Finite Element Analysis - Thermomechanics of Solids Part 2 pptx

... ) ( ( ( TEN 22 ) TEN 22 TEN 22( ) TEN 22 TEN 22 ) TEN 22 T (()( () ( (()( CC UC C CU C = = = a b c n n ) ) ) 2 2 Ua Cb n TEN 2 22= () U n 2 U n 2 U n 2 U n 2 U n 2 U n 2 U n 2 U n 2 U n 2 U n 2 U n 2 ′ = ′ AB T GCG 0749_Frame_C 02 ... C T 1 TT 22 2 T 2 T 2 T )()(,) ()(,) () (,) () (,) ()(,) () (,) () TEN b a TEN a b TEN b a TEN a b TEN b a TEN a b TEN b...

Ngày tải lên: 11/08/2014, 04:20

... ++ + −−− −−+ −−− −+ 11 1 2 1 3 1 2 11 1 1 1 3 11 1 2 11 1 2 1 2 11 1 2 1 2 010 2 0 3 0 00 1 0 2 0 () () ( 111 1 2 22 2 2 22 2 2 2 3 1 2 22 2 2 2 3 22 2 2 22 1 2 2 2 3 1 010 2 0 3 0 00 yy xy x xy ... b b T b T b T ββΦΦγγββ ϕϕ ϕϕ ϕϕ 22 2 2 2 2 2 2 2 2 2 2 ′ =e (, , ,) (, , ) ()xyzt xyz t mb mb mb ββΦΦγγ 22 2 T ββββββΦΦ ΦΦ00 00ΦΦ γγ γγ γγ mb...

Ngày tải lên: 11/08/2014, 04:20

... E d dx σ = 0 EA du dx 2 2 0= . E,A L P 0749_Frmae_C03 Page 44 Wednesday, February 19, 20 03 5:01 PM © 20 03 by CRC CRC Press LLC 48 Finite Element Analysis: Thermomechanics of Solids in which, for ... 0749_Frmae_C03 Page 43 Wednesday, February 19, 20 03 5:01 PM © 20 03 by CRC CRC Press LLC 44 Finite Element Analysis: Thermomechanics of Solids 2. δ ( f...

Ngày tải lên: 11/08/2014, 04:20

... the deformed position of (X,Y) = (L,L). ∂ ∂∂ = ∂ ∂ + ∂ ∂       2 12 12 2 11 2 2 2 22 1 2 1 2 E xx E x E x . EaXaXYaY EbXbXYbY EcXcXYcY 11 1 2 23 2 22 1 2 23 2 12 1 2 23 2 =++ =++ =++. EaaXaY EbbXbY EccXcY 11 ... d d dX d dX d dX 0 123 123 111 2 22 3 33 =⋅×= == = XX X XXX XeX eX e . dx d j i x dV d d d JdV J =⋅× === xx x FC 12 3 0 1 2 ,()(), det det J...

Ngày tải lên: 11/08/2014, 04:20

... −wI p I α [][]. 13 3 2 1 s w c pc s w c pc s w c pc w p I 1 1 1 2 2 2 3 3 3 3 22 022 022 001 = ′ =− == ′ =− == ′ =− = ′ =→ = d d d d d d d d α α α / / / . cc c pc 23 1 2 12= = =/ and / α . spc c c pc c c c 11 2 1 2 2 1 1 32 2 2 21 21 1 =− =− =−       =−       α α α α / / . / ... − − 22 22 22 22 22 2 12 9 LW IF F F FF IF II U TTT TT (a) (b) (c) VEC...

Ngày tải lên: 11/08/2014, 04:20

... February 19, 20 03 5:07 PM © 20 03 by CRC CRC Press LLC 1 12 Finite Element Analysis: Thermomechanics of Solids The balance of linear momentum, together with the stress-strain and strain- displacement ... 19, 20 03 5:07 PM © 20 03 by CRC CRC Press LLC 114 Finite Element Analysis: Thermomechanics of Solids in which B T is the thermal analog of the strain-di...

Ngày tải lên: 11/08/2014, 04:20

... Wednesday, February 19, 20 03 5:08 PM © 20 03 by CRC CRC Press LLC 120 Finite Element Analysis: Thermomechanics of Solids There are two classes of errors in finite -element analysis: Modeling ... hardware and soft- ware, especially computer-aided design (CAD) systems. Today, a number of highly developed, user-friendly finite -element codes are available commerciall...

Ngày tải lên: 11/08/2014, 04:20

... ,,ee e, e e e e e e e e e e e e e fkukukuku fkukuk + + + + + + + + + + + + + + + =+++ =++ 14 21 11 2 21 12 2 22 13 2 23 14 2 24 32 21 3 31 2 2 3 32 2 , ,,,,,,,, ,, ,, , () () () () () () ,, , , ,3 3 33 24 3 34 () ()e e e e uku + + + + + uu uu uu uu uuuuuuuu uuuuuuu ... u uuu eeee eeee eeee ee ,,,, ,,,, ,,,, ,, 11 2 2 3 5 4 6 11 2 12 3 13 4 14 5 21 5 22 4 23 9 24 8 3...

Ngày tải lên: 11/08/2014, 04:20

... that (11.37) γγ j H λ j 2 λ j jj jj 2 =− γγγγ γγγγ H H K M MK=         =         10 01 11 12 12 22 kk kk . () [ ] [ ] , λλ 22 11 22 2 11 22 12 2 0++ + +=kk kk k λ +− =− + ± + − + [] =− + ± − − [] , [][][ ] [][] 2 11 22 11 22 2 11 22 12 2 11 22 11 22 2 12 2 1 2 4 1 2 4 kk kk ... Finally, for l 22 2 13 12 1 12= − =/(/) / . L 2 10 12 1 12...

Ngày tải lên: 11/08/2014, 04:20

... Wednesday, February 19, 20 03 5:19 PM © 20 03 by CRC CRC Press LLC 180 Finite Element Analysis: Thermomechanics of Solids 13.5 EXERCISES 1. Find the exact solution for a circular rod of length L, radius ... February 19, 20 03 5:19 PM © 20 03 by CRC CRC Press LLC 174 Finite Element Analysis: Thermomechanics of Solids For the assumed conditions, the dynamic the...

Ngày tải lên: 11/08/2014, 04:20