scholarly journals An Energy-Work Relationship Integration Scheme for Nonconservative Hamiltonian Systems

2008 ◽  
Vol 2008 ◽  
pp. 1-5 ◽  
Author(s):  
Fu Jingli ◽  
Chen Benyong ◽  
Xie Fengping
Keyword(s):  
Numerical Integration ◽  
Hamiltonian Systems ◽  
Discrete Analog ◽  
Integration Scheme ◽  
Parallel Composition ◽  
Integration Schemes ◽  
Numerical Integration Scheme ◽  
New Energy ◽  
Relation Scheme ◽  
Work Relationship

This letter focuses on studying a new energy-work relationship numerical integration scheme of nonconservative Hamiltonian systems. The signal-stage, multistage, and parallel composition numerical integration schemes are presented for this system. The high-order energy-work relation scheme of the system is constructed by a parallel connection of n multistage scheme of order 2 which its order of accuracy is 2n. The connection, which is discrete analog of usual case, between the change of energy and work of nonconservative force is obtained for nonconservative Hamiltonian systems.This letter also shows that the more the stages of the schemes are, the less the error rate of the scheme is for nonconservative Hamiltonian systems. Finally, an applied example is discussed to illustrate these results.

scholarly journals Is There an Optimal Choice of Configuration Space for Lie Group Integration Schemes Applied to Constrained MBS?

2013 ◽  
Author(s):  
Andreas Müller ◽  
Zdravko Terze
Keyword(s):  
Numerical Integration ◽  
Configuration Space ◽  
Lie Group ◽  
Optimal Choice ◽  
Rigid Bodies ◽  
Integration Scheme ◽  
Integration Schemes ◽  
Numerical Integration Scheme ◽  
Group Integration ◽  
Lie Group Integration

Recently various numerical integration schemes have been proposed for numerically simulating the dynamics of constrained multibody systems (MBS) operating. These integration schemes operate directly on the MBS configuration space considered as a Lie group. For discrete spatial mechanical systems there are two Lie group that can be used as configuration space: SE(3) and SO(3) × ℝ3. Since the performance of the numerical integration scheme clearly depends on the underlying configuration space it is important to analyze the effect of using either variant. For constrained MBS a crucial aspect is the constraint satisfaction. In this paper the constraint violation observed for the two variants are investigated. It is concluded that the SE(3) formulation outperforms the SO(3) × ℝ3 formulation if the absolute motions of the rigid bodies, as part of a constrained MBS, belong to a motion subgroup. In all other cases both formulations are equivalent. In the latter cases the SO(3) × ℝ3 formulation should be used since the SE(3) formulation is numerically more complex, however.

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.

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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