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A large thin rectangular plate is subjected to certain traction boundary conditions on its thin edges. The following stress function is proposed for this problem: p(x,y) = A x¹ + Bx²y² + Cy² (i) use the biharmonic equation to find restrictions, if any, on values of A, B, and C (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.

A large thin rectangular plate is subjected to certain traction boundary conditions on its thin edges. The following stress function is proposed for this problem: p(x,y) = A x¹ + Bx²y² + Cy² (i) use the biharmonic equation to find restrictions, if any, on values of A, B, and C (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.

Elements Of Electromagnetics
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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A large thin rectangular plate is subjected to certain traction boundary conditions on its thin edges. The following stress function is proposed for this problem: 2 p(x,y) = A x² + B x²y² + Cy² (i) use the biharmonic equation to find restrictions, if any, on values of A, B, and C (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 =+q and y=+ b
Transcribed Image Text:A large thin rectangular plate is subjected to certain traction boundary conditions on its thin edges. The following stress function is proposed for this problem: 2 p(x,y) = A x² + B x²y² + Cy² (i) use the biharmonic equation to find restrictions, if any, on values of A, B, and C (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 =+q and y=+ b
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