Solid Mechanics | 18. Recap by Abraham | Learn Smarter with Allrounder.ai
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18. Recap

This lecture focuses on the derivation of the Linear Momentum Balance (LMB) in a cylindrical coordinate system, demonstrating the forces due to traction on various planes and the influence of body forces. The analysis covers approximations involved in calculating forces based on the assumption of constant traction across specified planes, leading to unique results distinct from Cartesian coordinates. The conclusion emphasizes the differing equations arising in cylindrical coordinates when compared to Cartesian coordinates, setting the stage for further exploration in future lectures.

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Sections

  • 1

    Recap

    This section reviews the Linear Momentum Balance (LMB) formulation in the cylindrical coordinate system, highlighting key derivations and simplifications.

    Learning Practice

  • 2

    A Simpler Approach To Find The Traction Force

    This section provides a simplified approach to determine the traction force acting on a cylindrical element within a cylindrical coordinate system, using basic assumptions about traction constancy.

    Learning Practice

  • 3

    Force On +r And −r Planes

    This section discusses the derivation of forces acting on the +r and −r planes in a cylindrical coordinate system, emphasizing the assumptions of constant traction.

    Learning Practice

  • 4

    Force On +θ And −θ Planes

    This section discusses the calculations of forces acting on the +θ and -θ planes within a cylindrical coordinate system, emphasizing the constant traction assumption and the implications of varying basis vectors.

    Learning Practice

  • 5

    Total Force Due To Traction

    This section discusses the derivation of total force due to traction in a cylindrical coordinate system.

    Learning Practice

  • 6

    Body Force

    This section focuses on understanding body forces in cylindrical coordinate systems, particularly how body forces are calculated based on the cylindrical element's volume.

    Learning Practice

  • 7

    Rate Of Change Of Linear Momentum

    This section discusses the rate of change of linear momentum in a cylindrical coordinate system, emphasizing its derivation and relation to the balance law.

    Learning Practice

  • 8

    Final Balance

    This section delves into the final balance of linear momentum in a cylindrical coordinate system by deriving equations for different directional components.

    Learning Practice

References

ch18.pdf

Class Notes

Memorization

What we have learnt

  • Linear Momentum Balance inv...
  • Forces due to traction on c...
  • Equations derived in cylind...

Final Test

Revision Tests