
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 twopoint boundaryvalue problem for a fourthorder Euler equation. The Memorandum shows that the solution of the minimization problem can be characterized by an initialvalue 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