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

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.

8 sections

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Sections

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  1. 1

    This section reviews the Linear Momentum Balance (LMB) formulation in the...

  2. 2
    A Simpler Approach To Find The Traction Force

    This section provides a simplified approach to determine the traction force...

  3. 3
    Force On +r And −r Planes

    This section discusses the derivation of forces acting on the +r and −r...

  4. 4
    Force On +θ And −θ Planes

    This section discusses the calculations of forces acting on the +θ and -θ...

  5. 5
    Total Force Due To Traction

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

  6. 6

    This section focuses on understanding body forces in cylindrical coordinate...

  7. 7
    Rate Of Change Of Linear Momentum

    This section discusses the rate of change of linear momentum in a...

  8. 8
    Final Balance

    This section delves into the final balance of linear momentum in a...

What we have learnt

  • Linear Momentum Balance involves calculations based on the cylindrical coordinate system.
  • Forces due to traction on cylindrical elements are determined under simplifying assumptions.
  • Equations derived in cylindrical coordinates differ markedly from those in Cartesian coordinates.

Key Concepts

-- Linear Momentum Balance (LMB)
A principle that relates the forces acting on a body to the rate of change of momentum of that body.
-- Cylindrical Coordinate System
A three-dimensional coordinate system where each point is defined by a radial distance, an angle, and a height along a vertical axis.
-- Traction
The internal force per unit area acting on the surface of an object.
-- Taylor Expansion
A mathematical series that approximates a function by expanding it in terms of its derivatives at a particular point.

Additional Learning Materials

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