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COMPARISON OF THE LINEAR BUCKLING ANALYSIS FOR DIFFERENT THICKNESS OF A FLAT PLATEName : Muhammad bin RamlanMatrix No. : P 57600Subject : Finite Element Method In Civil EngineeringYear : 2011 / 2012Lecturer : Prof Ir Dr Wan Hamidon bin Wan Badaruzzaman Comparison Of The Linear Buckling Analysis For Different Thickness Of A Flat Plate | 1
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Table of Content ITEMS PAGEAbstract 3Introduction 3Objective 3Problem Definition 4Description of Finite Element Method (FEM) 4Description of LUSAS 5Finite Element Modelling 5Result 6Discussion 9Conclusion 9 Comparison Of The Linear Buckling Analysis For Different Thickness Of A Flat Plate | 2
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AbstractThis report investigates the capability of the finite element software LUSAS todeal with buckling analysis for the flat plate material under different materialproperties.It was analysed that different types of material properties will cause differenttypes of buckling effects. From the analysis, a thicker flat plate will provide alarger buckling value. Whilst for a thin flat plate, the buckling value will besmaller.This report allowed me to have a good introduction to this board area ofengineering related to modelling structure under the effect of buckling effect.IntroductionThis project will evaluate on determining the buckling load for a flat plate. Tworectangular panels with sizes of 2 m x 0.5 m is subjected to in-planecompressive loading. The material property for the flat panel includes Poison’sRatio of 0.3 and Young Modulus of 70E9 N/m2.Analyses are conducted by using LUSAS software. The panel is meshed using 64semiloof shell elements and is simply supported on all sides. An in planecompressive load of a total 24 N is applied to of the short edges, parallel to thelong sides. Unit used are N, m, kg, s, C throughout.ObjectiveThe 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. Comparison Of The Linear Buckling Analysis For Different Thickness Of A Flat Plate | 3
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Problem DefinitionA flat panel of various thicknesses is being tested to identify and analyse of thebuckling load. It is anticipated that the difference in thickness of a certainmaterial will influence the buckling load that the material produces. In thisreport, 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 throughoutthis 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 whodeveloped the Ritz method of numerical analysis and minimisation ofvibrational calculus to calculated approximate solutions to vibration systems.He then went on to publish a paper in 1956 which defined in more detail thenumerical analysis. His paper centred on the "stiffness and deflection ofcomplex structures".In the early 70’s the only computers able to carry out Finite Element Analysiswere mainframe computers which were generally owned by such industries asaeronautics, automotive, defence, and nuclear. However the technologicalrevolution of the following decades has seen the rapid decline in the price ofcomputers and huge leaps forward in their processing power. The capabilities Comparison Of The Linear Buckling Analysis For Different Thickness Of A Flat Plate | 4
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of the Finite Element Method are now a far cry from that of the 70s, it is nowcapable of analysing any structure to incredible accuracy.Description of LUSASLUSAS is a finite element analysis software program which can solve all typesof linear and nonlinear stress, dynamics, composite and thermal engineeringanalysis 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 ModellingThe finite element modelling using LUSAS was run as per below:a. Creating a new modelb. Inserting the feature geometryc. Select the meshingd. Specifying the geometric propertiese. Specifying the material propertiesf. Specifying the support appliedg. Select the loading applied to the elementh. Eigenvalue analyst controli. Saving the modelj. Running the Analysisk. Printing the buckling load factorl. Calculating the critical buckling load Comparison Of The Linear Buckling Analysis For Different Thickness Of A Flat Plate | 5
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ResultA. Plate 1 (1mm thickness) Figure 1: Loading Distribution On Plate 1 Figure 2: Deformed Mesh Layers On Plate 1 Comparison Of The Linear Buckling Analysis For Different Thickness Of A Flat Plate | 6
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This model was analysed using three eigenvalue buckling analysis, the loadfactors are equivalent to the eigenvalues. Load factors are the values by whichthe 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 1The applied load (24N) must be multiplied by the first load factor (19.8891) togive the value of loading which causes buckling in the first mode shape. Theinitial buckling load is therefore 24 x 19.8891 = 477.34 N. Same method goesfor the other modes.B. Plate 2 (5mm thickness) Figure 4: Loading Distribution On Plate 2 Comparison Of The Linear Buckling Analysis For Different Thickness Of A Flat Plate | 7
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Figure 5: Deformed Mesh Layers On Plate 2This model was analysed using three eigenvalue buckling analysis, the loadfactors are equivalent to the eigenvalues. Load factors are the values by whichthe 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 2The applied load (24N) must be multiplied by the first load factor (2486.14) togive the value of loading which causes buckling in the first mode shape. Theinitial buckling load is therefore 24 x 2486.14 = 59667.36 N. Same method goesfor the other modes. Comparison Of The Linear Buckling Analysis For Different Thickness Of A Flat Plate | 8
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DiscussionBuckling is a failure mode. Buckling is categorized by a sudden failure of astructural member subjected to high compressive strength, where the actualcompressive stress at the point is less than the ultimate compressive stressthat the material is capable of withstanding.The results of the analysis show that the changes of the flat plate thickness willinfluence the buckling value. The increase of the thickness of the flat plate isparallel towards the increase of the buckling value. Table 1 below shows therelationship 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 63954.00ConclusionFrom the analysis, it shows that the finite element method can be applied tocalculate the complex structural. It is done by segregating the structure tocertain element. It can be concluded that different types of material propertieswill cause different types of buckling effects. From the analysis, a thicker flatplate will provide a larger buckling value. Whilst for a thin flat plate, thebuckling value will be smaller. Comparison Of The Linear Buckling Analysis For Different Thickness Of A Flat Plate | 9
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