Finding Principal Stresses of a Stress Tensor

by Gabriel Malestein

Submitted : Fall 2014

This paper presents a general solution for finding the eigenvalues of a stress tensor. Beginning with a 3D stress tensor presented as a 3x3 matrix, a transformation vector, called an eigenvector, is found. The eigenvector produces a corresponding eigenvalue which acts as a scaling factor. When applied to a physical body, the eigenvalues are the principal stresses at a given point, which are all normal stresses to 3 orthogonal planes. This reduces the mathematical complexity of a stress tensor by allowing calculations to be done without consideration for shear stresses.

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