finite element analysis i - search - university of …staff.um.edu.mt/martin.muscat/lecture...

MEC 3500 - FINITE ELEMENT ANALYSIS ICredits: 4Lectures/Tut.: 2hr/wkLabs: 3 sessionsPrerequisite: MEC 2401, MEC 3402Leads to: MEC 4405

SyllabusPart 1 (Exam – 50%):

Introduction to the theory of the finite element method – discretization of the problem, elements and nodes, general approximations, symmetry and boundary conditions

Interpolation functions for different type of elements – 1-2-3 dimensional elements

Formulation and solution of the finite element system equations for elasticity problems, 1-2-3 dimensional elements, the axisymmetric case.

Part 2 (Continuous assessment - 50%):

Introduction to commercial finite element programs – pre-processing, material non-linearity, geometric non-linearity, buckling problems, transient response problems, mesh generation, model validation, boundary conditions, loading, solving the system equations, post-processing.

Practical examples in 1-2-3 dimensional problems in stress analysis, heat transfer, fluid mechanics, dynamics.

AssessmentExam 50%Continuous assessment 50%Reference texts:Finite element analysis, theory and practice – M.J.FaganFinite element analysis, theory and application with Ansys – S.MoaveniBasic principles of the finite element method – K.M.EntwistleConcepts and applications of finite element analysis – R.D.Cook, D.S.Malkus, M.E.PleshaThe finite element method, volumes 1,2,3 – O.C.Zienkiewicz, R.L.Taylor

FEA 1 – Dr Martin Muscat 2003 © - Lecture 1 1

LECTURE 1 INTRODUCTION

WHAT IS FINITE ELEMENT ANALYSIS ?

A MATHEMATICAL TOOL TO SOLVE PROBLEMS

STRUCTURAL HEAT TRANSFER FLUIDS DYNAMICS ELECTROMAGNETIC ELECTRICAL CIRCUITS


A NUMERICAL TECHNIQUE - THERE ARE SOME APPROXIMATIONS INVOLVED IN THE SOLUTIONS

IN F.E.A. THE ACCURACY OF THE SOLUTION DEPENDS ON THE WAY THE OBJECT IS MODELLED MATHEMATICALLY

TYPE OF ELEMENT LOADING BOUNDARY CONDITIONS

WHAT IS REQUIRED TO USE FINITE ELEMENT ANALYSIS ?

SOUND ENGINEERING KNOWLEDGE

PROPER UNDERSTANDING OF THE PROBLEM


IN THIS PART OF THE MODULE :

WE WILL PUT PARTICULAR EMPHASIS ON THE PRACTICAL SIDE OF F.E.A.

WE WILL NOT BE PROGRAMMING F.E.A. FROM SCRATCH BUT WILL BE USING ANSYS AS OUR F.E.A. PACKAGE

NO NOTES – JUST PAY ATTENTION IN CLASS

TEXTBOOK – Finite element analysis – Theory and Practice – M.J.Fagan

ANSYS help files


GOOD IDEA TO READ THE TEXTBOOK BEFORE ATTENDING CLASS

AN ENGINEERING PROBLEM (e.g. Beam under bending) NORMALLY REQUIRES FINDING THE DISTRIBUTION OF AN UNKNOWN VARIABLE – Temperature, Displacement, stresses, etc.

MAIN STEPS IN F.E.A.

1. DISCRETISATION OF THE PROBLEM

Divide the model into elements – different type of elements (solid/beam/plate)

Elements are connected at nodes – we must have an appropriate number and an appropriate distribution of elements

The unknown variable is assumed to act over each element in a predefined manner


– linear element v.s. quadratic element – this leads to step 2

2. SELECTION OF THE APROXIMATING FUNCTION (e.g. for the displacement)

In ANSYS we have elements of different order for each type (solid/beam/plate) of element.

3. APPLY LOADS AND BOUNDARY CONDITIONS

4. SET UP THE SYSTEM EQUATION – GENERALLY IT IS OF THE FORM [K]{u}={F} [K] is the stiffness matrix {u} is the vector of unknowns {F} is the vector of applied

nodal forces


5. SOLVE THE SYSTEM EQUATION to obtain the unknown variables at each node – In ANSYS we have a choice of different solvers

6. CALCULATE THE DERIVED VARIABLES – strains, stresses, heat flow

STEPS 1TO 4 – PRE-PROCESSINGSTEP 5 – SOLUTIONSTEP 6 – POSTPROCESSING

SAMPLE ANALYSIS2-D CANTILEVER – Solid elements, beam elements


HELP FILE

TOURAnsys Command Reference – Explain some commands for keypoints, lines, volumes, etc – show equivalent in menu system – use them to build a model.Ansys Element Reference – Go through ‘Element input’, ‘Solution output’, ‘Co-ordinate systems’ folders & explain all terms there.Element pictorial summary – go through some elements


THE HELP FILES ARE YOUR CONTINUOUS POINT OF REFERENCE WHEN USING ANSYS

YOU CAN USE THE MENU SYSTEM OR THE COMMAND SYSTEM

TO LEARN, START WITH THE MENU SYSTEM BUT FOR CLASS TESTS IT IS COMPULSARY TO USE THE COMMAND LINE

WORK TO DO: READ THE OPERATIONS GUIDE

(1.5 hrs)FEA 1 – Dr Martin Muscat 2003 © - Lecture 1 9

THE BASIC ANALYSIS PROCEDURE GUIDE (5 hrs)

THE IDEA IS TO GET AN OVERVIEW OF WHAT CAN BE DONE – DO NOT GO INTO TOO MUCH DETAIL. – TRY TO READ 1 HOUR EACH DAY UNTIL THE NEXT LAB SESSION

Next lecture ask me on any difficulties – we will then start on examples.

Contact Lab officer to get user account so that you can start working from today.

7 lab sessions – 14 hours7 class lectures – 14 hours1 group assignment -10% - 10 hours3 tests – 40% - 26 hours private study1 theoretical exam – 50% - 36 hours private study


SOME MORE INSTRUCTIONS :

ANSYS CREATES A NUMBER OF FILES WHILE IT IS BEING USED

IT IS BEST TO MAKE ANSYS WORK IN THE TEMP DIRECTORY OF YOUR WORKSTATION

TEMP HAS READ & WRITE PERMISSIONS FOR ALL USERS.

CREATE A SUBDIRECTORY WITHIN THE TEMP FOLDER.

CHANGE THE WORKING DIRECTORY FROM THE ANSYS LAUNCHER TO YOUR


DIRECTORY IN THE TEMP FOLDER.

WHEN YOU HAVE FINISHED WORKING IN THE TEMPORARY DIRECTORY MOVE ALL IMPORTANT FILES TO YOUR HOME DIRECTORY ON THE SERVER

KEEP A BACKUP OF THE INPUT TEXT FILE ON FLOPPY DISCS.

NORMALLY YOU DO NOT NEED THE FOLLOWING FILES AND YOU CAN REMOVE THEM TO SAVE SOME DISK SPACE:file.err – error & warning messagesfile.tri – triangularized stiffness

matrixFEA 1 – Dr Martin Muscat 2003 © - Lecture 1 12

file.esav – element matricesetc….

RUN THE FOLLOWING EXAMPLES AND TRY TO BECOME FAMILIAR WITH THE APDL COMMANDS USED.

I ENCOURAGE YOU TO EXPLORE DIFFERENT OPTIONS AVAILABLE IN THE POSTPROCESSOR IN ORDER TO VIEW RESULTS.

ADVENTOUROUS STUDENTS CAN CHANGE THE GEOMETRY, BOUNDARY CONDITIONS AND LOADING AS THEY WISH OR ELSE CARRY OUT SOME DIFFERENT PROBLEM THAT THEY CAN THINK ABOUT


EXAMPLE 1 – Cantilever using beam elements/prep7 !enter preprocessor

!

!Parameter definition

E=200E3 !Young's modulus

NU=0.3 !Poisson's ratio

length=1000

depth=100

area=depth*1

izz=1*depth*depth*depth/12

force=-650

!

!Choose element type - plane stress unit thickness

et,1,beam3

r,1,area,izz,depth

ex,1,e

nuxy,1,nu

!

! Build f.e.model of cantilever

k,1,0,0

k,2,length,0

l,1,2

lesize,1,,,10

lmesh,all

!

!Apply boundary conditions & load

nsel,s,loc,x,0

d,all,all,0

nsel,s,loc,x,length

f,all,fy,force

nsel,all

!

/solu

solve

!

/post1


!

!plot bending moment diagram

etable,imoment,smisc,6

etable,jmoment,smisc,12

plls,imoment,jmoment

!

!plot bending stress variation at top surface

etable,imaxbs,ls,2

etable,jmaxbs,ls,5

plls,imaxbs,jmaxbs

EXAMPLE 2 – Cantilever using 2-D solid elements/prep7 !enter preprocessor

!




length=1000

depth=100

force=-650

!


et,1,plane82

ex,1,e

nuxy,1,nu

!


k,1,0,0

k,2,length,0

k,3,length,depth

k,4,0,depth

l,1,2

l,2,3

l,3,4


l,4,1

al,1,2,3,4

lesize,2,,,8

lesize,4,,,8

lesize,1,,,20

lesize,3,,,20

amesh,all

!


nsel,s,loc,x,0

d,all,all,0

nsel,s,loc,x,length

nsel,r,loc,y,depth/2

f,all,fy,force

nsel,all

!

/solu

solve

EXAMPLE 3 – Point load acting on plate/prep7 !enter preprocessor

!




width=200

hlength=500

force=-100

!


et,1,plane82

ex,1,e

nuxy,1,nu

!



k,1,0,0

k,2,width,0

k,3,width,hlength

k,4,0,hlength

l,1,2

l,2,3

l,3,4

l,4,1

al,1,2,3,4

! The following lines can be used to vary the mesh density and do a mesh convergence! study!lesize,2,,,32

!lesize,4,,,32

!lesize,1,,,18

!lesize,3,,,18

amesh,all

!


nsel,s,loc,y,0

d,all,uy,0

nsel,s,loc,y,hlength

nsel,r,loc,x,width/2

f,all,fy,force

nsel,all

!

/solu

solve


finite element analysis i - search - university of …staff.um.edu.mt/martin.muscat/lecture...

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