This lesson covers the concept of relative displacement tensor, rotation tensor, and strain tensor in the context of mechanical engineering. It delves into the definition of strain tensor and how it is related to relative displacement tensor and rotation tensor. The lesson also explains how these tensors are affected when a component is loaded, causing displacements and deformations. It further discusses the concept of affine transformation, the determination of principal strains, and the conditions for rigid body displacement. The lesson concludes with the explanation of strain compatibility conditions and how to derive them.

- The strain tensor is related to the relative displacement tensor and rotation tensor.
- When a component is loaded, it undergoes displacements and deformations.
- Affine transformation is used to determine the changes in length in the x, y, and z direction between two points.
- The conditions for rigid body displacement are derived from the coefficients of the displacement terms.
- The determination of principal strains involves solving a cubic equation involving the principal strain.
- Strain compatibility conditions are derived from the strains and are used to ensure the strains satisfy certain constant conditions.

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