A fictitious crack XFEM with two new solution algorithms for cohesive crack growth modeling in concrete structures

2015 ◽  
Vol 32 (2) ◽  
pp. 473-497 ◽  
Author(s):  
Xiaodong Zhang ◽  
Tinh Quoc Bui
Keyword(s):  
Finite Element ◽  
Nonlinear System ◽  
Crack Growth ◽  
Concrete Structures ◽  
Research Paper ◽  
Cohesive Crack ◽  
Multiple Cracks ◽  
System Of Equations ◽  
Nonlinear System Of Equations ◽  
Content Type

Purpose – The purpose of this paper is to achieve numerical simulation of cohesive crack growth in concrete structures. Design/methodology/approach – The extended finite element method (XFEM) using four-node quadrilateral element associated with the fictitious cohesive crack model is used. A mixed-mode traction-separation law is assumed for the cohesive crack in the fracture process zone (FPZ). Enrichments are considered for both partly and fully cracked elements, and it thus makes the evolution of crack to any location inside the element possible. In all. two new solution procedures based on Newton-Raphson method, which differ from the approach suggested by Zi and Belytschko (2003), are presented to solve the nonlinear system of equations. The present formulation results in a symmetric tangent matrix, conveniently in finite element implementation and programming. Findings – The inconvenience in solving the inversion of an unsymmetrical Jacobian matrix encountered in the existing approach is avoided. Numerical results evidently confirm the accuracy of the proposed approach. It is concluded that the developed XFEM approach is especially suitable in simulating cohesive crack growth in concrete structures. Research limitations/implications – Multiple cracks and crack growth in reinforced concretes should be considered in further studies. Practical implications – The research paper presents a very useful and accurate numerical method for engineering application problems that has ability to numerically simulate the cohesive crack growth of concrete structures. Originality/value – The research paper provides a new numerical approach using two new solution procedures in solving nonlinear system of equations for cohesive crack growth in concrete structures that is very convenient in programming and implementation.

A Full-System Approach of the Elastohydrodynamic Line/Point Contact Problem

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
W. Habchi ◽  
D. Eyheramendy ◽  
P. Vergne ◽  
G. Morales-Espejel
Keyword(s):  
Finite Element ◽  
Nonlinear System ◽  
System Approach ◽  
Jacobian Matrix ◽  
Point Contact ◽  
System Of Equations ◽  
Nonlinear System Of Equations ◽  
Full System ◽  
Element Discretization ◽  
Fully Coupled

The solution of the elastohydrodynamic lubrication (EHL) problem involves the simultaneous resolution of the hydrodynamic (Reynolds equation) and elastic problems (elastic deformation of the contacting surfaces). Up to now, most of the numerical works dealing with the modeling of the isothermal EHL problem were based on a weak coupling resolution of the Reynolds and elasticity equations (semi-system approach). The latter were solved separately using iterative schemes and a finite difference discretization. Very few authors attempted to solve the problem in a fully coupled way, thus solving both equations simultaneously (full-system approach). These attempts suffered from a major drawback which is the almost full Jacobian matrix of the nonlinear system of equations. This work presents a new approach for solving the fully coupled isothermal elastohydrodynamic problem using a finite element discretization of the corresponding equations. The use of the finite element method allows the use of variable unstructured meshing and different types of elements within the same model which leads to a reduced size of the problem. The nonlinear system of equations is solved using a Newton procedure which provides faster convergence rates. Suitable stabilization techniques are used to extend the solution to the case of highly loaded contacts. The complexity is the same as for classical algorithms, but an improved convergence rate, a reduced size of the problem and a sparse Jacobian matrix are obtained. Thus, the computational effort, time and memory usage are considerably reduced.

Spatial Kinematic Synthesis of Adaptive Hard-Automation Modules: An RS-SRR-SS Adjustable Spatial Motion Generator

1986 ◽  
Vol 108 (3) ◽  
pp. 292-299 ◽  
Author(s):  
G. N. Sandor ◽  
S. P. Yang ◽  
L. J. Xu ◽  
P. De
Keyword(s):  
Numerical Methods ◽  
Nonlinear System ◽  
Analytical Methods ◽  
Robotic Manipulators ◽  
Optimization Techniques ◽  
System Of Equations ◽  
Spatial Motion ◽  
Nonlinear System Of Equations ◽  
Kinematic Synthesis ◽  
Motion Generator

Purely mechanical, single-actuator adaptive hard-automation modules can perform highly repetitive simple tasks much more economically, energy-efficiently and accurately than multi-degree-of-freedom, multiple-actuator robotic manipulators. As an example, an RS-SRR-SS adjustable spatial motion generator is synthesized by analytical methods with two exact prescribed positions (including orientations) for each of two different motion tasks, by numerical methods to solve a nonlinear system of equations and by optimization techniques to minimize the motion errors at additional, approximately prescribed positions.

Nonlinear System Of Equations For Multicomponent Analysis Of Artificial Food Coloring

2010 ◽  
Author(s):  
I. E. Santosa ◽  
L. K. Budiasih ◽  
Khairurrijal ◽  
Mikrajuddin Abdullah ◽  
Wahyu Srigutomo ◽  
...  
Keyword(s):  
Nonlinear System ◽  
System Of Equations ◽  
Nonlinear System Of Equations ◽  
Multicomponent Analysis ◽  
Artificial Food
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