Esercitazione 2 - Mesh ad elementi finiti

DOF DISPL

1 -0.241359368543755 E -02

2 -0.231827484256329 E -02

3 -0.389221210940746 E -05

....

NODAL STRESS & STRAIN BASED ON ENERGY - BASED MEAN

DEFORMATION ELEMENT : 1

IN

EPSX EPSY GAMMAXY EPSZ EPS1

0.370 E -04 -0.182 E -04 -0.137 E -03 0.000 E +00 0.149 E -03

EPS2 THETA

-0.130 E -03 0.146 E +03

STRESS ELEMENT : 1

IN

SIGX SIGY TAUXY SIGZ SIG1

0.101 E +04 -0.495 E +03 -0.186 E +04 0.000 E +00 0.226 E +04

SIG2 THETA

Computational Structural Analysis 53

B.3. Plotting the results B. User manual

-0.175 E +04 0.146 E +03

ENERGY ELEMENT : 1

IN

VOLUME ENERGY ENERGY % E %

SUM

0.217 E -03 0.327 E -04 0.00224 0.00224

......

MEAN NODAL DEFORMATIONS

NODE EPSX EPSY GAMMAXY

1 0.261 E -04 -0.226 E -03 -0.381 E -04

2 0.243 E -04 -0.254 E -03 -0.363 E -04

3 0.133 E -04 -0.192 E -03 -0.536 E -04

....

MEAN NODAL STRESSES

NODE SIGX SIGY TAUXY

1 0.71001 E +03 -0.61475 E +04 -0.51915 E +03

2 0.66203 E +03 -0.69180 E +04 -0.49363 E +03

3 0.36194 E +03 -0.52348 E +04 -0.72923 E +03

....

ENERGY STORED THE STRUCTURE

IN

TOT VOL TOT EN TOT EN %

0.242 E +01 0.146 E +01 0.100 E +03

After printing the nodal displacements and identifying the maximum and the minimum, the code

writes the strains, stresses and energy in each element. Then the mean nodal values of these

quantities are reported, obtained through the mean rule decided by the user. Finally, a summary

line with the total volume and strain energy is reported.

B.3 Plotting the results

The results, in terms of deformed shape and internal forces diagrams are plotted by the MATLAB

algorithm in Appendix D. The data is taken by the code from the file PLOT.DAT.

54 Computational Structural Analysis

C

Structural analysis code

! STRESS 2 D ALGORITHM

1 !

2 MODULE GLOBALVAR

3 IMPLICIT DOUBLE PRECISION (A -H ,O - Z )

4 INTEGER :: ICODE

5 ! MESH

6 INTEGER :: IMESH , IDMESH

7 ! GEOMET

8 INTEGER :: NNODE , NELE , NTYPE

9 REAL (2) , DIMENSION (: ,:) , ALLOCATABLE , SAVE :: COORD , CTYPE

10 INTEGER , DIMENSION (:) , ALLOCATABLE , SAVE :: ITYPE

11 INTEGER , DIMENSION (: ,:) , ALLOCATABLE , SAVE :: IN

12 ! SCODE

13 INTEGER :: NDOF

14 INTEGER , DIMENSION (: ,:) , ALLOCATABLE , SAVE :: IDOF

15 ! LOADS

16 REAL (2) , DIMENSION (: ,:) , ALLOCATABLE , SAVE :: ELOADS

17 REAL (2) , DIMENSION (:) , ALLOCATABLE , SAVE :: VLOADS , THERM

18 ! ASSEMB

19 REAL (2) , DIMENSION (6 ,6):: ST

20 REAL (2) , DIMENSION (6):: EQFG

21 REAL (2) , DIMENSION (: ,:) , ALLOCATABLE , SAVE :: VK

22 ! SOLVE

23 REAL (2) , DIMENSION (:) , ALLOCATABLE , SAVE :: VDISP

24 ! STRESS

25 REAL (2) , DIMENSION (: ,:) , ALLOCATABLE , SAVE :: SIGNOD , EPSNOD

26 REAL (2) , DIMENSION (:) , ALLOCATABLE , SAVE :: SUMWEIGHT

27 INTEGER :: IMEAN

28 END MODULE GLOBALVAR

29

30 PROGRAM FRAME

31 USE GLOBALVAR

32 CHARACTER :: TITLE , REC

33 OPEN (9 , FILE = " TEMPORARY . txt " , STATUS = " UNKNOWN " )

34 OPEN (11 , FILE = " INPUTmesh . txt " , STATUS = " UNKNOWN " )

35 OPEN (12 , FILE = " OUTPUTmesh . txt " , STATUS = " UNKNOWN " )

36 READ (11 ,*) TITLE

37 READ (11 ,*) REC

38 READ (11 ,*) ICODE

39 IF ( ICODE <0. OR . ICODE >1) THEN

40 WRITE (12 , ’ (" WRONG ␣ NUMBER ␣ FOR ␣ TYPE ␣ OF ␣ ANALYSIS ") ’)

41 STOP

42 ELSE

43 IF ( ICODE ==0) THEN

44 WRITE (12 , ’ ("**** ␣ PLAIN ␣ STRESS ␣ ANALYSIS ␣ ****") ’)

45 ELSE

46 WRITE (12 , ’ ("**** ␣ PLAIN ␣ STRAIN ␣ ANALYSIS ␣ ****") ’)

47 END IF

48 END IF

49 READ (11 ,*) REC

50 READ (11 ,*) IMESH

51 IF ( IMESH ==1) THEN

52 READ (11 ,*) REC

53 READ (11 ,*) IDMESH

54 WRITE (12 , ’ (/) ’)

55 WRITE (12 , ’ ("**** ␣ AUTOGENERATED - MESH ␣ TYPE " , I2 ," ␣ ****") ’) IDMESH

56 CALL MESH

57 ELSE

58 WRITE (12 , ’ (/) ’)

59 WRITE (12 , ’ ("**** ␣ USER ␣ INPUT - MESH ␣ ****") ’)

60 END IF

61 CALL GEOMET

62 CALL SCODE

63 CALL LOADS

64 CALL ASSEMB

65 CALL SOLVE

66 CALL STRESS2D

67 CALL PLOT2D

68 CLOSE (9)

69 CLOSE (11)

70 CLOSE (12)

71 END PROGRAM FRAME

72

73 ! SUBROUTINE GEOMET

74 SUBROUTINE GEOMET

75 USE GLOBALVAR

76 INTEGER :: IDNODE , IDTYPE , IDELE ,I , J

77 CHARACTER :: REC

78 ! READING / WRITING NODES

79 WRITE (12 , ’ (/) ’)

80 WRITE (12 , ’( T1 ,"**** ␣ GEOMETRY ␣ ****" ,/) ’)

81 IF ( IMESH ==0) THEN

82 READ (11 ,*) REC

83 READ (11 ,*) NNODE

84 END IF

85 WRITE (12 , ’ (2 X ," NUMBER ␣ OF ␣ NODES ␣ =" , I4 ,/) ’) NNODE

86

Computational Structural Analysis 55

C. Structural analysis code

WRITE (12 ,101) ’ NODE ’ , ’ COORD ␣ X ’ , ’ COORD ␣ Y ’

87 IF ( IMESH ==0) THEN

88 ALLOCATE ( COORD ( NNODE ,2))

89 END IF

90 DO I =1 , NNODE

91 IF ( IMESH ==0) THEN

92 READ (11 ,*) IDNODE , COORD ( IDNODE ,:)

93 WRITE (12 ,102) IDNODE , COORD ( IDNODE ,:)

94 ELSE

95 WRITE (12 ,102) I , COORD (I ,:)

96 END IF

97 END DO

98 READ (11 ,*) REC

99 READ (11 ,*) NTYPE

100 WRITE (12 , ’ (/) ’)

101 WRITE (12 , ’ (2 X ," NUMBER ␣ OF ␣ TYPES ␣ =" , I2 ,/) ’) NTYPE

102 WRITE (12 , ’ (2 X , A10 ,5(4 X , A10 )) ’) ’ TYPE ’ , ’ YOUNG ’ , ’ POISSON ’ , ’ ALPHA ’ , ’ SELFWEIGHT ’ , ’ THICKNESS ’

103 ALLOCATE ( CTYPE ( NTYPE ,5))

104 DO I =1 , NTYPE

105 READ (11 ,*) IDTYPE , CTYPE ( IDTYPE ,:)

106 WRITE (12 , ’ (2 X , I10 ,5(4 X , E10 .4)) ’) IDTYPE , CTYPE ( IDTYPE ,:)

107 END DO

108 IF ( IMESH ==0) THEN

109 READ (11 ,*) REC

110 READ (11 ,*) NELE

111 ALLOCATE ( IN ( NELE ,3))

112 ALLOCATE ( ITYPE ( NELE ))

113 END IF

114 ALLOCATE ( THERM ( NELE ))

115 WRITE (12 , ’ (/) ’)

116 WRITE (12 , ’ (2 X ," NUMBER ␣ OF ␣ ELEMENTS ␣ =" , I4 ,/) ’) NELE

117 WRITE (12 , ’ (2 X , A10 ,4(4 X , A10 )) ’) ’ ELEMENT ’ , ’1 ST ␣ NODE ’ , ’2 ND ␣ NODE ’ , ’3 RD ␣ NODE ’ , ’ TYPE ’

118 DO I =1 , NELE

119 IF ( IMESH ==0) THEN

120 READ (11 ,*) IDELE ,( IN ( IDELE , J ) , J =1 ,3) , ITYPE ( IDELE )

121 WRITE (12 , ’ (2 X , I10 ,4(4 X , I10 )) ’) IDELE ,( IN ( IDELE , J ) , J =1 ,3) , ITYPE ( IDELE )

122 ELSE

123 WRITE (12 , ’ (2 X , I10 ,4(4 X , I10 )) ’)I ,( IN (I , J ) , J =1 ,3) , ITYPE ( I )

124 END IF

125 END DO

126 RETURN

127 !

128 ! FORMAT LIST

129 101 FORMAT (2 X , A10 ,4 X , A10 ,4 X , A10 )

130 102 FORMAT (2 X , I10 ,4 X , F10 .5 ,4 X , F10 .5)

131 103 FORMAT (2 X , A10 ,4 X , A10 ,4 X , A10 ,4 X , A10 ,4 X , A10 )

132 104 FORMAT (2 X , I10 ,4 X , F10 .5 ,4 X , F10 .5 ,4 X , F10 .5 ,4 X , F10 .5)

133 105 FORMAT (2 X , I10 ,3 X , F11 .1 ,4 X , F10 .5 ,4 X , F10 .6 ,4 X , F10 .5)

134 106 FORMAT (2 X , I10 ,4 X , I10 ,4 X , I10 ,4 X , I10 ,4 X , I10 )

135 END SUBROUTINE GEOMET

136

137 SUBROUTINE MESH

138 USE GLOBALVAR

139 INTEGER :: I ,J , IND , IND1 , IND2 , NINTX , NINTY , NSUB (2) , NX , NY

140 CHARACTER :: REC

141 INTEGER , DIMENSION (:) , ALLOCATABLE , SAVE :: NSUBX , NSUBY , NNODEX , NNODEY

142 REAL (2) , DIMENSION (:) , ALLOCATABLE , SAVE :: DX , DY

143 INTEGER , DIMENSION (: ,:) , ALLOCATABLE , SAVE :: TYPEL

144 REAL (2):: X0 , Y0 , WIDTH

145 READ (11 ,*) REC

146 READ (11 ,*) X0 , Y0

147 READ (11 ,*) REC

148 READ (11 ,*) NINTX , NINTY

149 ALLOCATE ( DX ( NINTX ))

150 ALLOCATE ( DY ( NINTY ))

151 ALLOCATE ( NNODEX ( NINTX ))

152 ALLOCATE ( NNODEY ( NINTY ))

153 ALLOCATE ( NSUBX ( NINTX ))

154 ALLOCATE ( NSUBY ( NINTY ))

155 ALLOCATE ( TYPEL ( NINTX , NINTY ))

156 NSUB (:)=0

157 NX =1

158 NY =1

159 DO I =1 , NINTX

160 READ (11 ,*) WIDTH , NSUBX ( I ) , TYPEL (I ,:)

161 DX ( I )= WIDTH / NSUBX ( I )

162 NNODEX ( I )= NSUBX ( I )

163 NX = NX + NNODEX ( I )

164 NNODEX ( I )= NNODEX ( I )+1

165 NSUB (1)= NSUB (1)+ NSUBX ( I )

166 END DO

167 DO I =1 , NINTY

168 READ (11 ,*) WIDTH , NSUBY ( I )

169 DY ( I )= WIDTH / NSUBY ( I )

170 NNODEY ( I )= NSUBY ( I )

171 NY = NY + NNODEY ( I )

172 NNODEY ( I )= NNODEY ( I )+1

173 NSUB (2)= NSUB (2)+ NSUBY ( I )

174 END DO

175 NNODE = NX * NY

176 NELE =2.* NSUB (1)* NSUB (2)

177 ALLOCATE ( COORD ( NNODE ,2))

178 ALLOCATE ( ITYPE ( NELE ))

179 IND =0

180 DO I =1 , NINTY

181 DO K =1 , NSUBY ( I )/2

182 DO J =1 , NINTX

183 ITYPE ( IND +1: IND + NSUBX ( J )*4)= TYPEL (J , I )

184 IND = IND + NSUBX ( J )*4

185 END DO

186 END DO

187 END DO

188 COORD =0.

189 IND =0

190 K =1

191 L =1

192 XX =0.

193 YY =0.

194 DO K =1 , NINTX

195 IF ( K ==1) THEN

196 M =1

197 ELSE

198 M =2

199 END IF

200 DO I =M , NNODEX ( K )

201 DO L =1 , NINTY

202

56 Computational Structural Analysis

C. Structural analysis code IF ( L ==1) THEN

203 N =1

204 ELSE

205 N =2

206 END IF

207 DO J =N , NNODEY ( L )

208 IND = IND +1

209 COORDY = Y0 + YY +( J -1)* DY ( L )

210 COORDX = X0 + XX +( I -1)* DX ( K )

211 COORD ( IND ,1)= COORDX

212 COORD ( IND ,2)= COORDY

213 END DO

214 YY = COORDY - Y0

215 END DO

216 YY =0.

217 END DO

218 XX = COORDX - X0

219 END DO

220 NBLOCKX = NSUB (1)/2

221 NBLOCKY = NSUB (2)/2

222 NTRIANGBLOCK =8

223 IND =1

224 IND1 =1

225 IND2 = IND1

226 ALLOCATE ( IN ( NELE ,3))

227 IN (: ,:)=0

228 IF ( IDMESH ==1) THEN

229 DO I =1 , NBLOCKY

230 DO J =1 , NBLOCKX

231 IN ( IND ,1)= IND1

232 IN ( IND ,2)= IND1 + NY

233 IN ( IND ,3)= IND1 + NY +1

234 IN ( IND +1 ,1)= IND1 + NY

235 IN ( IND +1 ,2)= IND1 +2* NY

236 IN ( IND +1 ,3)= IND1 + NY +1

237 IN ( IND +2 ,1)= IND1 +2* NY

238 IN ( IND +2 ,2)= IND1 +2* NY +1

239 IN ( IND +2 ,3)= IND1 + NY +1

240 IN ( IND +3 ,1)= IND1 +2* NY +1

241 IN ( IND +3 ,2)= IND1 +2* NY +2

242 IN ( IND +3 ,3)= IND1 + NY +1

243 IN ( IND +4 ,1)= IND1 +2* NY +2

244 IN ( IND +4 ,2)= IND1 + NY +2

245 IN ( IND +4 ,3)= IND1 + NY +1

246 IN ( IND +5 ,1)= IND1 + NY +2

247 IN ( IND +5 ,2)= IND1 +2

248 IN ( IND +5 ,3)= IND1 + NY +1

249 IN ( IND +6 ,1)= IND1 +2

250 IN ( IND +6 ,2)= IND1 +1

251 IN ( IND +6 ,3)= IND1 + NY +1

252 IN ( IND +7 ,1)= IND1 +1

253 IN ( IND +7 ,2)= IND1

254 IN ( IND +7 ,3)= IND1 + NY +1

255 IND = IND + NTRIANGBLOCK

256 IND1 = IND2 +(2* J )* NY

257 END DO

258 IND2 = IND2 +2

259 I