A direct numerical integration scheme for visco-hyperelastic models using radial return relaxation

2010 ◽  
Vol 19 (1-3) ◽  
pp. 129-140 ◽  
Author(s):  
Stéphane Lejeunes ◽  
Stéphane Méo ◽  
Adnane Boukamel
Keyword(s):  
Numerical Integration ◽  
Integration Scheme ◽  
Numerical Integration Scheme ◽  
Direct Numerical Integration ◽  
Hyperelastic Models

scholarly journals A direct numerical integration scheme for visco-hyperelastic models using radial return relaxation

2010 ◽  
pp. 129-140
Author(s):  
Stéphane Lejeunes ◽  
Stéphane Méo ◽  
Adnane Boukamel
Keyword(s):  
Numerical Integration ◽  
Taylor Expansion ◽  
Integration Scheme ◽  
Exponential Mapping ◽  
First Order ◽  
Numerical Integration Scheme ◽  
Exponential Solution ◽  
Evolution Laws ◽  
Direct Numerical Integration ◽  
Hyperelastic Models

In this paper, a numerical integration scheme of the evolution laws for viscohyperelastic models is proposed. The starting points of the method are the exponential mapping (Reese et al., 1998) and the radial return (Weber et al., 1990; Simo, 1988). The originality of this work lies in the substitution of a differential tensorial system by a scalar one with two equations and two unknowns and in a first order Taylor expansion of them. In this way an analytical approximated exponential solution is finally obtained.

Dynamic Analysis of Shipping Cask Subjected to Sequential Bolt Preload and Impact Loads

2009 ◽  
Author(s):  
Tsu-te Wu
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Numerical Integration ◽  
Dynamic Responses ◽  
Integration Scheme ◽  
Impact Loads ◽  
Element Mesh ◽  
Bolt Preload ◽  
Numerical Integration Scheme ◽  
Structural Responses

This paper presents an improved methodology for evaluating the dynamic responses of shipping casks subjected to the sequential HAC impact loads. The methodology utilizes the import technique of the finite-element mesh and the analytical results form one dynamic analysis using explicit numerical integration scheme into another dynamic analysis also using explicit numerical integration scheme. The new methodology presented herein has several advantages over conventional methods. An example problem is analyzed to illustrate the application of the present methodology in evaluating the structural responses of a shipping cask to the sequential HAC loading.

The Effects of Main-Flow Radial Velocity on the Stability of Developing Laminar Pipe Flow

1976 ◽  
Vol 43 (2) ◽  
pp. 209-212 ◽  
Author(s):  
F. C. T. Shen ◽  
T. S. Chen ◽  
L. M. Huang
Keyword(s):  
Radial Velocity ◽  
Main Flow ◽  
Integration Scheme ◽  
Neutral Stability ◽  
Radial Velocity Component ◽  
Numerical Integration Scheme ◽  
Critical Reynolds Numbers ◽  
The Stability ◽  
Direct Numerical Integration ◽  
Sommerfeld Equation

In studying the stability due to axisymmetric disturbances of the developing flow of an incompressible fluid in the entrance region of a circular tube, a generalized version of the Orr-Sommerfeld equation was derived which takes account of the radial velocity component in the main flow. The new terms in the generalized Orr-Sommerfeld equation are inversely proportional to the Reynolds number. The resulting eigenvalue problem consisting of the disturbance equation and the boundary conditions was solved by a direct numerical integration scheme along with an iteration procedure. Neutral stability curves and critical Reynolds numbers at various axial locations are presented. A comparison of the present results with those from the conventional Orr-Sommerfeld equation in which the effect of the main-flow radial velocity is neglected, shows that inclusion of the radial velocity contributes to a destabilization of the main flow.

Inelastic, Nonlinear Analysis of Stiffened Shells of Revolution by Numerical Integration

1974 ◽  
Vol 96 (2) ◽  
pp. 121-130 ◽  
Author(s):  
H. S. Levine ◽  
V. Svalbonas
Keyword(s):  
Numerical Integration ◽  
Cross Sections ◽  
Thermal Loading ◽  
Large Deflection ◽  
Kinematic Hardening ◽  
Integration Scheme ◽  
Shells Of Revolution ◽  
Stiffened Shells ◽  
Numerical Integration Scheme ◽  
Deflection Analysis

This paper describes the latest addition to the STARS system of computer programs, STARS-2P, for the plastic, large deflection analysis of axisymmetrically loaded shells of revolution. The STARS system uses a numerical integration scheme to solve the governing differential equations. Several unique features for shell of revolution programs that are included in the STARS-2P program are described. These include orthotropic nonlinear kinematic hardening theory, a variety of shell wall cross sections and discrete ring stiffeners, cyclic and nonproportional mechanical and thermal loading capability, the coupled axisymmetric large deflection elasto-plastic torsion problem, an extensive restart option, arbitrary branching capability, and the provision for the inelastic treatment of smeared stiffeners, isogrid, and waffle wall constructions. To affirm the validity of the results, comparisons with available theoretical and experimental data are presented.

A Modified Gaussian Integration Scheme in Element Free Method

2002 ◽  
Vol 18 (1) ◽  
pp. 17-27
Author(s):  
Jopan Sheng ◽  
Chung-Yue Wang ◽  
Kuo-Jui Shen
Keyword(s):  
Numerical Integration ◽  
Solid Mechanics ◽  
Gaussian Quadrature ◽  
Quadrature Rule ◽  
Integration Scheme ◽  
Quadrature Point ◽  
Physical Domain ◽  
Gaussian Integration ◽  
Numerical Integration Scheme ◽  
Element Free

ABSTRACTIn this paper, a modified numerical integration scheme is presented that improves the accuracy of the numerical integration of the Galerkin weak form, within the integration cells of the analyzed domain in the element-free methods. A geometrical interpretation of the Gaussian quadrature rule is introduced to map the effective weighting territory of each quadrature point in an integration cell. Then, the conventional quadrature rule is extended to cover the overlapping area between the weighting territory of each quadrature point and the physical domain. This modified numerical integration scheme can lessen the errors due to misalignment between the integration cell and the boundary or interface of the physical domain. Some numerical examples illustrate that this newly proposed integration scheme for element-free methods does effectively improve the accuracy when solving solid mechanics problems.

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