Introduction to Continuum Mechanics 3 Episode 6 docx

... vector on the left end face x\ ~ 0. 4.12. For any stress state T., we define the deviatoric stress S to be Stress Power 2 03 where Div denotes the divergence with respect to ... normal stress acting. 4 .6. For the following state of stress findTn' and T 1 ^' where e x ' is in the direction of ej + 2e 2 + 3e 3 and 63 & apos;is in...

Ngày tải lên: 13/08/2014, 16:21

... to the basis at the reference configuration 3. 73. From Eqs. (3. 30.4a), obtain Eqs. (3. 30.5). 3. 74. Verify Eq. (3. 30.8b) and (3. 30.8d). 3. 75. Verify Eq.( 3. 30.9b) and (3. 30.9d). 3. 76. ... (3. 30.9d). 3. 76. Derive Eqs. (3. 30.10). 3. 77. Using Eqs. (3. 30.10) derive Eqs. (3. 30.12a) and (3. 30.12d). 3. 78. Verify Eqs. (3. 30. 13 a) and (3. 30.13d). Ki...

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... the lateral surface vanishes. The unit vector on the plane *3 = a is 63 , so that the surface traction for the stress tensor of Eq. (5. 13. 1) is given by Similarly, there will ... we have a unit normal vector n = (l/a)(x2*2 + X 3* $)- Therefore, the surface traction on the lateral surface Substituting from Eqs. (5. 13. 3) and (5. 13. 5), we have Thus...

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... Elastic Solid 279 From the compatibility equations, Eqs. (3. 16. 8), (3. 16. 9) and (3. 16. 7), we have Thus, G(XI £1) = a K\ + J3x2 + y. In the absence of body forces, the equations ... and 52 planes automatically ensures the symmetry with respect to the 53 plane. (c) All planes that are perpendicular to the 3 plane have their normals parallel...

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... (5 .33 .9) and (5 .33 .11), as those cor- responding to a change of rectangular Cartesian basis, then we come to the conclusion that the constitutive equation given by Eq. (5 .33 .6) ... 7\i>0. 5 .65 . Verify that if <p (x\, X2) satisfy Eq. (5. 16. 7), than it does correspond to a compatible strain field. 5 .66 . Show that if the bending moment...

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... have Thus, i.e., 36 0 Navier-Stokes Equation For Incompressible Fluids 6. 7 Navier-Stokes Equation For Incompressible Fluids Substituting the constitutive equation [Eq. (6. 6.4)] into the ... given by Eq. (6. 13. 3), however, the driving force now is Newtonian Viscous Fluid 36 1 These are known as the Navier-Stokcs Equations of motion for incompressible Ne...

Ngày tải lên: 13/08/2014, 16:21