## Structural Analysis

## Application of MS-Excel "Solver" to Buckling Analysis of Thin Walled Structures

Written by Toshimi Taki

Prepared on January 25, 2014

Revised on February 8, 2014

**Introduction**

I developed an MS-Excel template for analysis of elastic buckling stress of thin-walled structures. Examples of thin-walled structures are shown in figure 1. The structures are simply supported at both ends and subjected to the edge compression loads.

Figure 1. Examples of Thin-Walled Structures Loaded in Compression

**Application of MS-Excel "Solver" to Elastic Buckling Analysis of Thin-Walled Structures**

The modelling is based on finite strip analysis. The structure is devided into strips as shown in figure 2. The elastic stiffeness matrix and the geometric stiffeness matrix of each element are calculated. A set of deflection of grid points is assumed and the strain energy and the work done by external force of each element is calculated and summed for whole structure. Then, Rayleigh quotient (total strain energy devided by total work done by external force) is calculated. "Solver" is used to minimize the Rayleigh quatient to obtain buckling load (eigen value) and buckling mode.

Figure 2. Finite Strip Model

**MS-Excel Template for Elastic Buckling Analysis of Thin-Walled Structures**

Click here to download MS-Excel template "buckling_20140208.xlsx" (121KB).

You need to install add-in tool "Solver" to MS-Excel.

The example in the template is shown in figures 3 and 4.

Figure 3. Example -- Finite Strip Model for Z-Stiffened Panel

Figure 4. Result -- Buckling Deformation

**Buckling Load Comparisons with Reference**

Buckling loads of Channel section beam and Z-stiffened panel are analyzed by the present method and compared with the results by Notemboom [1].

Reference [1]: R. P. Notemboom, "Finite Strip Elements in Thin OPlate Buckling Amalysis," Report LR-642, Delft University of Technology, 1990.

(1) Channel Section Under Compression

Figure 5 shows section of channel with inward lips. Figure 6 shows buckling load comparison.

Figure 5. Section of Channel with Inward Lips

Figure 6. Buckling Load Comparison of Channel Under Compression

(2) Buckling Load Compression of Z-Stiffened Panel Under Compression

Figure 7 shows comparison with the buckling stress of Z-stiffened panel analyzed by Notenboom [1].

Figure 7. Buckling Load of Z-Stiffened Panel Under Compression