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. (iv) check that the equilibrium equations are satisfied (v) determine the traction boundary conditions at x =+q and y=+h
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. (iv) check that the equilibrium equations are satisfied (v) determine the traction boundary conditions at x =+q and y=+h
Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter7: Analysis Of Stress And Strain
Section: Chapter Questions
Problem 7.7.13P: An clement of material in plane strain (see figure) is subjected to strains ex= 480 × 10-6, Ey= 70 ×...
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