a little anisotropy.

Comparison of numerical integration formulas

2010 ◽  
Vol 54 (12) ◽  
pp. 1-16
Author(s):  
N. K. Bakirov ◽  
I. R. Gallyamov
Keyword(s):  
Numerical Integration ◽  
Integration Formulas
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