The 3D Hooke's law is0₂o6₂OxyXZ0₂yzE(1+v)(1−2v)1-v2U000U1-v2000001-v 000021-2v0000001-2v00000w wEzExz0 1-2v|yz)where E is the Young's modulus, vis the Poisson's ratio.a) Derive the stiffness matrix and compliance matrix for plane strain condition (&xz = &yz= Ezz = 0).b) Derive the stiffness matrix and compliance matrix for plane stress condition (0xz = 0 yz=O₂z = 0).Ey.c) Show that for uniaxial stress condition (σ #0, all other stress components are zero), theYoung's modulus can be expressed as E = ºx, and the Poisson's ratio as v=-²ExEx

is the Young's modulus, is poisson's ratio.

The 3D Hooke's law is oy 0₂ O xz O yz 1-v D V V 1-v E U (1+0)(1-2v) 0 0 0 0 0 0 2 22 1-v 0 0 0 0 0 1-2v 0 &xz 0 1-20 Eyz 000 0 1-20 0 0 0 0 0 Ex ww ww Ey Ez Ex where E is the Young's modulus, v is the Poisson's ratio. a) Derive the stiffness matrix and compliance matrix for plane strain condition (ɛ, =&₂ = 0). b) Derive the stiffness matrix and compliance matrix for plane stress condition ( = O₂ = 0). c) Show that for uniaxial stress condition (0, 0, all other stress components are ze Young's modulus can be expressed as E = Ox, and the Poisson's ratio as v = -x E Ex

The 3D Hooke's law is oy 0₂ O xz O yz 1-v D V V 1-v E U (1+0)(1-2v) 0 0 0 0 0 0 2 22 1-v 0 0 0 0 0 1-2v 0 &xz 0 1-20 Eyz 000 0 1-20 0 0 0 0 0 Ex ww ww Ey Ez Ex where E is the Young's modulus, v is the Poisson's ratio. a) Derive the stiffness matrix and compliance matrix for plane strain condition (ɛ, =&₂ = 0). b) Derive the stiffness matrix and compliance matrix for plane stress condition ( = O₂ = 0). c) Show that for uniaxial stress condition (0, 0, all other stress components are ze Young's modulus can be expressed as E = Ox, and the Poisson's ratio as v = -x E Ex

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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