Explicitly show that Boussinesqs problem as illustrated in Fig. 13.2 is solved by the superposition of a

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Explicitly show that Boussinesq’s problem as illustrated in Fig. 13.2 is solved by the superposition of a Galerkin vector and Lame´’s potential given by relation (13.3.13). Verify that the Cartesian displacements and stresses are given by:

U= 0x = Tyz = Px Z 4R R P 3xz 2TR R P 3yz 2TR R 3Pz 2TR$ 3Pyz 2RS 12v R+Z Txy V = - (12v) (1-2v) 3Pxz 2TR Z

Fig 13.2

Equation 13.3.13

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Elasticity Theory Applications And Numerics

ISBN: 9780128159873

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Authors: Martin H. Sadd Ph.D.

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Question Posted: Jan 15, 2024 05:03 AM

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Explicitly show that Boussinesqs problem as illustrated in Fig. 13.2 is solved by the superposition of a

Question:

U= 0x = Tyz = Px Z 4R R P 3xz 2TR R P 3yz 2TR R 3Pz 2TR$ 3Pyz 2RS 12v R+Z Txy V = - (12v) (1-2v) 3Pxz 2TR Z Py 4R R Z R Z R P 3.xyz 2R R 12v R+z R (2R+z) + R+Z R(R+z) + 3 R R+z R(R+ 2) 2 (2R+z) (1-2v) (2R+z)xy R(R+ 2) W = P 4R +2) 2(1-v) +

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Elasticity Theory Applications And Numerics

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