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

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.

11 sections

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Sections

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  1. 1
    Strain Matrix In Cylindrical Coordinate System

    This section explains how the strain tensor is represented as a matrix in...

  2. 1.1
    Representation Of Gradient

    This section discusses the representation of the gradient in cylindrical...

  3. 1.2
    Representation Of Displacement

    This section discusses how to express the displacement vector in cylindrical...

  4. 1.3
    Representation Of Displacement Gradient

    This section describes the representation of the displacement gradient in...

  5. 1.4
    Representation Of Strain Tensor

    This section presents the representation of the strain tensor in the...

  6. 2
    Physical Significance Of Strain Components

    This section explores the physical significance of the strain components in...

  7. 2.1
    Significance Of Ε Rr
  8. 2.2
    Significance Of Ε Θθ

    This section discusses the physical significance and implications of the...

  9. 2.3
    Significance Of Γ Rθ

    This section discusses the significance of the strain components in...

  10. 2.4
    Significance Of Other Components

    This section explores the physical significance of various strain components...

  11. 3
    Relating Stress And Strain In Cylindrical Coordinate System For Isotropic Materials

    This section discusses the relationship between stress and strain in...

What we have learnt

  • The strain tensor is represented as a matrix in cylindrical coordinates.
  • Different components of strain have unique physical significance, reflecting various deformations in cylindrical structures.
  • Understanding the relationship between stress and strain is critical for analyzing isotropic materials under cylindrical conditions.

Key Concepts

-- Strain Tensor
A mathematical representation of the deformation of materials expressed as a matrix.
-- Cylindrical Coordinates
A coordinate system that specifies each point by its distance from a reference point, its angle from a reference direction, and its height.
-- Radial Strain
The longitudinal strain occurring in the radial direction of a cylindrical body.
-- Hoop Strain
The circumferential strain that accounts for elongation of a line element directed along the circumferential direction of a cylinder.
-- Shear Strain
A measure of how much a line segment deforms when subject to a shear force.

Additional Learning Materials

Supplementary resources to enhance your learning experience.