Solid Mechanics | 5. Linear Momentum Balance by Abraham | Learn Smarter
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5. Linear Momentum Balance

The chapter delves into the essential principles of stress equilibrium equations, explaining how stress varies within a body under force and detailing the application of Newton's laws. It covers linear and angular momentum balance, emphasizing their mathematical derivation and implications for understanding body mechanics. By utilizing traction contributions and body forces, the chapter provides a framework for analyzing internal stress distributions within materials.

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Sections

  • 1

    Introduction

    The introduction covers the fundamental concepts of stress equilibrium equations and their importance in understanding stress distributions within a body.

    Learning Practice

  • 2

    Linear Momentum Balance

    This section discusses the concept of linear momentum balance and its application in determining stress distribution within a body.

    Learning Practice

  • 2.1

    Traction Contribution

    This section discusses the contribution of traction to stress equilibrium in a body, how to calculate the traction forces on a cuboidal volume, and its implications in determining stress distribution.

    Learning Practice

  • 2.2

    Body Force Contribution

    This section discusses the contribution of body forces to the total force acting on a cuboidal volume within a defined mechanical system.

    Learning Practice

  • 2.3

    Dynamics Term

    This section introduces the concept of linear momentum in mechanics and explores how it varies within a deforming body.

    Learning Practice

  • 2.4

    Final Balance

    The section discusses the application of Newton’s second law to derive the Linear Momentum Balance equation for a cuboidal volume, emphasizing the interplay of forces acting on the body.

    Learning Practice

  • 2.5

    Representation In A Coordinate System

    This section details how the Linear Momentum Balance (LMB) equation can be expressed in a coordinate system to analyze the distribution of stress within a body.

    Learning Practice

  • 3

    Angular Momentum Balance

    This section discusses the balance of angular momentum for a rigid body, focusing on how net external torque relates to the rate of change of angular momentum.

    Learning Practice

  • 3.1

    Traction Contribution

    This section elaborates on how traction influences stress distribution within a solid body, focusing on the application of Newton's laws and the stress tensor.

    Learning Practice

  • 3.2

    Body Force Contribution

    This section discusses the body force contribution to stress equilibrium, explaining how body forces are integrated over the volume of a cuboid to determine the total force acting on it.

    Learning Practice

References

ch5.pdf

Class Notes

Memorization

What we have learnt

  • Stress equilibrium equation...
  • Newton's second law applied...
  • Angular momentum balance is...

Final Test

Revision Tests