Stress Analysis
Stress Analysis
Embedded Files
Project Problem:
Project Problem:
Consider a block of size 30 mm x 20 mm x 10 mm made of two metallic materials. The middle one-third of the block is made of Aluminum and the rest is made of Steel. The displacements of 10 material points of the block have been measured after certain loading is applied, and they are given in the Table below.
(a) Determine the distributions (i.e. as functions of coordinates of material points) of displacements, strains and stresses in the block, in the xyz co-ordinate system. Use suitable material properties for steel and aluminum.
(b) Determine the principal stresses and strains, their directions, maximum shear stress, and the octahedral stresses at each of the corner points of the block.
(c) For the chosen materials, using the Von Mises failure criterion, determine which mid-point along the length of the edges on the left face of the block have failed by material yielding (the point at the middle of the edges).
(d) Calculate the % change in the length of the diagonal on the front face of the block passing through the bottom-left corner.
Solution:
Solution:
The Project problem was solved by tackling the deliverables separately. I have explained the logic flow for the code below. The process started with identifying the goals, the assumptions for material properties and then implementing different stress and strain relations and concepts as discussed below to formulate a python code.
Stress, strain, displacement distributions
Principal stress, strain, Oct. stress, Max shear stress for corner points
Von Mises
Diagonal deformation %
Goals
Goals
Assumptions
Assumptions
Steel Young’s Modulus (E) = 210 GPa
Steel Poisson’s Ratio (ν) = 0.3
Aluminium Young’s Modulus (E) = 70 GPa
Aluminium Poisson’s Ratio (ν) = 0.33
HS steel of yield strength 2000 MPa
Polynomial of degree 2 fitted.
Goals 1 & 2:
Goals 1 & 2:
Goal 3:
Goal 3:
Goal 4:
Goal 4:
Summary:
Summary:
The code performs a 3D stress and strain analysis of a deformable body under load. Using a 2nd-degree polynomial, it models displacement and calculates strain and stress components through differentiation. Key results include:
Displacement Field: Approximated using before-and-after coordinates.
Strain and Stress: Normal and shear components derived.
Principal Stresses/Strains: Maximum and minimum values calculated via stress/strain invariants.
Direction Cosines: Indicate principal stress orientation.
Failure Analysis: Von Mises stress compared to thresholds for material failure.
Diagonal Strain: Deformation along the front face diagonal.
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