P57600 Lusas Report

Comparison Of The Linear Buckling Analysis For Different Thickness Of A Flat Plate | 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


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


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.


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

sides. Simply supported at all sides.

6 Load 24N of in-plane compressive load is applied to one of the short edges, parallel to the long sides.

24N of in-plane compressive load is applied to one of the short edges, parallel to 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


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


Result

A. Plate 1 (1mm thickness)

Figure 1: Loading Distribution On Plate 1

Figure 2: Deformed Mesh Layers On Plate 1


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


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.


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 thickness

Mode Compressive

Load (N) Load Factor

Buckling Load (N)

1mm 1 24 19.8891 477.34 2 24 21.1524 507.66 3 24 21.318 511.63

5mm 1 24 159.113 59667.36 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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P57600 Lusas Report