Practical Guide to the Packaging of Electronics: Thermal and Mechanical Design and Analysis, Third Edition by Ali Jamnia

Author:Ali Jamnia [Jamnia, Ali]
Language: eng
Format: azw3
ISBN: 9781498753951
Publisher: CRC Press
Published: 2016-11-30T16:00:00+00:00

where σ is stress, E is Young’s modulus of elasticity, and ε is strain. Multiply each side by the cross-sectional area, and we obtain

Aσ = EAε

Note that the right-hand side is equivalent to force and strain is the derivative of displacement with respect to length, thus,

or

For each element, we balance the force at each node. For the first element:

(10.3)

For the second element:

(10.4)

Notice that in a general formulation, the stiffness and the length of the two elements are different. Now combine the two elements:

(10.5)

In matrix notation, this equation is written as

[K]{u} = {F}

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