UNIVERSIY OF MHAMED BOUGHERRA BOUMERDESFACULTY OF ENGINEER SCIENCE

Analysis of a cantilever beam with ABAQUS Software

2015/2016 MIS 14

INDEXPresentation of the problemIntroductionSteps of workThe analysisThe monitorWhat are the mode shapes ?The resultsConclusion

Presentation of the problem: The goal of this work is to make an analysis of a canteliver beam subjected to a static load of 120 MPa in order to find the maximal VON MISES stress and the first 10 frequency of mode shape .The beam with dimmensions [ (width )l = 300 mm , e= 150 mm , (depth ) L= 1500 mm ] is made of steel with density of 7500 Kg/m3 Young Modulus E=200 Gpa and poisson ration = 0.3 . Introduction : the analysis is done by a software named abaqus.Abaqus is a finite element analysis software which is designed for modeling a variety of material behavior in both static and dynamic situations. The program has an extensive material behavior library that allows for using data obtained from the testing laboratory to be directly input into the model definition. Abaqus is well suited to solve linear and non linear problems, to model assemblies , Static, dynamic and heat transfer analysis etcThe advantage of ABAQUS is in process optimization, material comparisons, and general forming analysis. This allows for reducing time, effort, and material costs involved with trial and error manufacturing techniques.An other advantage of abaqus is the ability to do a wide variety of analysis such as analysis of acoustic sound waves, failure analysis/fracture mechanics, heat transferetc.

steps of work : the basic steps of work on abaqus are :- The creation of the part geometry and regions for sections.- Define material properties and assign sections to parts.- Create the assembly.- Define analysis steps and output requests. - Define contact and other interactions on regions.- Apply loads and BCs.- Split the part or the assembly into meshable regions and mesh.- Submit manage and monitor analysis job . - examine the results.

Abaqus is a software which doesnt use predifined units , its up to the user to take the responsibility to be sure to use the right units

The analysis:

before begining thie analysis we have to choose the units well use , in this case well work with : mm , Mpa , kgso: density = 7500e-9 kg/mm3 young modulus E= 200e3 Mpa

Below we have pictures of the important steps on this work The draw of the part:

The creation of the properties of the material :

the set of the load and boundary conditions :

the mesh of the part:

the submission of the job analysis:

The monitor:After an eigenfrequency step has been used to find the eigenvalues of a model, Abaqus automatically calculates the participation factor, the effective mass, for each mode so that these variables are available for use in subsequent linear dynamic analysis. The participation factor is a variable that indicates how strongly motion in the globalx-,y- orz-direction or rotation about one of these axes is represented in the eigenvector of that mode If the effective masses of all modes are added in any particular direction, the sum should give the total mass of the model

Lets take a closer look to the monitoring window , we find different outputs , error messages , warnings which helps us to do correctly the analysis , but the most interesting feature in this windows is the DATA File buton Which gives us access to a summarize of all the steps of abaqus analysis And all the results

By opening the Data File we can see that abaqus works on steps :In the begining it calculates the number of elements , nodes and variables of the problem

Then it does the static analysis which is the first step , it calculate the mass of the part , the center of the mass and different moments.

Finally comes the calculation of the frequencies , the participation factor and the effective mass for each mode

What are the mode shapes ?The vibrational modes aren't a property of a particulartypeof material, they are a property of a particularpieceof material, with a particular size and a particular shape, and held in a particular way.Anormal modeof anoscillating systemis a pattern of motion in which all parts of the system movesinusoidallywith the same frequency . The free motion described by the normal modes takes place at the fixed frequencies. These fixed frequencies of the normal modes of a system are known as its natural frequencies orresonant frequencies.

The results :this is the representation of the maximal and minimal von mises stress

The representation of the maximum strain E

Below is the Representation of the displacement for each mode:

We notice that the frequencies are increasing with the increase of the mode shapes. As depicted in the table belowmode Frequency (cycle/time)

1 1.7556

2 3.4286

3 10.525

4 12.732

5 18.504

6 27.323

7 27.742

8 38.315

9 44.152

10 50.385

Conclusion: The results of our study are acceptable and usable with no fear . In a general point of view Abqus is an amazing software with notable capacities but it has also some lacks which may appear in certain case like the obligation of simplifying the study specially in the creation of models and the mesh. Or the impossibility of going backward from a dynamic study to a static one.