FINITE ELEMENT ANALYSIS I



MEC 3500 - FINITE ELEMENT ANALYSIS I

Credits: 4

Lectures/Tut.: 2hr/wk

Labs: 3 sessions

Prerequisite: MEC 2401, MEC 3402

Leads to: MEC 4405

Syllabus

Part 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.

Assessment

Exam 50%

Continuous assessment 50%

Reference texts:

Finite element analysis, theory and practice – M.J.Fagan

Finite element analysis, theory and application with Ansys – S.Moaveni

Basic principles of the finite element method – K.M.Entwistle

Concepts and applications of finite element analysis – R.D.Cook, D.S.Malkus, M.E.Plesha

The finite element method, volumes 1,2,3 – O.C.Zienkiewicz, R.L.Taylor

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-PROCESSING

STEP 5 – SOLUTION

STEP 6 – POSTPROCESSING

SAMPLE ANALYSIS

2-D CANTILEVER – Solid elements, beam elements

| |[pic] | |

| |HELP FILE TOUR | |

Ansys 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)

➢ 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 hours

7 class lectures – 14 hours

1 group assignment -10% - 10 hours

3 tests – 40% - 26 hours private study

1 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 messages

file.tri – triangularized stiffness matrix

file.esav – element matrices

etc….

• 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

!

!Parameter definition

E=200E3 !Young's modulus

NU=0.3 !Poisson's ratio

length=1000

depth=100

force=-650

!

!Choose element type - plane stress unit thickness

et,1,plane82

ex,1,e

nuxy,1,nu

!

! Build f.e.model of cantilever

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

!

!Apply boundary conditions & load

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

!

!Parameter definition

E=200E3 !Young's modulus

NU=0.0 !Poisson's ratio

width=200

hlength=500

force=-100

!

!Choose element type - plane stress unit thickness

et,1,plane82

ex,1,e

nuxy,1,nu

!

! Build f.e.model of cantilever

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

!

!Apply boundary conditions & load

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

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download