Comparison of numerical integration techniques for orbital applications

1974 ◽  
pp. 149-166 ◽  
Author(s):  
Hays Moore
Keyword(s):  
Numerical Integration ◽  
Integration Techniques

Variations on a theme – Euler and the logsine integral

2012 ◽  
Vol 96 (537) ◽  
pp. 451-458 ◽  
Author(s):  
Nick Lord
Keyword(s):  
Numerical Integration ◽  
Integration Techniques ◽  
Image Position ◽  
Variations On A Theme ◽  
Standard Integration

This article concerns the evaluation of the ‘logsine’ integralWe shall encounter it in several guises. Indeed, standard integration techniques used below readily show that (1) has the same value as the following integrals:En passant, it is worth noting that forms (6) and (7) are the best behaved for numerical integration.I first met the logsine integral as a callow youth in that strange hinterland of results that you may not have met at school but were not guaranteed to meet later on either.

On the numerical integration in generalized/extended finite element method analysis for crack propagation problems

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Bruna Caroline Campos ◽  
Felício Bruzzi Barros ◽  
Samuel Silva Penna
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Mechanics ◽  
Numerical Integration ◽  
Extended Finite Element Method ◽  
Extended Finite Element ◽  
Content Type ◽  
Integration Techniques ◽  
Integration Strategies ◽  
Element Method

Purpose The purpose of this paper is to evaluate some numerical integration strategies used in generalized (G)/extended finite element method (XFEM) to solve linear elastic fracture mechanics problems. A range of parameters are here analyzed, evidencing how the numerical integration error and the computational efficiency are improved when particularities from these examples are properly considered. Design/methodology/approach Numerical integration strategies were implemented in an existing computational environment that provides a finite element method and G/XFEM tools. The main parameters of the analysis are considered and the performance using such strategies is compared with standard integration results. Findings Known numerical integration strategies suitable for fracture mechanics analysis are studied and implemented. Results from different crack configurations are presented and discussed, highlighting the necessity of alternative integration techniques for problems with singularities and/or discontinuities. Originality/value This study presents a variety of fracture mechanics examples solved by G/XFEM in which the use of standard numerical integration with Gauss quadratures results in loss of precision. It is discussed the behaviour of subdivision of elements and mapping of integration points strategies for a range of meshes and cracks geometries, also featuring distorted elements and how they affect strain energy and stress intensity factors evaluation for both strategies.

Numerical Integration Technique in Computation of Extended Finite Element Method

2012 ◽  
Vol 446-449 ◽  
pp. 3557-3560 ◽  
Author(s):  
Feng Wang ◽  
Di Zhang ◽  
Jing Yu ◽  
Hui Xu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Integration ◽  
Extended Finite Element Method ◽  
Extended Finite Element ◽  
Displacement Mode ◽  
Integration Techniques ◽  
Discontinuous Medium ◽  
Control Equation ◽  
Element Method

The extended finite element method (XFEM) is the most effective numerical method to solve discontinuous dynamic problems so far. It makes research within a standard finite element framework and reserves all merits of CFEM. In other side, it needs not mesh repartition to geometric and physical interface. Numerical integration techniques of the XFEM computation are studied, including displacement mode of the XFEM, control equation and infirm solution form of discontinuous medium mechanics problem, region scatteration, element integral strategy.

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