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A Boundary Element Application of Plastic Hinges Development in a Circular Ring

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Abstract:

Circular ring is the most popular specimen in industry. The location of a crack in a circular ring can strongly affect the sequence of plastic hinge development which in turn affects stability of a circular ring which has been obtained theoretically in Young [1] but not any numerically. Boundary element method is employed to investigate these effects. In fact, the ring will collapse if the number of plastic hinges is up to four. The results show the potential application of the boundary element method in this project.

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Info:

Periodical:

Applied Mechanics and Materials (Volumes 71-78)

Pages:

4476-4482

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.71-78.4476

Citation:

Cite this paper

Online since:

July 2011

Authors:

Lih Jier Young, Pau Lo Hsu, Syh Shiuh Yeh, Yu Fang Cheng

Keywords:

Boundary Element Method (BEM), Plastic Hinge, Stability

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© 2011 Trans Tech Publications Ltd. All Rights Reserved

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References

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182.

Google Scholar

165.

Google Scholar

115.

Google Scholar

036 -0. 068 -0. 189 -0. 318 BEM.

Google Scholar

175.

Google Scholar

156.

Google Scholar

114.

Google Scholar

034 -0. 062 -0. 180 -0. 309 Accuracy.

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[96] 15.

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[94] 55.

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[99] 13.

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[94] 44.

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[91] 18.

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[95] 24.

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[97] 17% Table 2: θ and values of M/PR at the formation of first hinge (for a/t=0. 3, and R/t=10). α θ First Hinge 0ﾟ 15ﾟ 30ﾟ 45ﾟ 60ﾟ 75ﾟ 90ﾟ 180ﾟ Theoretical 0ﾟ.

Google Scholar

177.

Google Scholar

160.

Google Scholar

111.

Google Scholar

032 -0. 070 -0. 189 -0. 316.

Google Scholar

190 0ﾟAt crack 15ﾟ.

Google Scholar

177.

Google Scholar

160.

Google Scholar

110.

Google Scholar

031 -0. 072 -0. 190 -0. 317 -0. 189 15ﾟAt crack 30ﾟ.

Google Scholar

178.

Google Scholar

160.

Google Scholar

109.

Google Scholar

031 -0. 072 -0. 192 -0. 318.

Google Scholar

188 90ﾟAt Mmax 45ﾟ.

Google Scholar

178.

Google Scholar

160.

Google Scholar

109.

Google Scholar

031 -0. 072 -0. 191 -0. 318.

Google Scholar

186 90ﾟAt Mmax 60ﾟ.

Google Scholar

178.

Google Scholar

160.

Google Scholar

109.

Google Scholar

031 -0. 072 -0. 191 -0. 318.

Google Scholar

186 90ﾟAt crack 75ﾟ.

Google Scholar

182.

Google Scholar

163.

Google Scholar

110.

Google Scholar

032 -0. 073 -0. 194 -0. 323.

Google Scholar

186 75ﾟAt crack 90ﾟ.

Google Scholar

184.

Google Scholar

164.

Google Scholar

113.

Google Scholar

032 -0. 073 -0. 193 -0. 321.

Google Scholar

184 90ﾟBoth BEM 0ﾟ.

Google Scholar

177.

Google Scholar

160.

Google Scholar

111.

Google Scholar

032 -0. 070 -0. 189 -0. 316.

Google Scholar

190 0ﾟAt crack 15ﾟ.

Google Scholar

177.

Google Scholar

160.

Google Scholar

110.

Google Scholar

031 -0. 072 -0. 189 -0. 316 -0. 189 15ﾟAt crack 30ﾟ.

Google Scholar

178.

Google Scholar

160.

Google Scholar

109.

Google Scholar

031 -0. 071 -0. 192 -0. 317.

Google Scholar

188 90ﾟAt Mmax 45ﾟ.

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178.

Google Scholar

160.

Google Scholar

109.

Google Scholar

031 -0. 071 -0. 191 -0. 318.

Google Scholar

186 90ﾟAt Mmax 60ﾟ.

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178.

Google Scholar

160.

Google Scholar

109.

Google Scholar

031 -0. 072 -0. 191 -0. 313.

Google Scholar

186 90ﾟAt crack 75ﾟ.

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182.

Google Scholar

163.

Google Scholar

110.

Google Scholar

032 -0. 073 -0. 191 -0. 322.

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186 75ﾟAt crack 90ﾟ.

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184.

Google Scholar

164.

Google Scholar

112.

Google Scholar

032 -0. 073 -0. 193 -0. 318.

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186 90ﾟBoth Accuracy 0ﾟ.

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[99] 99.

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[99] 99.

Google Scholar

[99] 99.

Google Scholar

[99] 99.

Google Scholar

[99] 99.

Google Scholar

[99] 99.

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[99] 99.

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[99] 99% 15ﾟ.

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[99] 86.

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[98] 92.

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[99] 86.

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[98] 99.

Google Scholar

[99] 76.

Google Scholar

[99] 29.

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[99] 37.

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[99] 85% 30ﾟ.

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[98] 97.

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[99] 89.

Google Scholar

[99] 92.

Google Scholar

[98] 95.

Google Scholar

[98] 89.

Google Scholar

[99] 12.

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[98] 74.

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[99] 25% 45ﾟ.

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[99] 84.

Google Scholar

[99] 86.

Google Scholar

[99] 86.

Google Scholar

[98] 99.

Google Scholar

[98] 97.

Google Scholar

[99] 21.

Google Scholar

[99] 47.

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[98] 91% 60ﾟ.

Google Scholar

[99] 92.

Google Scholar

[99] 82.

Google Scholar

[99] 93.

Google Scholar

[99] 82.

Google Scholar

[99] 88.

Google Scholar

[99] 87.

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[98] 32.

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[99] 97% 75ﾟ.

Google Scholar

[99] 87.

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[99] 81.

Google Scholar

[98] 98.

Google Scholar

[98] 98.

Google Scholar

[98] 93.

Google Scholar

[98] 59.

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[98] 58.

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[99] 96% 90ﾟ.

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[99] 85% 99, 83.

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[98] 92.

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[99] 93.

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[99] 98.

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[99] 89.

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[98] 95.

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[99] 88% Italicized terms indicate diagonal crack location Table 3: θ and values of M/PR at the formation of second hinge (for a/t=0. 3, and R/t=10). α θ Second Hinge 0ﾟ 15ﾟ 30ﾟ 45ﾟ 60ﾟ 75ﾟ 90ﾟ 180ﾟ 270ﾟ Theoretical 0ﾟ.

Google Scholar

150.

Google Scholar

132.

Google Scholar

089.

Google Scholar

010 -. 0. 083 -0. 189 -0. 305.

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178 -0. 305 90ﾟ, 270ﾟ 15ﾟ.

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169.

Google Scholar

153.

Google Scholar

103.

Google Scholar

027.

Google Scholar

079.

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188 -0. 312.

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179 -0. 295 90ﾟ 30ﾟ.

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181.

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164.

Google Scholar

114.

Google Scholar

035 -0. 067 -0. 189 -0. 318.

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182 -0. 318 270ﾟ 45ﾟ.

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181.

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164.

Google Scholar

114.

Google Scholar

035 -0. 067 -0. 189 -0. 318.

Google Scholar

182 -0. 318 270ﾟ 60ﾟ.

Google Scholar

181.

Google Scholar

164.

Google Scholar

114.

Google Scholar

035 -0. 067 -0. 189 -0. 318.

Google Scholar

182 -0. 318 270ﾟ 75ﾟ.

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183.

Google Scholar

174.

Google Scholar

131.

Google Scholar

038 -0. 050 -0. 172 -0. 312.

Google Scholar

169.

Google Scholar

351 270ﾟ 90ﾟ.

Google Scholar

150.

Google Scholar

169.

Google Scholar

157.

Google Scholar

112.

Google Scholar

004 -0. 100 -0. 235.

Google Scholar

150 -0. 480 270ﾟ BEM 0ﾟ.

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134.

Google Scholar

131.

Google Scholar

080.

Google Scholar

008 -0. 076 -0. 188 -0. 305 -0. 297 -0. 297 90ﾟ, 270ﾟ 15ﾟ.

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151.

Google Scholar

143.

Google Scholar

085.

Google Scholar

020 -0. 072 -0. 187 -0. 306 -0. 295 -0. 295 90ﾟ 30ﾟ.

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152.

Google Scholar

145.

Google Scholar

096.

Google Scholar

025 -0. 067 -0. 186 -0. 306 -0. 298 -0. 298 270ﾟ 45ﾟ.

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163.

Google Scholar

146.

Google Scholar

104.

Google Scholar

030 -0. 066 -0. 185 -0. 305 -0. 299.

Google Scholar

299 270ﾟ 60ﾟ.

Google Scholar

167.

Google Scholar

146.

Google Scholar

107.

Google Scholar

030 -0. 064 -0. 185 -0. 304 -0. 300 -0. 300 270ﾟ 75ﾟ.

Google Scholar

167.

Google Scholar

148.

Google Scholar

107.

Google Scholar

032 -0. 005 -0. 172 -0. 302 -0. 301.

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301 270ﾟ 90ﾟ.

Google Scholar

133.

Google Scholar

144.

Google Scholar

110.

Google Scholar

089.

Google Scholar

004 -0. 100 -0. 230 -0. 350 -0. 350 270ﾟ Accuracy 0ﾟ.

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[99] 99.

Google Scholar

[99] 99.

Google Scholar

[99] 99.

Google Scholar

[99] 99.

Google Scholar

[99] 99.

Google Scholar

[99] 99.

Google Scholar

[99] 00.

Google Scholar

[99] 99.

Google Scholar

[99] 99% 15ﾟ.

Google Scholar

[99] 86.

Google Scholar

[99] 56.

Google Scholar

[99] 84.

Google Scholar

[99] 24.

Google Scholar

[99] 59.

Google Scholar

[99] 24.

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[98] 24.

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[99] 32.

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[99] 98% 30ﾟ.

Google Scholar

[98] 96.

Google Scholar

[98] 99.

Google Scholar

[99] 87.

Google Scholar

[98] 85.

Google Scholar

[98] 69.

Google Scholar

[98] 87.

Google Scholar

[98] 68.

Google Scholar

[99] 89.

Google Scholar

[98] 63% 45ﾟ.

Google Scholar

[99] 95.

Google Scholar

[98] 94.

Google Scholar

[98] 84.

Google Scholar

[99] 93.

Google Scholar

[99] 53.

Google Scholar

[99] 37.

Google Scholar

[98] 69.

Google Scholar

[98] 98.

Google Scholar

[98] 72% 60ﾟ.

Google Scholar

[99] 89.

Google Scholar

[98] 93.

Google Scholar

[99] 69.

Google Scholar

[98] 69.

Google Scholar

[98] 98.

Google Scholar

[99] 79.

Google Scholar

[99] 35.

Google Scholar

[98] 95.

Google Scholar

[98] 83% 75ﾟ.

Google Scholar

[98] 97.

Google Scholar

[99] 39.

Google Scholar

[98] 93.

Google Scholar

[99] 89.

Google Scholar

[98] 94.

Google Scholar

[98] 63.

Google Scholar

[99] 34.

Google Scholar

[98] 95.

Google Scholar

[98] 83% 90ﾟ.

Google Scholar

[99] 03.

Google Scholar

[99] 67.

Google Scholar

[99] 20.

Google Scholar

[99] 43.

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[98] 89.

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[99] 45.

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[99] 68.

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[99] 42.

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[98] 64% Table 4: θ and values of M/PR at the formation of third hinge (for a/t=0. 3, and R/t=10). α θ Third Hinge 0ﾟ 15ﾟ 30ﾟ 45ﾟ 60ﾟ 75ﾟ 90ﾟ 180ﾟ 270ﾟ Theoretical 0ﾟ.

Google Scholar

150.

Google Scholar

132.

Google Scholar

089.

Google Scholar

010 -0. 083 -0. 189 -0. 305.

Google Scholar

178 -0. 305 90ﾟ, 270ﾟ 15ﾟ.

Google Scholar

165.

Google Scholar

150.

Google Scholar

103.

Google Scholar

028 -0. 070 -0. 183 -0. 305.

Google Scholar

202 -0. 305 270ﾟ 30ﾟ.

Google Scholar

216.

Google Scholar

198.

Google Scholar

147.

Google Scholar

065 -0. 040 -0. 166 -0. 300.

Google Scholar

216 -0. 300 30ﾟ(C) 45ﾟ.

Google Scholar

280.

Google Scholar

261.

Google Scholar

203.

Google Scholar

116 -0. 001 -0. 135 -0. 281.

Google Scholar

281 -0. 281 180ﾟ, 0ﾟ 60ﾟ.

Google Scholar

280.

Google Scholar

261.

Google Scholar

203.

Google Scholar

116 -0. 001 -0. 135 -0. 281.

Google Scholar

281 -0. 281 180ﾟ, 0ﾟ 75ﾟ.

Google Scholar

264.

Google Scholar

247.

Google Scholar

195.

Google Scholar

097 -0. 002 -0. 132 -0. 269.

Google Scholar

224.

Google Scholar

269 90ﾟ 90ﾟ.

Google Scholar

371.

Google Scholar

377.

Google Scholar

342.

Google Scholar

267.

Google Scholar

129 -0. 012 -0. 176.

Google Scholar

371 -0. 371 0ﾟ, 180ﾟ BEM 0ﾟ.

Google Scholar

150.

Google Scholar

131.

Google Scholar

089.

Google Scholar

010 -0. 082 -0. 189 -0. 305.

Google Scholar

178 -0. 304 90ﾟ, 270ﾟ 15ﾟ.

Google Scholar

163.

Google Scholar

148.

Google Scholar

102.

Google Scholar

028 -0. 070 -0. 180 -0. 303.

Google Scholar

199 -0. 302 270ﾟ 30ﾟ.

Google Scholar

214.

Google Scholar

195.

Google Scholar

146.

Google Scholar

064 -0. 040 -0. 166 -0. 297.

Google Scholar

215 -0. 295 30ﾟ(C) 45ﾟ.

Google Scholar

278.

Google Scholar

258.

Google Scholar

200.

Google Scholar

114 -0. 001 -0. 133 -0. 279.

Google Scholar

277 -0. 280 180ﾟ, 0ﾟ 60ﾟ.

Google Scholar

278.

Google Scholar

257.

Google Scholar

200.

Google Scholar

115 -0. 001 -0. 133 -0. 278.

Google Scholar

277 -0. 279 180ﾟ, 0ﾟ 75ﾟ.

Google Scholar

264.

Google Scholar

245.

Google Scholar

193.

Google Scholar

096 -0. 002 -0. 130 -0. 265.

Google Scholar

222.

Google Scholar

267 90ﾟ 90ﾟ.

Google Scholar

369.

Google Scholar

375.

Google Scholar

340.

Google Scholar

265.

Google Scholar

127 -0. 012 -0. 174.

Google Scholar

368 -0. 365 0ﾟ, 180ﾟ Accuracy 0ﾟ.

Google Scholar

[99] 99.

Google Scholar

[99] 23.

Google Scholar

[99] 99.

Google Scholar

[99] 99.

Google Scholar

[99] 33.

Google Scholar

[99] 89.

Google Scholar

[99] 99.

Google Scholar

[99] 84.

Google Scholar

[99] 59% 15ﾟ.

Google Scholar

[98] 83.

Google Scholar

[98] 59.

Google Scholar

[99] 48.

Google Scholar

[99] 37.

Google Scholar

[99] 52.

Google Scholar

[98] 34.

Google Scholar

[99] 29.

Google Scholar

[98] 34.

Google Scholar

[98] 98% 30ﾟ.

Google Scholar

[98] 87.

Google Scholar

[98] 32.

Google Scholar

[99] 20.

Google Scholar

[98] 74.

Google Scholar

[98] 78.

Google Scholar

[99] 87.

Google Scholar

[99] 12.

Google Scholar

[99] 57.

Google Scholar

[98] 32% 45ﾟ.

Google Scholar

[99] 34.

Google Scholar

[99] 03.

Google Scholar

[98] 63.

Google Scholar

[98] 47.

Google Scholar

[98] 49.

Google Scholar

[98] 47.

Google Scholar

[99] 21.

Google Scholar

[98] 54.

Google Scholar

[99] 52% 60ﾟ.

Google Scholar

[99] 32.

Google Scholar

[98] 38.

Google Scholar

[98] 43.

Google Scholar

[99] 32.

Google Scholar

[99] 23.

Google Scholar

[98] 49.

Google Scholar

[98] 87.

Google Scholar

[98] 69.

Google Scholar

[99] 34% 75ﾟ.

Google Scholar

[98] 87.

Google Scholar

[99] 24.

Google Scholar

[98] 78.

Google Scholar

[98] 58.

Google Scholar

[99] 39.

Google Scholar

[98] 53.

Google Scholar

[98] 59.

Google Scholar

[99] 03.

Google Scholar

[99] 32% 90ﾟ.

Google Scholar

[99] 35.

Google Scholar

[99] 49.

Google Scholar

[99] 42.

Google Scholar

[99] 42.

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[98] 64.

Google Scholar

[99] 54.

Google Scholar

[98] 89.

Google Scholar

[99] 20.

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[98] 43% Table 5: Sequence of hinge formation. α θ 0ﾟ 15ﾟ 30ﾟ 45ﾟ 60ﾟ 75ﾟ 90ﾟ 180ﾟ 270ﾟ 0ﾟ 1 2, 3 4 2, 3 15ﾟ 1 2 4 3 30ﾟ 1 4 2 45ﾟ 4 3 1 3 2 60ﾟ 4 1 3 2 75ﾟ 1 3 4 2 90ﾟ 3, 4 1 3, 4 2 No Crack 3, 4 1, 2 3, 4 1, 2.

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