computer program fem2d(ch13).ppt - tamu...

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The Finite Element MethodComputer Program FEM2D

Read: Chapter 13CONTENTS

Logical units of a FEM2D program Flow chart of a typical processor

unit Element calculations Computer program FEM2D Input data to FEM2D Example problem for FEM2D

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LOGICAL UNITS OF FEM2D

Computer Program FEM2DF15: 3JN Reddy

3JN Reddy

FEM2D Program FLOWCHART

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FEM2D Program DATA INPUT

(13.4.2)(13.4.3)

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FEM2D Program DATA INPUT

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FEM2D Program DATA INPUT

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FEM2D Program DATA INPUT

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FEM2D Program DATA INPUTCards 5-7 are read only when you give the mesh information

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FEM2D Program DATA INPUTCards 8-11 are read only when mesh is generated for complicated domains.

FEM2D Program DATA INPUT

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FEM2D Program DATA INPUT

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Cards 12-14 are read only when mesh is generated for rectangular domains.

Cards 15 and 16 are read for all problems

FEM2D Program DATA INPUT

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Cards 17-20 are NOT read for eigenvalue problems

FEM2D Program DATA INPUT

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Cards 21-23 are read for all problems

FEM2D Program DATA INPUT

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INOD(I,J) – Array of the local node numbers of the side

FEM2D Program DATA INPUT

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Card 28 is only readfor viscous flow problems of Chapter 10

Cards 29 and 30 areread only elasticity problems of Ch. 11

FEM2D Program DATA INPUT

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Card 31 is read only for plate bending problems of Chapter 12

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FEM2D Program DATA INPUT

Card 32 is read for all problems EXCEPT for eigenvalue problems

Card 33 is read for time-dependent and eigenvalue problems

FEM2D Program DATA INPUT

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Cards 34-37 are read for only time-dependent problems

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FEM2D Program DATA INPUT

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TO RUN THE EXECUTABLE PROGRAM FEM2D.EXE

Executable Computer Programs from the book, AnIntroduction to the Finite Element Method by J. N. Reddy,3rd ed., McGraw--Hill, 2006.

Notes:Programs FEM1D and FEM2D are a revised versions of theprograms from the second edition of the book. The revisions areminor. Both FEM1D and FEM2D were compiled using theMicrosoft Fortran compiler, with a fixed array dimensions.Hence, only a limited size problem can be analyzed using thecompiled versions of the programs. The programs were compiledwith a maximum number of degrees of freedom of 2,500. If yourcomputer has the storage and you have the source programs, youmay recompile the program after changing the DIMENSIONstatements in the programs.

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TO RUN THE EXECUTABLE PROGRAM FEM2D.EXE

To run a program on a PC, the files should be downloaded to your PCinto a folder (say, FEM_Reddy). The user is required to prepare a datafile for each problem he or she wants to solve, using the instructions inTable 7.3.2 for FEM1D and Table 13.4.1 for FEM2D. Most errors aremistakes made in the preparation of the data files. Therefore, you mustcheck the data files when you see 'run-time error' message or theprogram is not executed (by returning just the echo of the input datafile). All files should be in the same folder where FEM1D.EXE andFEM2D.EXE are placed.

To run the program: Double click on the executable file (say, FEM2D.EXE).

A window (called Command Prompt window) will pop open (withwhite letter and black background). It will read

File name missing or blank – please enter file nameUNIT 5?

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TO RUN THE EXECUTABLE PROGRAM FEM2D.EXE

Type the input file name (with its extension) and press Enter. Forexample, if the file name you prepared is labeled as Prob1.inp, youmay type it as prob1.inp (not case sensitive). The Command Promptwindow will now display

File name missing or blank – please enter file nameUNIT 6?

Type the output file name (with its extension) and press Enter. Forexample, if you want the computer to return the output to fileProb1.out, you may type it as prob1.out. Note that you do not preparethis file; it will be created by the computer. The Command Promptwindow will disappear, indicating that it has taken the data file andexecuted the program. You will find the file prob1.out in the samefolder where you are running the program. Depending on the resultsyou see, you may have to correct the data file.

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1 2 3

6

9

1 1

1

1 2

3 4

x

y

A = 1

A = 1

u = 0

0=∂∂−=

∂∂=

yu

nuqn

4

0nuqx

¶= - =

¶ u = 0

7 8

5

●●

●

● ● ●

● ●

●

2

11 22 00

1 in a square of 2 units( 1, 0, ( ) 1)

ua a a f x

- == = = =

Example 1: Example 8.3.1 of the book

Problem Type, ITYPE = 0; steady-state, ITEM = 0; NEIGN = 0Gradient computation is for heat transfer-like Problems, i.e., compute the x and y-components of the flux vector (IGRAD = 1)

11 22,x yu uq a q ax y

¶ ¶= - = -

¶ ¶

Problem description

FEM Mesh and boundary conditions

2 x 2 mesh of linear rectangular elementsNX = NY = 2; IELTYP = 1; NPE = 4; MESH = 1X0 = Y0 = 0.0; DX(1) = 0.5, DX(2) = 0.5

DY(1) = 0.5, DY(2) = 0.5NSPV = 5, Global nodes 3, 6, 7, 8, and 9 have specified PVs with specified values being zeros; no convection

Quadrant model

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Ex 8.3.1: Solution of the Poisson equation on a square domain (quadrant)0 1 0 0 ITYPE,IGRAD,ITEM,NEIGN1 4 1 0 IELTYP,NPE,MESH,NPRNT2 2 NX,NY0.0 0.5 0.5 X0,DX(I)0.0 0.5 0.5 Y0,DY(I)5 NSPV3 1 6 1 7 1 8 1 9 1 ISPV(I,J)0.0 0.0 0.0 0.0 0.0 VSPV(I)0 NSSV1.0 0.0 0.0 A10, A1X, A1Y1.0 0.0 0.0 A20, A2X, A2Y0.0 A000 ICONV1.0 0.0 0.0 F0, FX, FY

Example 1: Example 8.3.1 of the bookINPUT DATA to FEM2D

2

11 22 00

0

( 1, 1, 0)

u ut

c a a a

¶- =

¶= = = =

Example 2: Find the eigenvalues of the problem in Example 1

Problem Type, ITYPE = 0; IGRAD = 0 Eigenvalue analysis, ITEM = 1; NEIGN = 1

Problem description

FEM Mesh and boundary conditions

4 x 4 mesh of linear rectangular elementsNX = NY = 4; IELTYP = 1; NPE = 4; MESH = 1X0 = Y0 = 0.0; DX(1) = 0.5, DX(2) = 0.5,DX(3) = 0.5, DX(4) = 0.5, DY(1) = 0.5, DY(2) = 0.5, DY(3) = 0.5, DX(4) = 0.5NSPV = 16, Global nodes on the boundaryhave specified homogeneous PVs.

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6 10

1 3 4

15

25

1 x

y A = 2

u = 0

16 20

11

21

u = 0

0u =

A = 29

1 2 3 4

8

12

5

1613

13

8

18

0u =

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Example 2: Eigenvalues of the Poisson equation on a square domain (full)0 1 1 1 ITYPE,IGRAD,ITEM,NEIGN9 1 NVALU, NVCTR1 4 1 0 IELTYP,NPE,MESH,NPRNT4 4 NX,NY0.0 0.5 0.5 0.5 0.5 X0,DX(I)0.0 0.5 0.5 0.5 0.5 Y0,DY(I)

16 NSPV1 1 2 1 2 1 4 1 5 16 1 10 1 11 1 15 1 16 1

20 1 21 1 22 1 23 1 24 1 25 1 ISPV(I,J)1.0 0.0 0.0 A10, A1X, A1Y1.0 0.0 0.0 A20, A2X, A2Y0.0 A000 ICONV1.0 0.0 0.0 C0, CX, CY

Example 2: INPUT DATA to FEM2D

2

11 22 00

0

( 1, 1, 0)

u ut

c a a a

¶- =

¶= = = =

Example 3: Find the transient response of the problem in Example 1

Problem Type, ITYPE = 0; IGRAD = 0 Transient analysis, ITEM = 1; NEIGN = 1

Problem description

FEM Mesh and boundary conditions

4 x 4 mesh of linear rectangular elementsNX = NY = 4; IELTYP = 1; NPE = 4; MESH = 1X0 = Y0 = 0.0; DX(1) = 0.25, DX(2) = 0.25,DX(3) = 0.25, DX(4) = 0.25, DY(1) = 0.25, DY(2) = 0.25, DY(3) = 0.25, DX(4) = 0.25NSPV = 16, Global nodes on the boundaryhave specified homogeneous PVs.

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6 10

1 3 4

15

25

1 x

y1

u = 0

0=∂∂−=

∂∂=

yu

nuqn

16 20

11

21

u = 0

0=∂∂−

xu

19

1 2 3 4

8

12

5

1613

13

8

18

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Example 8.6.3: Transient analysis of an parabolic equation (membrane) 0 0 1 0 ITYPE,IGRAD,ITEM,NEIGN 1 4 1 0 IELTYP,NPE,MESH,NPRNT 4 4 NX,NY 0.0 0.25 0.25 0.25 0.25 X0,DX(I) 0.0 0.25 0.25 0.25 0.25 Y0,DY(I) 9 NSPV 5 1 10 1 15 1 20 1 21 1 22 1 23 1 24 1 25 1 ISPV 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 VSPV 0 NSSV 1.0 0.0 0.0 A10, A1X, A1Y 1.0 0.0 0.0 A20, A2X, A2Y 0.0 A00 0 ICONV 0.0 0.0 0.0 F0, FX, FY 1.0 0.0 0.0 C0, CX, CY

Example 3: INPUT DATA to FEM2D

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100 101 1 1 NTIME,NSTP,INTVL,INTIAL 0.025 0.5 0.5 1.0E-3 DT,ALFA,GAMA,EPSLN

0.400 0.375 0.300 0.175 0.0 0.375 0.35156 0.28125 0.16406 0.0 0.300 0.28125 0.225 0.13125 0.0 0.175 0.16406 0.13125 0.076563 0.0 0.0 0.0 0.0 0.0 0.0 Initial cond., GLU(I)

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Initial cond., GLV(I)

Example 3: INPUT DATA to FEM2D (continued)

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Example 8.6.4: Transient analysis of a rectangular membrane (hyperbolic) 0 0 2 0 ITYPE,IGRAD,ITEM,NEIGN 1 4 1 0 IELTYP,NPE,MESH,NPRNT 4 4 NX,NY 0.0 0.5 0.5 0.5 0.5 X0,DX(I) 0.0 0.25 0.25 0.25 0.25 Y0,DY(I) 9 NSPV 5 1 10 1 15 1 20 1 21 1 22 1 23 1 24 1 25 1 ISPV 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 VSPV 0 NSSV 12.5 0.0 0.0 A10, A1X, A1Y 12.5 0.0 0.0 A20, A2X, A2Y 0.0 A00 0 ICONV 0.0 0.0 0.0 F0, FX, FY 2.5 0.0 0.0 C0, CX, CY

Example 4: INPUT DATA to FEM2D

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100 101 1 1 NTIME,NSTP,INTVL,INTIAL 0.025 0.5 0.5 1.0E-3 DT,ALFA,GAMA,EPSLN

0.400 0.375 0.300 0.175 0.0 0.375 0.35156 0.28125 0.16406 0.0 0.300 0.28125 0.225 0.13125 0.0 0.175 0.16406 0.13125 0.076563 0.0 0.0 0.0 0.0 0.0 0.0 Initial cond., GLU(I)

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Initial cond., GLV(I)

Example 4: INPUT DATA to FEM2D (continued)