Second Variations for the Stress Wave Problem Using the Euler-Lagrange and Adjoint Formulations

Abstract

The adjoint system can be arranged in a manner so it is a reflected mirror of the original system in time. Generalized boundary conditions employ many types of springs relating the various spatial partial derivatives. They are defined to satisfy the boundaries of the original and adjoint system relationship for the bilinear expression. Algorithms for use in the finite element method are simplified since the adjoint system gives exactly the same solutions as those of the original system. The second necessary condition for an extremum is satisfied by showing that the second variation of the functional is positive semi-definite.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1984
Accession Number
ADA149716

Entities

People

  • C. N. Shen

Organizations

  • United States Army Armament Research, Development and Engineering Center

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Calculus
  • Calculus Of Variations
  • Differential Equations
  • Engineering
  • Equations
  • Finite Element Analysis
  • Frequency
  • Mathematics
  • Military Research
  • Partial Differential Equations
  • Sensitivity
  • Stress Waves
  • Variational Methods
  • Variational Principles
  • Wave Equations
  • Waves

Readers

  • Control Systems Engineering.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)