Solid Mechanics | 17. Cylindrical Coordinate System by Abraham | Learn Smarter
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17. Cylindrical Coordinate System

17. Cylindrical Coordinate System

The lecture focuses on deriving the Linear Momentum Balance in a cylindrical coordinate system, essential for analyzing deformation in cylindrical bodies. It introduces the concept of basis vectors in cylindrical coordinates, explains the formulation of linear momentum balance, and details the calculation of forces acting on cylindrical elements. Key aspects include using Taylor’s series for stress components and evaluating changes in basis vector orientations, which are crucial for accurate momentum analysis.

8 sections

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Sections

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  1. 1
    Cylindrical Coordinate System

    This section introduces the cylindrical coordinate system, explaining its...

  2. 1.1
    Basis Vectors

    This section discusses the basis vectors in the cylindrical coordinate...

  3. 1.2
    Cylindrical Element

    This section derives the Linear Momentum Balance in cylindrical coordinates...

  4. 2
    Lmb Formulation

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

  5. 2.1
    Force On +z And −z Plane

    This section discusses the calculation of forces acting on the +z and -z...

  6. 2.2
    Taylor’s Series Expansion

    This section delves into the application of Taylor's series expansion for...

  7. 2.3
    Partial Derivative Of Basis Vectors W.r.t. Θ

    This section discusses the concept of partial derivatives of basis vectors...

  8. 2.4
    Final Simplification

    This section discusses the final simplification of the linear momentum...

What we have learnt

  • The cylindrical coordinate system is vital for studying deformation in cylindrical shapes.
  • Basis vectors in cylindrical coordinates change with the angle θ, affecting the analysis of forces.
  • Using Taylor's series helps to approximate varying stress components in the context of cylindrical elements.

Key Concepts

-- Cylindrical Coordinate System
A coordinate system defined by the distance from a reference axis and the angle around that axis, commonly used for cylindrical shapes.
-- Basis Vectors
Vectors that define the coordinate system at a point; in cylindrical coordinates, they vary based on the angle θ.
-- Linear Momentum Balance
A principle stating that the rate of change of momentum of a system equals the sum of the forces acting on it.
-- Taylor's Series
An approximation method used to represent functions as infinite sums of terms calculated from the values of their derivatives at a single point.

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