Elasticity: Theory, Applications, and Numerics 3rd Edition

ISBN 13
978-0124081369
ISBN 10
0124081363
Authors
Martin H. Sadd Ph.D.
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23 documents found.
571936
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978-0124081369 Chapter 1
1.1. (scalar)5401 (matrix) 402 000 201 (scalar)7400000201 (vector) 2 4 3 (matrix) 350 10180 461 110 240 111 110 240 111 (scalar)251104160111 (scalar)6141 (a) 332211 332313 322212 312111 333323321331322322221221311321121111 332211 333332323131232322222121131312121111 332211 =++=++= = = =++++++++= ++++++++= =++= = = =++++++++= ++++++++= =++=++= bbbbbbbb bbbbbb bbbbbb bbbbbb bb bbabbabbabbabbabbabbabbabbabba babababa aa aaaaaaaaaaaaaaaaaaaa aaaa ii ji jiij iiijij jkij ijij ii (scalar)6114 (matrix) 112 112 224 (scalar)17240120044 (vector) 6 3 4 (matrix) 8160 480 261 240 120 021 240 120 021 (scalar)304160140041 (scalar)5221 (b) 332211 332313 322212 312111 333323321331322322221221311321121111 332211 333332323131232322222121131312121111 332211 =++=++= = = =++++++++= ++++++++= =++= = = =++++++++= ++++++++= =++=++= bbbbbbbb bbbbbb bbbbbb bbbbbb bb bbabbabbabbabbabbabbabbabbabba babababa aa aaaaaaaaaaaaaaaaaaaa aaaa ii ji jiij iiijij jkij ijij ii (scalar)2101 (matrix) 101 000 101 (scalar)1000000001 (vector) 0 1 1 (matrix) 360 270 001 030 120 001 030 120 001 (scalar)15090140001 (scalar)3021 (d) (scalar)2011 (matrix) 000 011 011 (scalar)3000001011 (vector) 1 1 2 (matrix) 1841 931 722 410 201 111 410 201 111 (scalar)251610401111 (scalar)5401 (c) 332211 332313 322212 312111 333323321331322322221221311321121111 332211 333332323131232322222121131312121111 332211 332211 332313 322212 312111 333323321331322322221221311321121111 332211 333332323131232322222121131312121111 332211 =++=++= = = =++++++++= ++++++++= =++= = = =++++++++= ++++++++= =++=++= =++=++= = = =++++++++= ++++++++= =++= = = =++++++++= ++++++++= =++=++= bbbbbbbb bbbbbb bbbbbb bbbbbb bb bbabbabbabbabbabbabbabbabbabba babababa aa aaaaaaaaaaaaaaaaaaaa aaaa bbbbbbbb bbbbbb bbbbbb bbbbbb bb bbabbabbabbabbabbabbabbabbabba babababa aa aaaaaaaaaaaaaaaaaaaa aaaa ii ji jiij iiijij jkij ijij ii ii ji jiij iiijij jkij ijij ii 1.2. conditions eappropriat esatisfy th andclearly 011 101381+= 101381+= 101 381 + = 110 2 1 231 112 2 1 )( 2 1 )( 2 1 )a( ][)( ijij jiijjiijij aa aaaaa ++= conditions eappropriat esatisfy th andclearly 030 302542+= 302542+= 302 542 + = 020 2 1 450 022 2 1 )( 2 1 )( 2 1 )b( ][)( ijij jiijjiijij aa aaaaa ++= conditions eappropriat esatisfy th andclearly 011 100302+= 100302+= 100 302 + =
Elasticity: Theory-- Applications-- and Numerics 3rd Edition
571956
Homework Help
978-0124081369 Chapter 15 Part 1
15.1. ( ) +=+ =+)()(22xyxyebbezzzi ( ) +=+ =+)()(22xyxyebbezzzi ( ) + = + =+ )()(22 xyxy ebbe zzzi ++++===+=+++++++=++++++==+==+3sin3cossincos)1(2sincos3sin3cos)1(2)1(2)cossin()1(1)1(44)()(2:Field Stress)log()21()1(8)1(21tan2)log()12()1(8)1(21tan2]1)43[()1(4)2()1(8)2()1(8)43(][:property cyclicCheck )1(8)1(8)1(8______222222222222221xyxyyxyxyxyxyxCbbbbrbbbbrirbbrzbiRezzyxyxyxbyxxyxybvyxyxyxbyxxyxybubbiibiibivu ++++===+=+++++++=++++++==+==+3sin3cossincos)1(2sincos3sin3cos)1(2)1(2)cossin()1(1)1(44)()(2:Field Stress)log()21()1(8)1(21tan2)log()12()1(8)1(21tan2]1)43[()1(4)2()1(8)2()1(8)43(][:property cyclicCheck )1(8)1(8)1(8______222222222222221xyxyyxyxyxyxyxCbbbbrbbbbrirbbrzbiRezzyxyxyxbyxxyxybvyxyxyxbyxxyxybubbiibiibivu ++ ++ = = = + =+ + ++ + + + = + ++ + + + = =+ = =+ 3sin3cossincos )1(2 sincos3sin3cos )1(2 )1(2 )cossin( )1( 1 )1(4 4)()(2 :Field Stress )log()21( )1(8)1(2 1 tan 2 )log()12( )1(8)1(2 1 tan 2 ]1)43[( )1(4 )2( )1(8 )2( )1(8 )43(][ :property cyclicCheck )1(8 )1(8 )1(8 ______ 22 22 22 22 22 22 22 1 xyxy yxyx yxyx y x C bbbb r bbbb r i r bb rz bi Rezz yx yx yx b yx xy x y b v yx yx yx b yx xy x y b u b b i ib i ib ivu +=+=++=++=3sin3coscos3sin)1(43sin3coscossin3)1(4sincos3sin3cos)1(43sin3cossincos)1(2xyyxyxyyxxyxyxxyxyxyxybbbbrbbbbrbbbbrbbbbr +=+=++=++=3sin3coscos3sin)1(43sin3coscossin3)1(4sincos3sin3cos)1(43sin3cossincos)1(2xyyxyxyyxxyxyxxyxyxyxybbbbrbbbbrbbbbrbbbbr + = + = ++ = ++ = 3sin3coscos3sin )1(4 3sin3coscossin3 )1(4 sincos3sin3cos )1(4 3sin3cossincos )1(2 xyyxy xyyxx yxyxxy xyxyxy bbbb r bbbb r bbbb r bbbb r 3iii 3iii 3 ii i partsimaginary and real Separating partsimaginary and real Separating partsimaginary and real Separating +++++=)(log)()2sin2(cos)()(log)()43(yxyxyxiribbiiibbiiribbi +++++=)(log)()2sin2(cos)()(log)()43(yxyxyxiribbiiibbiiribbi + + ++ + = )(log )( )2sin2(cos )( )(log )( )43( yxyxyx ir ibbi i ibbi ir ibbi + =+ =+ = = 221xy 221xy 22 1 x y log )1(8 1 )1(8 log )1(8 )43( case)strain plane(for )()()()(2 log )1(4 )(,log )1(4 )( potentials thechoose
Elasticity: Theory-- Applications-- and Numerics 3rd Edition
571939
Homework Help
978-0124081369 Chapter 4
4.1. = +++++= +++++= +++++= +++++= +++++= +++++= +++++= +++++= +++++= +++++= +++++= +++++= 313131233112313331223111 233123232312233323222311 123112231212123312221211 333133233312333333223311 223122232212223322222211 113111231112113311221111 313131233112313331223111 233123232312233323222311 123112231212123312221211 333133233312333333223311 223122232212223322222211 113111231112113311221111 666564636261 565554535251 464544434241 363534333231 262524232221 161514131211 result theimplies relations two theseComparing 222 222 222 222 222 222 (4.2.3) from While 222 222 222 222 222 222 (4.2.1)relation From CCCCCC CCCCCC CCCCCC CCCCCC CCCCCC CCCCCC C eCeCeCeCeCeC eCeCeCeCeCeC eCeCeCeCeCeC eCeCeCeCeCeC eCeCeCeCeCeC eCeCeCeCeCeC eCeCeCeCeCeC eCeCeCeCeCeC eCeCeCeCeCeC eCeCeCeCeCeC eCeCeCeCeCeC eCeCeCeCeCeC ij zxyzxyzyxzx zxyzxyzyxyz zxyzxyzyxxy zxyzxyzyxz zxyzxyzyxy zxyzxyzyxx zxyzxyzyxzx zxyzxyzyxyz zxyzxyzyxxy zxyzxyzyxz zxyzxyzyxy zxyzxyzyxx 4.2. 2 * * 1 (4.2.4) is which thusand , and in symmetric isit of definition thefrombut )( 2 1 2 1 2 12 1 2 1 (4.2.4) iswhich , ijlkijklijkl klijklklijlkijkllkijlkklijkl klijklklijklklijklij jiklijklkljiklklijkljiij kljikljiklijklij CClkC eCeCCeCeC eCeCeC+== eCeCeC+== eCeCeC +== CCeCeC eCeC = =+=+= === == 4.3. ijijkkij ijijkkjiijijkk kljkiljlikklijklijklij ee eeeee eeC += =+= ++=++= ++== 2 ,2)( and letting )( )( 4.4. )( )1(2)21)(1( )21)(1( and )1(2 Since ) 3 2 ()( 3 2 Since )(, and (4.2.7)relation with thisComparing )( (4.2.6)
Elasticity: Theory-- Applications-- and Numerics 3rd Edition
571941
Homework Help
978-0124081369 Chapter 6
6.1. xx xx x x x x e Ee Edxdydz dU U dxdydz E dxdydz E d dxdydz x u ddudxdydzF x dxdydz x u d dxdydzduFdydzdu dydzdx x u d x dudxdydz x dxdydz x u ddudydz dxdydzduFdydzdudydzdx x u uddx x dU x xx xx x xxx == == = = = + + = + + + += + + += 2 1 22 bygiven isdensity energy strain theThus 2 )( )()( 22 2 0 00 00 0 2 000 6.2. ( ) 2 2 1 2 12 2 1 2 2 11 222 2 )1(2 2 1 2 )2( 2 1 )( 2 and 22 1 )( Also 2) 22 22 2 2 1 ()2( 1 )( 2)( 2 1 , Now 2 1 )( II E I E II E U III EE U IIIIIIIU IIIeeeeeeIIeeI eeeeU ijijkk kkjjijij eeeee eeijijijijjjiiekkjje ijijkkjj += + = == + = +=+= ==== += e e 6.3. 2222222)(2)222(21221121212222zyxzxyzxyzyxkkjjijijijkkijijijijEEEEEEUeU++++++++=+=+=== 2222222)(2)222(21221121212222zyxzxyzxyzyxkkjjijijijkkijijijijEEEEEEUeU++++++++=+=+=== 2222222 )( 2 )222( 2 1 22 11 2 1 2 1 2 2 2 2 zyxzxyzxyzyx kkjjijijijkkijijijij EE EEEE UeU ++ +++++ + = + = + === 2222222)111()(12zxyzxyzyxzyxeeeeee++++++++= 2222222)111()(12zxyzxyzyxzyxeeeeee++++++++= 2222222 ) 1 1 1 ()( 1 2 zxyzxyzyxzyx eeeeee ++++++++= 2222222 )222()( 12 1 )2( 2 1 2 1 zxyzxyzyxzyx ijijkkjjijijijkkijij eeeeeeeee eeeeeeeeU ++++++++= +=+== 6.4. ( ) ( ) mnmnmnkkmnmnkkmnjj ijjnimjnimijkkjnjmknkmjj mn jnim mn ij ij mn ij mn ij ijkk mn jj mn kk jj mn ijijkkjj eeeee eeee e U e e e e e e e ee e e e e e e U eeeeU =+=++= +++= = since Now = since Now = since Now + + + = += 22)( 2 1 2 1 2 1 2 1 )(e 6.5. sderivativeother for the Likewise 2)( )()( 2 1 )( :system coordinate principalin (6.1.9)Relation 11321 1 2 3 2 2 2 1 2 321 =+++= +++++= eeee e U eeeeeeU
Elasticity: Theory-- Applications-- and Numerics 3rd Edition
571945
Homework Help
978-0124081369 Chapter 8 Part 3
8.39. )cos31( 2 cos 2 )cos1( 2 sin 2 3)2cos3123cos()2sin23sin(143223223)2sin23sin()2cos323cos(143)cos31(2sin2)cos3(2cos23=+==BABArrBrABArrBrAr 3)2cos3123cos()2sin23sin(143223223)2sin23sin()2cos323cos(143)cos31(2sin2)cos3(2cos23=+==BABArrBrABArrBrAr 3 ) 2 cos 3 1 2 3 cos() 2 sin 2 3 sin( 1 4 3 2 2 3 2 2 3 ) 2 sin 2 3 sin() 2 cos3 2 3 cos( 1 4 3 )cos31( 2 sin 2 )cos3( 2 cos 2 3 = + = = B A BA r r B r A BA r r B r A r )cos1(sin)cos1(cos++= )cos1(sin)cos1(cos++= )cos1( sin )cos1( cos + + = ) 2 sin 3 5 2 3 sin() 2 cos5 2 3 cos( 1 4 3 :coordinateangular theChanging ) 2 sin 3 1 2 3 (sin) 2 cos 2 3 (cos 1 4 3 ) 2 cos 2 3 (cos) 2 sin3 2 3 (sin 1 4 3 ) 2 cos 3 5 2 3 (cos) 2 sin5 2 3 (sin 1 4 3 gives relations stress general theinto results thesengSubstituti 3 )2( ,, 2 3 gave problem theon condtionsBoundary ])2sin()2()2cos()2(sincos[)1( ])2cos()2sin(cossin[)1( ])2cos()45()2sin()45( cos)1(sin)1([ ])2cos()2sin(cossin[ 2 2 22 2 ++ = ++ += == = + = ++ += = === += +++= ++++ += +++= r r BA r BA r BA r BA r A A CBD DCBAr DCBAr DC BAr DCBAr r r r r r 8.40*. A r A r A r A r A r A r A r A r A r r r r / of contoursplot wish toWe sin 2 3 2 cos 2 sin2 2 3 2 cos 2 sin 2 cos 2 sin4 2 3 2 cos4 2 sin 2 cos 2 sin4 2 3 )cos1( 2 sin 2 cos)cos1( 2 3 2 )cos1( 2 sin 2 3 )cos1( 2 cos 2 3 )cos3( 2 cos 2 3 :I Mode max 2222 4224 2222 2 2 max = = + = + = + + = + = + = + = = B r B r B2222222 B2222222 B 2222222 r B r B r B r B rmax+= rmax+= r max + = r r r / of contoursplot wish toWe )3cos(1 2 2 sin 2 coscos6 2 cos 2 sincos9 2 cos 2 sin 2 )cos31(cos)cos31(sin++= )cos31(cos)cos31(sin++= )cos31( cos)cos31( sin ++ = 2 2 2 2 )cos31( 2 cos 2 )cos1( 2 sin 2 3 )cos31( 2 sin 2 :II Mode max 2 2222 2 2 += + + + = = + = = max - Contours Mode I max
Elasticity: Theory-- Applications-- and Numerics 3rd Edition

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