Answered: σ = 5 0 0 -6 0 -12 0 -12 Pa 1

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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1) Second order stress tensor represents the state of stress at a point in a mechanical part (SEE IMAGES). The eigenvalues of σ are the principal stresses at the corresponding point, which are important for determining when the mechanical part will yield. Use the characteristic equation to determine the principal stresses of σ. Please show your steps.

2) Given that an eigenvector, v, corresponding to a particular eigenvalue, λ˜, of σ must satisfy (σ − λ˜I)v = 0, find the eigenvectors associated with the eigenvalues from (b). You may use software to verify your answer but please show your steps. Draw the eigenvector and eigenvalue.

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