Validation of Numerical Methods by Analytical Benchmarks, and Verification of Exact Solutions by Numerical Methods
In this lecture, we discuss the validation of various numerical methods in structural topology optimization. This is done by computing numerically optimal topologies (e.g. for perforated plates in plane stress), using various numbers of ground elements an
- PDF / 1,235,813 Bytes
- 17 Pages / 439.37 x 666.142 pts Page_size
- 60 Downloads / 172 Views
9DOLGDWLRQRI1XPHULFDO0HWKRGVE\$QDO\WLFDO %HQFKPDUNVDQG9HULILFDWLRQRI([DFW6ROXWLRQV E\1XPHULFDO0HWKRGV *HRUJH,15R]YDQ\ DQG7RPDV]6RNyá
'HSDUWPHQWRI6WUXFWXUDO0HFKDQLFV%XGDSHVW8QLYHUVLW\RI7HFKQRORJ\DQG(FRQRPLFV %XGDSHVW+XQJDU\ )DFXOW\RI&LYLO(QJLQHHULQJ:DUVDZ8QLYHUVLW\RI7HFKQRORJ\:DUVDZ3RODQG
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
9DOLGDWLRQ RI 1XPHULFDO 0HWKRGV LQ 6WUXFWXUDO 7RSRORJ\ 2SWLPL]DWLRQ 7KHDXWKRUKDVUHSHDWHGO\H[SUHVVHGFRQFHUQDERXWWKHODFNRI³TXDOLW\FRQWURO´LQ WRSRORJ\RSWLPL]DWLRQ5R]YDQ\3RPH]DQVNL*DVSDUDQG4XHULQ5R]YDQ\ /HZLQVNL4XHULQDQG/RJRDDQG5R]YDQ\3RPH]DQVNL4XHULQ*DVSDUDQG /RJRE +LVPHWKRGRIYHULI\LQJQXPHULFDOVROXWLRQVLQWRSRORJ\RSWLPL]DWLRQ LVEDVHGRQWKHIDFWWKDWWKHRSWLPDOWRSRORJ\RISHUIRUDWHGSODWHVLQSODQHVWUHVVXQGHU DFRPSOLDQFHFRQVWUDLQWWHQGVWRWKDWIRUSODQHWUXVVHVLIWKHYROXPHIUDFWLRQRIWKH SODWHDSSURDFKHV]HUR5R]YDQ\2OKRII%HQGVRHHWDO%HQGVRHDQG +DEHU$OODLUHDQG.RKQ5R]YDQ\D 0RVWRIWKHDXWKRUVLQQX PHULFDO WRSRORJ\ RSWLPL]DWLRQ VLPSO\ FRPSDUH WKHLU VROXWLRQV RSWLFDOO\ ZLWK WKH H[DFWRSWLPDOWUXVVWRSRORJ\DQGDUHVDWLVILHGZLWKDYDJXHUHVHPEOHQFH7KLVLVD G. Rozvany, T. Lewiński (Eds.), Topology Optimization in Structural and Continuum Mechanics, CISM International Centre for Mechanical Sciences, DOI 10.1007/978-3-7091-1643-2_4, © CISM, Udine 2014
54
G.I.N. Rozvany and T. Sokół
YHU\VXEMHFWLYHPHWKRGIRUYHULI\LQJWRSRORJ\RSWLPL]DWLRQPHWKRGVDQGVROXWLRQV ,QRUGHUWRHQDEOHDUHOLDEOHFKHFNRQQXPHULFDOVROXWLRQVLQWRSRORJ\RSWLPL]D WLRQ/HZLQVNL6RNRODQGWKHDXWKRUDUHGHULYLQJDQDO\WLFDOO\DVHULHVRIH[DFWWUXVV WRSRORJLHVIRUSRSXODUEHQFKPDUNSUREOHPV5R]YDQ\/HZLQVNLDQG5R]YDQ\ DDQGE6RNRODQG/HZLQVNL5R]YDQ\DQG6RNRO6RNRODQG 5R]YDQ\ 7KHDFWXDOYHULILFDWLRQRIDVROXWLRQFRQVLVWVRIWKHIROORZLQJSUR FHGXUH5R]YDQ\HW
Data Loading...