DIRECT DERIVATION OF THE INVARIANT IMBEDDING EQUATIONS FOR BEAMS FROM A VARIATIONAL PRINCIPLE,

Abstract

The report describes the use of invariant imbedding techniques to a problem involving the equilibrium configuration of a beam. The equilibrium configuration of a beam supporting a distributed load, free at one end and clamped at the other, is characterized by a minimum of potential energy. Using the traditional reasoning leads to the formulation of an unstable two-point boundary-value problem for a fourth-order Euler equation. The Memorandum shows that the solution of the minimization problem can be characterized by an initial-value problem. Relationships between the set of invariant imbedding equations and the Euler equations are described. An analytic solution to a simple problem is given to demonstrate the technique. (Author)

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1969
Accession Number
AD0700032

Entities

People

  • D. W. Alspaugh
  • Robert E. Kalaba

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Energy
  • Equations
  • Euler Equations
  • Mathematics
  • Potential Energy
  • Reasoning
  • Variational Principles

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Structural Dynamics.