A very thick structure is subjected to certain traction boundary conditions on its surface. The cross-section and the applied load do not vary with the z-coordinate. The following stress function is proposed for this problem: -y p(x,y) = Sin (x) (A x²e + B e") (i) use the biharmonic equation to find restrictions, if any, on values of A and B (ii) calculate all stress components (iii) calculate all strain components in terms of A, B, and C as well as the Young modulus and Poisson's ratio E and y, respectively. (iv) check that the equilibrium equations are satisfied (v) determine the traction boundary conditions at x =± a and y=tb
A very thick structure is subjected to certain traction boundary conditions on its surface. The cross-section and the applied load do not vary with the z-coordinate. The following stress function is proposed for this problem: -y p(x,y) = Sin (x) (A x²e + B e") (i) use the biharmonic equation to find restrictions, if any, on values of A and B (ii) calculate all stress components (iii) calculate all strain components in terms of A, B, and C as well as the Young modulus and Poisson's ratio E and y, respectively. (iv) check that the equilibrium equations are satisfied (v) determine the traction boundary conditions at x =± a and y=tb
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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Transcribed Image Text:A very thick structure is subjected to certain traction boundary conditions
on its surface. The cross-section and the applied load do not vary with the z-coordinate. The
following stress function is proposed for this problem:
-y
p(x,y) = Sin (x) (A x²e + B e)
(i) use the biharmonic equation to find restrictions, if any, on values of A and B
(ii) calculate all stress components
(iii) calculate all strain components in terms of A, B, and C as well as the Young modulus and
Poisson's ratio E and y, respectively.
(iv) check that the equilibrium equations are satisfied
(v) determine the traction boundary conditions at x = ± a and
y=+b
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