Taki FE Spreadsheet 03 - elastica.xls

Figure 1. Types of Beam Structures

Application of MS-Excel "Solver" to Non-linear Beam Analysis

Written by Toshimi Taki Prepared on March 4, 2007

There are some types of beam structures as shown in figure 1.

If beam elements of "simple beam" structures are subject to lateral load only, this type of beam structure shows linear behaviour. "Simple beam" structures can be analysed easily. When beam elements in a beam structure are subject to lateral load and axial load, the structure shows non-linear behaviour. The examples of the non-linear beam problems are beam columns, Elastica and arch structures. Analytical method is applicable only to idealized structures such as uniform cross section beam column. You need to use non-linear finite element analysis to solve non-linear beam structures in real world. I have developed a new method to solve non-linear beam structures. This is a direct application of energy principle using MS-Excel "Solver". Application of MS-Excel "Solver" to Non-linear Beam Analysis "Elastica" is used as an example to show the method. Following figures show the results. For detail of the method, see my paper. Click here to download "Application of MS-Excel 'Solver' to Non-linear Beam Analysis (Rev. A)" (150KB) in pdf file. You need to install add-in tool "Solver" to MS-Excel. This template can be used for the other non-linear beam problems than "Elastica".

Figure 2. Model for Elastica

Figure 3. Result -- Deflection

Figure 4. Result -- Load-Deflection Curve

You may also be interested in a discussion with the author posted in the Site News.

Calculation Reference
Bruhn
Finite Element