Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Volume 112, Issue 7, Pages 655-684Publisher
WILEY
DOI: 10.1002/nme.5519
Keywords
meshfree Galerkin methods; maximum-entropy approximants; numerical integration; virtual element method; patch test; stability
Funding
- National Science Foundation [CMMI-1334783]
- Directorate For Engineering [1334783] Funding Source: National Science Foundation
- Div Of Civil, Mechanical, & Manufact Inn [1334783] Funding Source: National Science Foundation
Ask authors/readers for more resources
Over the past two decades, meshfree methods have undergone significant development as a numerical tool to solve partial differential equations (PDEs). In contrast to finite elements, the basis functions in meshfree methods are smooth (nonpolynomial functions), and they do not rely on an underlying mesh structure for their construction. These features render meshfree methods to be particularly appealing for higher-order PDEs and for large deformation simulations of solid continua. However, a deficiency that still persists in meshfree Galerkin methods is the inaccuracies in numerical integration, which affects the consistency and stability of the method. Several previous contributions have tackled the issue of integration errors with an eye on consistency, but without explicitly ensuring stability. In this paper, we draw on the recently proposed virtual element method, to present a formulation that guarantees both the consistency and stability of the approximate bilinear form. We adopt maximum-entropy meshfree basis functions, but other meshfree basis functions can also be used within this framework. Numerical results for several two-dimensional and three-dimensional elliptic (Poisson and linear elastostatic) boundary-value problems that demonstrate the effectiveness of the proposed formulation are presented. Copyright (c) 2017 John Wiley & Sons, Ltd.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available