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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 =++=++=        […]

10.1. 22 4 224 2 2 2 2 2 2 16 4 2 1 , 2 1 lines previous Solving )( 2 1 ,)( 2 1 , zz zzzzzzzzzzyx y i xzy i xz zz i y z zy z […]

10.14. 4       = aez 2 2 4 4             z z z z i 1 2 1   + −+   […]

11.1. exist moduli elastict independen 21only that implies thus and symmetric ismatrix stiffness canisotropi 66 general the thusand s,Hooke‘ From      =   ij kl kl ij ijkl kl ij ee C e == = […]

11.16*. :cases isotropic and corthotropifor PlotsMATLAB 0, 1 case, isotropic For the 0 )( cos )( cos )]()sin)(coscos(sin )()sin)(coscosRe[(sin2 0 sincos sincos sincos sincos )( sin )]()sin(cos)()sinRe[(cos2 sincos cos1 sincos cos1 )( sin )sin)(cossin(cos sin)( )]()cos(sin)()cosRe[(sin2 ))((2 )(, ))((2 )( […]

12.1. ( ) ( ) ijoijkk ijoijokkijij okkkkokkkk ijoijkkij T ij M ijij ijkkij M ij ijo T ij TTee TTTTee E TTe E TT E e TT EE eee EE e TTe −+−+=      −−−− […]

13.1. satisfied. be willequations sNavier’0)( and0 Since 0 )4(228 )(222 )(,4 2 3 222 3 222 == =   = +=+=   −   = +=+=   +   = ++==+= uu ee z w […]

13.15. nintegratio of functionarbitrary thedropped have wewhere,2 gIntegratin 2 1 0 )1(2 1 21)21)(1(4 0)0,( )1(421)1(421 2)( 12–13 ExerciseFrom )1(4)1(4 43 )1(4)1(4)1(4 2 )1(4)1(4 2 0and0with,),(,),(,0 :s Potentialq Boussines– FormicAxisymmetr )1(4 2 :ation Represent PapkovichGeneral 2 2 2 2 2 […]

14.1. ( ) ( ) 0 11 22 1 0 1 2 111 22 1 0 11 12 1 1 22 11 2 1 0 11 12 11 :constant and)( of case special For the 1.–7 Table conversion use and […]

15.1.     +−+ −  − −++ −  −= − − −  =       −  =       + =+      […]

15.11.* 625.0 6.1 1 16 9 45 48 1 1 45 48 1 1 )5.4)(5.0(32)5.1(45 )5.1(45 )5)(1(32)2(45 )2(45 54.0 85.1 1 16 9 45 68 1 1 45 68 1 1 )5.8)(75.0(16)5.1(45 )5.1(45 )310)(1(16)2(45 )2(45 37 11 16/9 When 13690 […]

16.1. functions ionapproximator ioninterpolat theare)( 2 1 ),( where ),( )( 2 1 )( 2 1 )( 2 1 ])()()[( 2 1 ),( ),(for form original theinto results thesengsubstitutiBack ,, and element, theofarea theis wherewhere )( 2 1 ,)( 2 […]

2.1.                 −− −− −− =−=                 ++ =+= +=== […]

3.1. −=+−= −++−= = +=−+= = == −== −==           = cossin)(cossincossin )sin(coscossincossin cossincossin2cossin : plane obliqueon Stresses cos sin )cos,sin(, 000 00 00 22 2222 XYYX YX S YnT XnT […]

4.1.                     = +++++= +++++= +++++= +++++= +++++= +++++= +++++= +++++= +++++= +++++= +++++= +++++= 313131233112313331223111 233123232312233323222311 123112231212123312221211 333133233312333333223311 223122232212223322222211 113111231112113311221111 […]

5.1. x y T l h h x 30o l x a b (a) x w (b) 0),0(),0( 40sin),(,40cos),( 0)0,()0,( == −== == yvyu pbxTpbxT xTxT o y o x yx 0),(),( 0),0(),0( == == ywTywT yTyT yx yx p […]

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 […]

7.1. xyxyxyxyxy xyy yxx yxyxyxyxy yxyxyxyxx yxyx yxyx yxyx yxyx yyxy xyxx E ee E e E e EE EE e ee ee ee ee eee eee  + =  == −− + = −− + = + −+ […]

8.1. 033 042240 042240 4 4 04 22 22 4 40 =++ ++= AAA yAyxAxA 024824 =++= AAA 8.2. 1 4 3 ,0, 2 2 3 0 inspecitonBy 4 3 4 2 2 2 2 2 32 2 4  […]

8.22. p rr rr A r A p r A uEEE p r A r A Brr r A p r A E B E ruru rr r r A p r A E up r A r A p […]

8.39. )cos31( 2 cos 2 )cos1( 2 sin 2 )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 […]

9.1. 654321 2 2 222222 1111 22 11 2 3 2 2 2 2 2 2 2 2 2 2 2 2 1,2,3,4 1,2 form general the yieldsresults theseCombining )( ˆ 0)( ˆ 0 )( ),( ),( ˆ )( ),( […]

9.20.* : PlotMATLAB 3 16 1 2 tanh,10,1010 a b For 2 tanh 11024 3 16 :form ldimensiona–Non 2 tanh 11024 3 16 : (9.5.12) relation From 3 4 4 4 3 3 5,3,1 5 4 5 3 4 5,3,1 […]