Accession Number : AD0700032

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

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : Alspaugh,D. W. ; Kalaba,R.

Report Date : SEP 1969

Pagination or Media Count : 20

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)

Descriptors :   (*BEAMS(STRUCTURAL), BENDING), (*BOUNDARY VALUE PROBLEMS, TRANSFORMATIONS(MATHEMATICS)), (*BOUNDARY VALUE PROBLEMS, NUMERICAL ANALYSIS), PARTIAL DIFFERENTIAL EQUATIONS, NUMERICAL INTEGRATION, DEFLECTION

Subject Categories : Numerical Mathematics
      Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE