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
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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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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