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Q3. Write a python code to do the following operations. 1. Create a stress tensor and a strain tensor in form of NumPy arrays: 1.0 -0.2 0.5 a= -0.2 4.3 0.0 0.5 0.0 5.2, 2. The hydrostatic stress is ayd 0.02 -0.01 0.03 0.2 -0.05 = -0.01 0.03 - (100) 1. -0.05 0.4 and the deviatoric stress is dey-hyd Define a function stress_hyd_dev () which takes in a stress tensor and returns the hydrostatic stress and the deviatoric stress. Then, apply this function to calculate the hydrostatic stress and the deviatoric stress of the stress defined in Question 1. 3. If we rotate the material, the representation of the stress tensor will change. Suppose that the coordinate system is (e₁,e.es). If we rotate the material about an axis - (₁.2. My) (a unit vector) by the angle e, the representation of the stress tensor will become o-Ro, where R is the rotation matrix cos@+u(1-cos) R=(1-cos) + ay sin ₁₂(1-cos 9)-, sin cos@+(1-cos) uyu(1-cos)+u, sin 6 (1-cos@)-₂ sine cos+u(1-cos) Define a function stress rot() which takes in a stress tensor, rotation axis and rotation angle and returns the stress tensor after rotation. Then, apply this function to calculate the stress tensor after rotating the material about u= (1, 1, 1) by the angle x/6. uu(1-cos) + ₂ sin ₂(1-cos)-₁ sin

Q3. Write a python code to do the following operations. 1. Create a stress tensor and a strain tensor in form of NumPy arrays: 1.0 -0.2 0.5 a= -0.2 4.3 0.0 0.5 0.0 5.2, 2. The hydrostatic stress is ayd 0.02 -0.01 0.03 0.2 -0.05 = -0.01 0.03 - (100) 1. -0.05 0.4 and the deviatoric stress is dey-hyd Define a function stress_hyd_dev () which takes in a stress tensor and returns the hydrostatic stress and the deviatoric stress. Then, apply this function to calculate the hydrostatic stress and the deviatoric stress of the stress defined in Question 1. 3. If we rotate the material, the representation of the stress tensor will change. Suppose that the coordinate system is (e₁,e.es). If we rotate the material about an axis - (₁.2. My) (a unit vector) by the angle e, the representation of the stress tensor will become o-Ro, where R is the rotation matrix cos@+u(1-cos) R=(1-cos) + ay sin ₁₂(1-cos 9)-, sin cos@+(1-cos) uyu(1-cos)+u, sin 6 (1-cos@)-₂ sine cos+u(1-cos) Define a function stress rot() which takes in a stress tensor, rotation axis and rotation angle and returns the stress tensor after rotation. Then, apply this function to calculate the stress tensor after rotating the material about u= (1, 1, 1) by the angle x/6. uu(1-cos) + ₂ sin ₂(1-cos)-₁ sin

Programming Logic & Design Comprehensive
Programming Logic & Design Comprehensive
9th Edition
ISBN:9781337669405
Author:FARRELL
Publisher:FARRELL
Chapter6: Arrays
Section: Chapter Questions
Problem 5GZ
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Q3. Write a python code to do the following operations. 1. Create a stress tensor and a strain tensor in form of NumPy arrays: -0.2 0.5 4.3 0.0 5.2 1.0 a= -0.2 0.5 0.0 2. The hydrostatic stress is 0.02 -0.01 0.03 €= -0.01 0.2 -0.05 0.03 -0.05 0.4 Ohyd = (tro) 1. and the deviatoric stress is deyddyd Define a function stress hyd_dev () which takes in a stress tensor and returns the hydrostatic stress and the deviatoric stress. Then, apply this function to calculate the hydrostatic stress and the deviatoric stress of the stress defined in Question 1. where R is the rotation matrix 3. If we rotate the material, the representation of the stress tensor will change. Suppose that the coordinate system is (e₁,e₂, es). If we rotate the material about an axis u= (₁,42,43) (a unit vector) by the angle 6, the representation of the stress tensor will become oRo, cos @ + u(1-cos) R=424(1-cos) + 3 sin u₁u₂(1-cos 9)-uy sin cos+u(1-cos) uu₂(1-cos 8) + u, sin 0 uu(1-cos 0) + u₂ sin 0 ₂(1-cos)-uj sin 0 cos 9+ (1-cos 8) ₁₁ (1-cos)-u₂ sin Define a function stress_rot() which takes in a stress tensor, rotation axis and rotation angle and returns the stress tensor after rotation. Then, apply this function to calculate the stress tensor after rotating the material about u= (1, 1, 1) by the angle x/6.
Transcribed Image Text:Q3. Write a python code to do the following operations. 1. Create a stress tensor and a strain tensor in form of NumPy arrays: -0.2 0.5 4.3 0.0 5.2 1.0 a= -0.2 0.5 0.0 2. The hydrostatic stress is 0.02 -0.01 0.03 €= -0.01 0.2 -0.05 0.03 -0.05 0.4 Ohyd = (tro) 1. and the deviatoric stress is deyddyd Define a function stress hyd_dev () which takes in a stress tensor and returns the hydrostatic stress and the deviatoric stress. Then, apply this function to calculate the hydrostatic stress and the deviatoric stress of the stress defined in Question 1. where R is the rotation matrix 3. If we rotate the material, the representation of the stress tensor will change. Suppose that the coordinate system is (e₁,e₂, es). If we rotate the material about an axis u= (₁,42,43) (a unit vector) by the angle 6, the representation of the stress tensor will become oRo, cos @ + u(1-cos) R=424(1-cos) + 3 sin u₁u₂(1-cos 9)-uy sin cos+u(1-cos) uu₂(1-cos 8) + u, sin 0 uu(1-cos 0) + u₂ sin 0 ₂(1-cos)-uj sin 0 cos 9+ (1-cos 8) ₁₁ (1-cos)-u₂ sin Define a function stress_rot() which takes in a stress tensor, rotation axis and rotation angle and returns the stress tensor after rotation. Then, apply this function to calculate the stress tensor after rotating the material about u= (1, 1, 1) by the angle x/6.
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