[IMPL] Implement transformation of stress/strain tensor to given coordinate system

[JiriKuzelka]

ℹ️ General Information

Component Name: Transformation to another coordinate system

Component Location: structural_mechanics/transform/

Suggested Python Name: transform_coordinate_system

FABER WG Relation:

Brief Description: Transforms a tensor into given coordinate system

Priority: 5 (1-10 scale)

Technical Complexity: 2 (1-10 scale)

Estimated Effort: 3 (1-10 scale)

Dependencies:

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Implementation Details

📋 Specification

A function implementing stress or strain tensor transformation for given set of points to another coordinate system which is given by directional cosines matrix.

Mathematical Formulation

For given stress tensor $$\sigma$$ with componenets in refernece coordinate system and matrix R of directional cosines of new coordinate system the stress tensor $$\sigma'$$ in new coordinate system can be computed as:

$$ \displaystyle \sigma' = R\sigma R^T $$

Inputs

Parameter	Symbol	Type	Description	Units	Constraints
stress/strain	$$\sigma/ \epsilon$$	array of floats	-	MPa / -	-
T	$$T$$	3x3 matrix of floats	directional cosines matrix	-	$$T^TT=I$$

Outputs

Parameter	Symbol	Type	Description	Units	Range
stress/strain	$$\sigma/ \epsilon$$	array of floats	-	MPa / -	$$(-\infty;\infty)$$

Expected Behavior

🔧 Implementation Guidelines

Function Signature

# Suggested function signature
def stress_transform_csys():
    pass
def strain_transform_csys():
    pass

Code Structure

Error Handling

✅ Validation & Txesting

Test Cases

Test Case	Inputs	Expected Outputs	Notes
Example 1
Example 2

Validation Criteria

• Mathematical accuracy verified against literature
• Edge cases handled appropriately
• Output format matches specification

📚 References & Resources

📝 Technical Notes

Performance Considerations

Edge Cases to Handle

Special Requirements