Open Access
Computer Methods in Applied Mechanics and Engineering
Reads0
Chats0
TLDR
In this article, a cubic Hermite collocation scheme for the solution of the coupled integro-partial differential equations governing the propagation of a hydraulic fracture in a state of plane strain is described.Abstract:
article i nfo We describe a novel cubic Hermite collocation scheme for the solution of the coupled integro-partial differential equations governing the propagation of a hydraulic fracture in a state of plane strain. Special blended cubic Hermite-power-law basis functions, with arbitrary index 0b αb1, are developed to treat the singular behavior of the solution that typically occurs at the tips of a hydraulic fracture. The implementation of blended infinite elements to model semi-infinite crack problems is also described. Explicit formulae for the integrated kernels associated with the cubic Hermite and blended basis functions are provided. The cubic Hermite collocation algorithm is used to solve a number of different test problems with two distinct propagation regimes and the results are shown to converge to published similarity and asymptotic solutions. The convergence rate of the cubic Hermite scheme is determined by the order of accuracy of the tip asymptotic expansion as well as the O(h 4 ) error due to the Hermite cubic interpolation. The errors due to these two approximations need to be matched in order to achieve optimal convergence. Backward Euler time-stepping yields a robust algorithm that, along with geometric increments in the time-step, can be used to explore the transition between propagation regimes over many orders of magnitude in time.read more
Citations
More filters
Dissertation
Implementation of isogeometric thin shell analysis within an object oriented computing environment
TL;DR: The purpose of this thesis is to implement the isogeometric rotation-free Kirchhoff-Love thin shell element proposed by Kiendl et al. for both geometrically linear and nonlinear analyses within an object-oriented environment and yielded a coherence with the reported results in relevant scientific publications.
Experimental and Numerical Investigation of Warm Deep Drawing Process of AA5052 Aluminum Alloy
TL;DR: In this paper, warm deep drawing (WDD) of AA5052-O aluminum alloy sheets with a thickness of 1mm was investigated at different forming temperatures of 25, 80, 160, and 240°C (in the two isothermal and nonisothermal conditions) and punch speeds of 260, 560 and 1950 mm min-1 using experimental tests and finite elements simulation.
Dissertation
Stress tensor symmetry preserving model applied to the 2-D viscoelastic flow of a biofilm
Proceedings ArticleDOI
Effect of molecular models on viscosity and thermal conductivity calculations
Andrew B. Weaver,Alina Alexeenko +1 more
TL;DR: In this article, the effect of molecular models on viscosity and thermal conductivity calculations is investigated using Direct Simulation Monte Carlo (DSMC) method for rarefied gas flows.
Journal ArticleDOI
Failure Analysis in Conceptual Phase toward a Robust Design: Case Study in Monopropellant Propulsion System
TL;DR: A framework to design a complex engineered system resistant against various factors that may cause failures, when design process is in the conceptual phase and information about detailed system and component is unavailable is presented.
References
More filters
Book
An Introduction to Fluid Dynamics
TL;DR: The dynamique des : fluides Reference Record created on 2005-11-18 is updated on 2016-08-08 and shows improvements in the quality of the data over the past decade.
Book
A practical guide to splines
TL;DR: This book presents those parts of the theory which are especially useful in calculations and stresses the representation of splines as linear combinations of B-splines as well as specific approximation methods, interpolation, smoothing and least-squares approximation, the solution of an ordinary differential equation by collocation, curve fitting, and surface fitting.
Numerical solution of boundary value problems for ordinary differential equations
TL;DR: In this article, the Riccati method is used to solve boundary value problems for Ordinary Differential Equations and to solve nonlinear problems for BVPSs in the standard form.
Book
Numerical solution of boundary value problems for ordinary differential equations
TL;DR: This book discusses Consistency, Stability, and Convergence higher-Order One-Step Schemes Collocation Theory Acceleration Techniques Higher-Order ODEs Finite Element Methods and Initial Value Methods.
Related Papers (5)
An improved uniformly convergent scheme in space for 1D parabolic reaction-diffusion systems
C. Clavero,José Luis Gracia +1 more