Answered: A laminae is considered a plate with…

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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Question

A laminae is considered a plate with only biaxial stresses in plane stress conditions. From Generalized Hooke’s
Law that you learnt in Strength of Materials, we know these equations to be true in such conditions.

Or in other words, we know the Compliance matrix that represents the laminae. Find the Stiffness matrix of the
same laminae. Or in other words, prove that the equations below are true for the same laminae. The equations
below are what we discussed in Lecture.

Assume the laminae has isotropic properties.

A laminae is considered a plate with only biaxial stresses in plane stress conditions. From Generalized Hooke's
Law that you learnt in Strength of Materials, we know these equations to be true in such conditions.
VO
<= [0₂-V0₁₂]
Exx
xxxx
E
Eyy
=
-H[o,,-vo,]
νσ.
E
€22 _V(0+0„)]
=
o yy
уу.
E
Or in other words, we know the Compliance matrix that represents the laminae. Find the Stiffness matrix of the
same laminae. Or in other words, prove that the equations below are true for the same laminae. The equations
below are what we discussed in Lecture.
0₂ = x ² [5 + v6 ]
XxX
1-
Assume the laminae has isotropic properties.
Txv=GY xy
xy
E
1 - 1 2 [Exy + VERA]

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