Solid Mechanics | 29. Linearity and superposition by Abraham | Learn Smarter
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29. Linearity and superposition

Energy methods are introduced as an alternative approach to solve deformation problems in solid mechanics. The chapter discusses the principles of linearity and superposition in relation to deformation, and explains the energy stored in bodies due to applied forces. Additionally, key concepts such as reciprocal relations and generalized forces are explored, highlighting their applications in solid mechanics.

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Sections

  • 1

    Introduction

    This section introduces energy methods as an alternative approach to solving deformation problems in mechanics.

    Learning Practice

  • 2

    Linearity And Superposition

    This section covers the concepts of linearity and superposition in solid mechanics, focusing on how deformation relates to applied forces in a linear manner.

    Learning Practice

  • 3

    Alternative Way To Prove Superposition

    This section explains an alternate method to prove the principle of superposition in solid mechanics through energy methods.

    Learning Practice

  • 4

    Corresponding Displacement/work Absorbing Displacement

    This section introduces the concepts of corresponding displacement and work absorbing displacement, explaining their role in energy methods related to deformation under applied forces.

    Learning Practice

  • 5

    Energy Stored In The Body Due To An Applied Force

    This section explores how energy is stored in a deformable body when a force is applied.

    Learning Practice

  • 6

    Reciprocal Relation

    This section discusses the reciprocal relation in solid mechanics, explaining how influence coefficients relate through energy considerations.

    Learning Practice

  • 7

    Maxwell-Betti-Rayleigh Reciprocal Theorem

    The Maxwell-Betti-Rayleigh reciprocal theorem establishes the equivalence of work done by forces in different loading scenarios on a deformed body.

    Learning Practice

  • 8

    Generalized Forces And Generalized Displacements

    This section introduces generalized forces and displacements, extending the principles of deformation analysis in mechanics to include moments and rotations.

    Learning Practice

References

ch29.pdf

Class Notes

Memorization

What we have learnt

  • Energy methods provide a si...
  • The principles of linearity...
  • The concept of correspondin...

Final Test

Revision Tests