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- Thread starter feynman1
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- #1

- 231

- 17

- #2

Chestermiller

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Sure.

- #3

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is plane stress never applicable here under this BC?Sure.

- #4

Chestermiller

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How can it be? It requires the z principal stress and one other principal stress to be equal.is plane stress never applicable here under this BC?

- #5

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i don't get you by 'equal'How can it be? It requires the z principal stress and one other principal stress to be equal.

- #6

Chestermiller

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If the stretching were in the x-direction (i.e., BC applied at x = 0), the strains in the y- and z-directions would be zero. That would mean that the stresses in the y and z directions would have to be equal.i don't get you by 'equal'

- #7

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'the strains in the y- and z-directions would be zero' for x=0 or for all x?If the stretching were in the x-direction (i.e., BC applied at x = 0), the strains in the y- and z-directions would be zero. That would mean that the stresses in the y and z directions would have to be equal.

- #8

Chestermiller

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At x = 0.'the strains in the y- and z-directions would be zero' for x=0 or for all x?

- #9

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at x=0, stress y=stress z not equal to 0, because strain x isn't 0. but plane stress requires stress z to be 0.At x = 0.

- #10

Chestermiller

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Rightat x=0, stress y=stress z not equal to 0, because strain x isn't 0. but plane stress requires stress z to be 0.

- #11

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but you seemed to disagree with plane stress being not applicable here.Right

- #12

Chestermiller

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Sure. So...?but you seemed to disagree with plane stress being not applicable here.

- #13

Chestermiller

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- #14

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* all available DOFs - translations in X and Y direction (for some elememts also rotation about the Z axis), Z translation is simply not considered in 2D analysis

- #15

Chestermiller

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- #16

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- 3D model: 36,98 MPa

- 2D plane stress model: 36,88 MPa

- beam model: 36,1 MPa

- analytical: 36 MPa

The only problem is with stress singularity caused by the unrealistic assumption of fixed constraint itself (both in case of 3D and 2D model) but it can be ignored and the results read slightly away from the very end of the beam.

- #17

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we have been discussing the plane stress theory. of course these results differ little as you go away from the fixed end.

- 3D model: 36,98 MPa

- 2D plane stress model: 36,88 MPa

- beam model: 36,1 MPa

- analytical: 36 MPa

The only problem is with stress singularity caused by the unrealistic assumption of fixed constraint itself (both in case of 3D and 2D model) but it can be ignored and the results read slightly away from the very end of the beam.

- #18

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plane stress says stress z=0.Sure. So...?

so is plane stress applicable here?

- #19

Chestermiller

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As I said, it certainly applies to shear at the boundary you described.plane stress says stress z=0.

so is plane stress applicable here?

- #20

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but principal stress z is already not 0, violating plane stress requirements, why do we mention shear anyway?As I said, it certainly applies to shear at the boundary you described.

- #21

Chestermiller

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It is zero if we apply shear at your boundary.but principal stress z is already not 0, violating plane stress requirements, why do we mention shear anyway?

- #22

Chestermiller

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- #23

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to fix the end with shear is really a brilliant idea of rendering the shaky plane stress applicable. but on 'the principal in-plane stresses are not zero, even at the boundary.', aren't the principal in-plane stresses 0 as you wrote in your equation?

- #24

Chestermiller

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Do you know how to determine the principal stresses for this specific state of stress? They are not zero. They are at two different angles to the boundary, offset from one another by 90 degrees.to fix the end with shear is really a brilliant idea of rendering the shaky plane stress applicable. but on 'the principal in-plane stresses are not zero, even at the boundary.', aren't the principal in-plane stresses 0 as you wrote in your equation?

- #25

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sorry i got it wrong and the principal stresses aren't 0. then we can come to the conclusion that for plane stress to be applicable when 1 end is fixed, that fixed end has to be sheared.Do you know how to determine the principal stresses for this specific state of stress? They are not zero. They are at two different angles to the boundary, offset from one another by 90 degrees.

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