A demonstration of the application 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. This 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. 19 pp. Refs. (KB)
This report is part of the RAND Corporation Research memorandum series. The Research Memorandum was a product of the RAND Corporation from 1948 to 1973 that represented working papers meant to report current results of RAND research to appropriate audiences.
This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit www.rand.org/pubs/permissions.
The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.