This document compares the linear buckling analysis of flat plates with different thicknesses. Two flat plates with thicknesses of 1mm and 5mm were modeled and analyzed using LUSAS finite element software. The results showed that thicker plates had higher buckling loads, with the 5mm plate's buckling load being over 10 times greater than the 1mm plate's load. In conclusion, a plate's thickness directly influences its buckling value, with thicker plates exhibiting higher buckling strengths.

1. COMPARISON OF THE LINEAR
BUCKLING ANALYSIS FOR DIFFERENT
THICKNESS OF A FLAT PLATE
Name : Muhammad bin Ramlan
Matrix No. : P 57600
Subject : Finite Element Method In Civil Engineering
Year : 2011 / 2012
Lecturer : Prof Ir Dr Wan Hamidon bin Wan Badaruzzaman
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2. Table of Content
ITEMS PAGE
Abstract 3
Introduction 3
Objective 3
Problem Definition 4
Description of Finite Element Method (FEM) 4
Description of LUSAS 5
Finite Element Modelling 5
Result 6
Discussion 9
Conclusion 9
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3. Abstract
This report investigates the capability of the finite element software LUSAS to
deal with buckling analysis for the flat plate material under different material
properties.
It was analysed that different types of material properties will cause different
types of buckling effects. From the analysis, a thicker flat plate will provide a
larger buckling value. Whilst for a thin flat plate, the buckling value will be
smaller.
This report allowed me to have a good introduction to this board area of
engineering related to modelling structure under the effect of buckling effect.
Introduction
This project will evaluate on determining the buckling load for a flat plate. Two
rectangular panels with sizes of 2 m x 0.5 m is subjected to in-plane
compressive loading. The material property for the flat panel includes Poison’s
Ratio of 0.3 and Young Modulus of 70E9 N/m2.
Analyses are conducted by using LUSAS software. The panel is meshed using 64
semiloof shell elements and is simply supported on all sides. An in plane
compressive load of a total 24 N is applied to of the short edges, parallel to the
long sides. Unit used are N, m, kg, s, C throughout.
Objective
The objective of this report is to:
a. Analyse the effect of buckling load for a different thickness types of flat
plate subjected to in-plane compressive loading.
b. Discuss the result of the analysis prior to the experiment.
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4. Problem Definition
A flat panel of various thicknesses is being tested to identify and analyse of the
buckling load. It is anticipated that the difference in thickness of a certain
material will influence the buckling load that the material produces. In this
report, a flat panel with the thickness of 1mm and 5mm are to be tested.
The table below are the material properties that are being used throughout
this test:
No. Item Plate 1 Plate 2
1 Plate Size 2 m x 0.5 m 2 m x 0.5 m
2 Plate Thickness 1 mm 5 mm
3 Young Modulus 70E9 N/m2 70E9 N/m2
4 Poisson Ratio 0.3 0.3
5 Support Type Simply supported at all Simply supported at all
sides. sides.
6 Load 24N of in-plane 24N of in-plane
compressive load is compressive load is
applied to one of the applied to one of the
short edges, parallel to short edges, parallel to
the long sides. the long sides.
Description of Finite Element Method (FEM)
Finite Element Analysis was initially developed in 1943 by Richard Courant who
developed the Ritz method of numerical analysis and minimisation of
vibrational calculus to calculated approximate solutions to vibration systems.
He then went on to publish a paper in 1956 which defined in more detail the
numerical analysis. His paper centred on the "stiffness and deflection of
complex structures".
In the early 70’s the only computers able to carry out Finite Element Analysis
were mainframe computers which were generally owned by such industries as
aeronautics, automotive, defence, and nuclear. However the technological
revolution of the following decades has seen the rapid decline in the price of
computers and huge leaps forward in their processing power. The capabilities
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5. of the Finite Element Method are now a far cry from that of the 70s, it is now
capable of analysing any structure to incredible accuracy.
Description of LUSAS
LUSAS is a finite element analysis software program which can solve all types
of linear and nonlinear stress, dynamics, composite and thermal engineering
analysis problems. The main components of the LUSAS are:
a. LUSAS Modeller - a fully interactive graphical user interface for model
building and viewing of results from an analysis.
b. LUSAS Solver - a powerful finite element analysis engine that
carries out the analysis of the problem defined in LUSAS Modeller.
Finite Element Modelling
The finite element modelling using LUSAS was run as per below:
a. Creating a new model
b. Inserting the feature geometry
c. Select the meshing
d. Specifying the geometric properties
e. Specifying the material properties
f. Specifying the support applied
g. Select the loading applied to the element
h. Eigenvalue analyst control
i. Saving the model
j. Running the Analysis
k. Printing the buckling load factor
l. Calculating the critical buckling load
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6. Result
A. Plate 1 (1mm thickness)
Figure 1: Loading Distribution On Plate 1
Figure 2: Deformed Mesh Layers On Plate 1
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7. This model was analysed using three eigenvalue buckling analysis, the load
factors are equivalent to the eigenvalues. Load factors are the values by which
the applied load is factored to cause buckling in the respective modes.
Eigenvalue results for the whole model is as per figure below:
Figure 3: Eigenvalue Result Value for Plate 1
The applied load (24N) must be multiplied by the first load factor (19.8891) to
give the value of loading which causes buckling in the first mode shape. The
initial buckling load is therefore 24 x 19.8891 = 477.34 N. Same method goes
for the other modes.
B. Plate 2 (5mm thickness)
Figure 4: Loading Distribution On Plate 2
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8. Figure 5: Deformed Mesh Layers On Plate 2
This model was analysed using three eigenvalue buckling analysis, the load
factors are equivalent to the eigenvalues. Load factors are the values by which
the applied load is factored to cause buckling in the respective modes.
Eigenvalue results for the whole model is as per figure below:
Figure 6: Eigenvalue Result Value for Plate 2
The applied load (24N) must be multiplied by the first load factor (2486.14) to
give the value of loading which causes buckling in the first mode shape. The
initial buckling load is therefore 24 x 2486.14 = 59667.36 N. Same method goes
for the other modes.
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9. Discussion
Buckling is a failure mode. Buckling is categorized by a sudden failure of a
structural member subjected to high compressive strength, where the actual
compressive stress at the point is less than the ultimate compressive stress
that the material is capable of withstanding.
The results of the analysis show that the changes of the flat plate thickness will
influence the buckling value. The increase of the thickness of the flat plate is
parallel towards the increase of the buckling value. Table 1 below shows the
relationship for both of plate thickness and buckling load.
Table 1 Result of Load Factor Due to Increasing of Plate Thickness
Plate Compressive Buckling Load
Mode Load Factor
thickness Load (N) (N)
1 24 19.8891 477.34
1mm 2 24 21.1524 507.66
3 24 21.318 511.63
1 24 159.113 59667.36
5mm 2 24 169.234 63460.32
3 24 170.544 63954.00
Conclusion
From the analysis, it shows that the finite element method can be applied to
calculate the complex structural. It is done by segregating the structure to
certain element. It can be concluded that different types of material properties
will cause different types of buckling effects. From the analysis, a thicker flat
plate will provide a larger buckling value. Whilst for a thin flat plate, the
buckling value will be smaller.
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