Finite Elements for Initial Value Problems in Dynamics

Abstract

The work of C. D. Bailey amply demonstrates that a variational principle is not a necessary prerequisite for the formulation of variational approximations to initial value problems in dynamics. While Bailey successfully applies global power series approximations to Hamilton's Law of Varying Action, the work herein shows that a straightforward extension to finite element formulations fails to produce a convergent sequence of solutions. The source of the difficulties and their elimination are discussed in some detail and a workable formulation for initial value problems is obtained. The report concludes with a few elementary examples showing the utility of finite elements in the time domain.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1980
Accession Number
ADA095344

Entities

People

  • T. E. Simkins

Organizations

  • United States Army Armament Research, Development and Engineering Center

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Boundary Value Problems
  • Calculus Of Variations
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Programming
  • Computers
  • Differential Equations
  • Engineering
  • Equations
  • Finite Element Analysis
  • Mechanical Properties
  • Mechanics
  • Numerical Analysis
  • Power Series
  • Security
  • Time Domain
  • Variational Principles

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Systems Analysis and Design