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.
Our mission to help improve policy and decisionmaking through research and analysis is enabled through our core values of quality and objectivity and our unwavering commitment to the highest level of integrity and ethical behavior. To help ensure our research and analysis are rigorous, objective, and nonpartisan, we subject our research publications to a robust and exacting quality-assurance process; avoid both the appearance and reality of financial and other conflicts of interest through staff training, project screening, and a policy of mandatory disclosure; and pursue transparency in our research engagements through our commitment to the open publication of our research findings and recommendations, disclosure of the source of funding of published research, and policies to ensure intellectual independence. For more information, visit www.rand.org/about/research-integrity.
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.