3.11e If the deformation mapping of a body in a naval machine is given by x(X) = (X + AXz)ên + (Xz+ BXı)êz+X3êng, where A and B are constants. Determine the components of the Euler strain tensors.

3.11e If the deformation mapping of a body in a naval machine is given by x(X) = (X + AXz)ên + (Xz+ BXı)êz+X3êng, where A and B are constants. Determine the components of the Euler strain tensors.

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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Concept explainers

Stress transformation

The term stress indicates the measure of internal forces that develop due to an external force's application on an object. When a specific external force is applied to an object, internal stress generates in the material. The value of stress can obtain by taking the ratio of the externally applied force and cross-sectional area of the object. There are different types of stress depending on the type of external force.

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3.11e If the deformation mapping of a body in a naval machine is given by
X(X) = (X₁ + AX₂)ê₁ + (X₂ + BX₁)êz + X3ê3,
where A and B are constants.
Determine the components of the Euler strain tensors.

The Grain strain tensor in HW-5 is [E] = 0.5 { [F]¹ [F] – [1] }.
The Euler strain tensor in HW-5 is [e] = 0.5 {[1] - [F] [F]-¹}.

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