Starting with the Navier equations (10.2.2) for plane strain, introduce the complex displacement U = u +

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Starting with the Navier equations (10.2.2) for plane strain, introduce the complex displacement U = u + iv, and show that:

a (au au z (2 + ) = (12 + az dz Integrate this result with respect to Z to get au au z z (2+) + a U +2 zaz zz

where f^′(z) is an arbitrary analytic function of z. Next, combining both the preceding equation and its conjugate, solve for ∂U/∂z, and simplify to get form (10.2.9).

Equation 10.2.2

Equation 10.2.9

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Elasticity Theory Applications And Numerics

ISBN: 9780128159873

4th Edition

Authors: Martin H. Sadd Ph.D.

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Question Posted: Jan 15, 2024 05:01 AM

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Starting with the Navier equations (10.2.2) for plane strain, introduce the complex displacement U = u +

Question:

a (au au z (2 + ) = (12 + az dz Integrate this result with respect to Z to get au au z z (2+) + a U +2 zaz zz au +2- = 0 -= f'(z) z

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Use Navier Equations Vu2VVu0 to construct the complex form uPu 2 ...View the full answer

Elasticity Theory Applications And Numerics

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