B and F Projection Methods for Nearly Incompressible Linear and Nonlinear Elasticity and Plasticity using Higher-order NURBS Elements

Abstract

This paper presents projection methods to treat the incompressibility constraint in small and large deformation elasticity and plasticity within the framework of Isogeometric Analysis. After reviewing some fundamentals of isogeometric analysis we investigate the use of higher-order Non-Uniform Rational B-Splines "NURBS" within the B projection method. The higher-continuity property of such functions is explored in nearly incompressible applications and shown to produce accurate and robust results. A new nonlinear F projection method, based on a modified minimum potential energy principle and inspired by the B method is proposed for the large-deformation case. It leads to a symmetric formulation for which the consistent linearized operator for fully nonlinear elasticity is derived and used in a Newton-Raphson iterative procedure. The performance of the methods is assessed on several numerical examples, and results obtained are shown to compare favorably with other published techniques.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 2007
Accession Number
ADA478643

Entities

People

  • T. Elguedj
  • Thomas J.R. Hughes
  • V. M. Calo
  • Yuri Bazilevs

Organizations

  • University of Texas at Austin

Tags

Communities of Interest

  • Air Platforms
  • Space

DTIC Thesaurus Topics

  • Boundary Value Problems
  • Compression
  • Computational Fluid Dynamics
  • Computational Science
  • Computer-Aided Design
  • Continuity
  • Elastic Properties
  • Energy
  • Equations
  • Finite Element Analysis
  • Fluid Mechanics
  • Geometry
  • Incompressibility
  • Materials
  • Mechanics
  • Potential Energy
  • Three Dimensional

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)