Solid Mechanics | 19. Strain Matrix in Cylindrical Coordinate System by Abraham | Learn Smarter
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19. Strain Matrix in Cylindrical Coordinate System

The chapter discusses the representation of the strain tensor as a matrix in cylindrical coordinate systems, deriving relevant equations and components, and relating stress to strain for isotropic materials. Key aspects such as the physical significance of various strain components and their implications for deformation in cylindrical structures are elaborated. It culminates with exercises that reinforce the understanding of concepts introduced.

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Sections

  • 1

    Strain Matrix In Cylindrical Coordinate System

    This section explains how the strain tensor is represented as a matrix in cylindrical coordinate systems, detailing the essential components and relationships.

    Learning Practice

  • 1.1

    Representation Of Gradient

    This section discusses the representation of the gradient in cylindrical coordinates, essential for analyzing strains in cylindrical coordinate systems.

    Learning Practice

  • 1.2

    Representation Of Displacement

    This section discusses how to express the displacement vector in cylindrical coordinates, detailing its decomposition along cylindrical basis directions.

    Learning Practice

  • 1.3

    Representation Of Displacement Gradient

    This section describes the representation of the displacement gradient in cylindrical coordinates, detailing its derivation and physical significance.

    Learning Practice

  • 1.4

    Representation Of Strain Tensor

    This section presents the representation of the strain tensor in the cylindrical coordinate system, highlighting its significance.

    Learning Practice

  • 2

    Physical Significance Of Strain Components

    This section explores the physical significance of the strain components in cylindrical coordinates, focusing on their interpretation in various directions relevant to deformation.

    Learning Practice

  • 2.1

    Significance Of Ε Rr

    Learning

  • 2.2

    Significance Of Ε Θθ

    This section discusses the physical significance and implications of the circumferential strain (ϵ θθ) in cylindrical coordinate systems.

    Learning Practice

  • 2.3

    Significance Of Γ Rθ

    This section discusses the significance of the strain components in cylindrical coordinates, focusing on the shear strain denoted by γ rθ and its implications.

    Learning Practice

  • 2.4

    Significance Of Other Components

    This section explores the physical significance of various strain components in cylindrical coordinates, focusing on shear and longitudinal strain.

    Learning Practice

  • 3

    Relating Stress And Strain In Cylindrical Coordinate System For Isotropic Materials

    This section discusses the relationship between stress and strain in isotropic materials within a cylindrical coordinate system, highlighting the formulation and implications of these relationships.

    Learning Practice

References

ch19.pdf

Class Notes

Memorization

What we have learnt

  • The strain tensor is repres...
  • Different components of str...
  • Understanding the relations...

Final Test

Revision Tests