Research Article
Oct 1963
Eigen-Matrix Method for Beams and Plates
This article has a reply.
VIEW THE REPLYThis article has a reply.
VIEW THE REPLYThis article has a reply.
VIEW THE REPLYPublication: Journal of the Structural Division
Volume 89, Issue 5
Abstract
A new, powerful approach to the problem of the bending of beams and plates is presented. Beginning with a certain form of expression for the deflection, the entire analysis procedure is derived from matrix algebra. This expression has as its basis a 4×4 square matrix, which is characteristic of the system considered, and which can be referred to the eigen-matrix. It can be stated, therefore, that the eigen-matrix is the solution for the system. Because of the fourth degree of governing differential equations for beams and plates, the eigen-matrix is in substance a 4×4 square matrix, and is frequently subdivided into 2×2 or 2×4 submatrices. This degree, which is higher than that in the theory of electricity, will derive an increased efficiency in computations. The last step of the individual examples leads to the treatment of the inverse of a 2×2 square matrix. Simultaneous equations of many unknowns can then be dispensed with, so that the analytical computation necessary is simplified.
Get full access to this article
View all available purchase options and get full access to this article.
Information & Authors
Information
Published In
Journal of the Structural Division
Volume 89 • Issue 5 • October 1963
Pages: 173 - 215
Copyright
© 1963 American Society of Civil Engineers.
History
Published in print: Oct 1963
Published online: Feb 1, 2021
Permissions
Request permissions for this article.
Authors
Affiliations
Bennosuke Tanimoto
Faculty of Engrg., Shinshu Univ., Nagano, Japan
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
View Options
Get Access
Access content
Please select your options to get access
Log in/Register
Log in via your institution (Shibboleth)
ASCE Members:
Please log in to see member pricing
Purchase
Save for later Item saved, go to cart Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
Get Access
Access content
Please select your options to get access
Log in/Register
Log in via your institution (Shibboleth)
ASCE Members:
Please log in to see member pricing
Purchase
Save for later Item saved, go to cart Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.