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Understanding Solid Mechanics: Stress Analysis Approaches

Understanding Solid Mechanics:

Stress Analysis Approaches

This course is your starting point towards really understanding solid mechanics. You need to understand the basics to enable you to apply good practice in your FE analysis, and this course will give you the knowledge you really need for a good understanding of the principals that every engineer or designer should know.

You don't need in-depth knowledge about FEA or computational simulation. A working knowledge of engineering design and analysis is all you need to start out with.

You will learn about the solid mechanics and basic theories that are widely used in engineering design, analysis and simulation.

Each session is a building block - over the five weeks, you will cover:

  1. Statics, Forces and Equilibrium in Design
  2. Elasticity, Stresses and Strains
  3. Constitutive/Material relationships
  4. Hand (or ‘Back-of-the-envelope’) calculations
  5. Boundary Conditions and Applied Loads

The course covers these topics in a concise and practical manner. Unlike traditional university courses, this course avoids lengthy mathematical derivations and highlights many practical examples to illustrate the application of solid mechanic theories in modelling and analysing engineering structures. Where possible, exercises that can be done by hand are included so that attendees can test their knowledge. Full solutions will be provided within a few weeks of completing the course.

 

Who should attend?

  • Engineers and designers wishing to understand the background to solid mechanics in order to improve their analysis and simulation capacity.
  • Engineers looking to refresh and improve their knowledge in solid mechanics.

The course is completely code independent.

Course Process and Details

This is a 5-session online training course, with each session lasting approximately 2 hours, depending on homework submissions, questions & discussions.

You can attend the sessions live, and/or stream on demand. For additional info on telephony charges please email e-learning @ nafems.org .

A full set of notes in PDF format will be available for download.

Personal passwords are provided to allow you to access e-learning backup material via our discussion forum. Reading lists, homework submissions and supplementary information are all available via the discussion forum.

To get the most out of the course, participation in forum discussions is very much encouraged. Typically the forum remains open for 4 weeks after the last live session, giving you plenty of time to catch up with homework, review and ask questions.

Note: homework is purely voluntary


Course Program

This set of courses is important for designers and engineers who wish to gain a good understanding of the basic solid mechanics:

Session 1 - Statics, Forces and Equilibrium in Design

  • Forces and Moments
  • Tension and Compression
  • Thermal expansion
  • Free body diagrams
  • St. Venant’s principle

Session 2 - Elasticity, Stresses and Strains

  • Stress and strain in coordinate axes
  • Uniaxial, biaxial and triaxial
  • Volumetric/Hydrostatic Analysis
  • Infinitesimal Strain
  • Non-linear Strain
  • Stresses/Strains at any orientation
  • Principal stresses/strains
  • Mohr’s circle
  • Von Mises stress

Session 3 - Constitutive/Material relationships

  • Uniaxial tests
  • Hooke’s Law
  • Young’s modulus
  • Poisson’s ratio
  • Bulk ratio
  • Shear modulus
  • Metal plasticity
  • Yielding and hardening
  • Fatigue
  • Fracture
  • Hyper-elastic (rubber) materials

Session 4 - Hand (or ‘Back-of-the-envelope’) calculations

  • Estimating forces and reactions
  • Roark's Formulas for Stress and Strain
  • Calculating stress concentrations
  • Peterson stress concentration factors
  • Lamé’s formulae for thick cylinders

Session 5 - Boundary Conditions and Applied Loads

  • Creating a problem definition
  • Specifying displacement boundary conditions
  • Identifying degrees of freedom
  • Preventing rigid body motion
  • Applying external loads
  • Simplifying real-life boundary conditions and external loads
  • Dealing with beams and shells
  • Prescribing bending moments
  • Dealing with cylinders
  • Dealing with contact conditions
  • Examples

The main objectives of the course are:
-To provide delegates with a good understanding of solid mechanics and basic theories that are widely used in engineering design, analysis and simulation
-To present many practical examples of engineering applications to reinforce the solid mechanics theories.


Mechanics depends upon an understanding of statics where motionless bodies of any shape, size and material are considered to be in a state of equilibrium under the action of external forces (session 1).

These bodies are deformable and hence undergo strains and stresses. By understanding the stress capacity of a body we can understand the load that it can carry and support (session 2).

However, each material behaves in a different way so that building a component from steel is very different than building it from plastic. Decisions on material usage requires an understanding of the constitutive or material relationships (session 3) so that the developing stresses when the body undergoes straining can be calculated.

In our desire to determine stresses in a certain component made of a certain material many hand calculations have been developed historically based on laboratory studies and in-field readings but understanding their presentation and their limitations is important (session 4).

Many components are part of larger systems and a very important part of understanding the statics is the understanding of the externally applied loads and boundary conditions or external restrictions that may exist (session 5).

 

 

PSE

PSE Competencies addressed by this training course

IDCompetence Statement
BMPSco26Describe the boundary conditions appropriate to fully-fixed and simply supported beams and shells and explain the link to bending stress.
FATap1Employ a fatigue diagram, consisting of Modified Goodman and Langer lines, to assess fatigue performance of components.
FATco15Discuss the concept of cumulative damage and explain how this is commonly handled.
FATco2Describe how the data used to construct an S-N curve are obtained.
FATco5Discuss the salient features of an S-N diagram for steels and explain the terms endurance limit, infinite life and low cycle fatigue.
FATkn4Sketch a sinusoidal stress variation and show the maximum stress, minimum stress, mean stress, alternating stress (or stress amplitude), stress range and stress ratio.
FEAap7Employ symmetric boundary conditions effectively.
FEAap8Employ asymmetric boundary conditions effectively.
FEAap9Employ cyclic symmetric boundary conditions effectively, where appropriate.
FEAev3Assess the significance of simplifying geometry, material models, loads or boundary conditions.
FEAkn10List the degrees of freedom to be constrained on an asymmetric boundary.
FEAkn9List the degrees of freedom to be constrained on a symmetric boundary.
FEAsy1Prepare an analysis specification, including modelling strategy, highlighting any assumptions relating to geometry, loads, boundary conditions and material properties.
MASco1Describe the salient features of a stress strain curve from a uniaxial tensile test on a typical steel and aluminium alloy.
MASco11Discuss the terms elastic-perfectly plastic, kinematic hardening, isotropic hardening, Bauschinger effect, hysteresis loop.
MASco2Explain the terms Isotropic, Orthotropic, Anisotropic and Homogeneous.
MASco3Explain the terms Ductility and Toughness and show how these are measured for metallic materials.
MESMap1Employ Free Body Diagrams effectively.
MESMap2Use tables to retrieve stress concentration data for common configurations.
MESMap3Employ Lame's equations to determine the stresses in thick cylinder and spheres subjected to internal and external pressure.
MESMap8Evaluate deformed shapes, shear force, bending moment and torque diagrams for simple structures.
MESMco10Explain the term Statically Indeterminate and illustrate with a few examples.
MESMco14Provide examples of Plane Stress and Plane Strain.
MESMco15Explain the Tresca and von Mises Failure Criteria in 2D, sketching the failure surface.
MESMco16Discuss the stress states that give rise to maximum differences between the Tresca and von Mises criteria.
MESMco18Explain how St. Venant's Principle may be of use in FEA.
MESMco2Explain the terms Uniaxial, Biaxial and Triaxial Stress.
MESMco4Discuss the terms True Stress and Natural Strain.
MESMco5Describe the stress distribution around a hole in an infinite plate subjected to uniaxial tension.
MESMkn1Define the variation in hydrostatic pressure with fluid depth.
MESMkn10Sketch Mohr Circle for a simple tensile test specimen, illustrating the plane of maximum shear.
MESMkn11Define Hooke's Law.
MESMkn12Define Poisson's Ratio.
MESMkn13Define the relationship between Young's Modulus, Poisson's Ratio and Shear Modulus.
MESMkn14Sketch the through-thickness shear stress distribution in a rectangular beam subjected to a shearing load.
MESMkn18List various Failure Hypotheses / Criteria.
MESMkn19State an appropriate failure criteria for brittle materials.
MESMkn20Define Tresca and von Mises Stress for a 3D stress state.
MESMkn20Define Tresca and von Mises Stress for a 3D stress state.
MESMkn21State the elastic Constitutive Relations in 2D, for a homogeneous, isotropic material.
MESMkn22State the radial stress boundary conditions at the inner and outer surfaces of an internally pressurised cylinder or sphere.
MESMkn8State Newton's 1st, 2nd and 3rd Laws.
MESMkn9Sketch a general 3D stress element showing all stress components.
PLASap1Define elastic perfectly plastic and bi-linear or multilinear hardening constitutive data as appropriate.
PLASco2Explain the terms Isotropic Hardening, Kinematic Hardening and Rate Independency.
Understanding Solid mechanics: Stress Analysis Approaches

 

Five-Session Online Training Course

2 hours per session
PDH Credits - 10

Attend the live sessions, or view the recordings at your convenience.

Not Available to Attend this Time?

Would you like us to notify you when the next course is open for enrollment? If so, add yourself to the eLearning Waitlist


Please click here to view the FAQ section, or if you need to contact NAFEMS about this course.

Engineering Board PDH Credits

*It is your individual responsibility to check whether these e-learning courses satisfy the criteria set-out by your state engineering board. NAFEMS does not guarantee that your individual board will accept these courses for PDH credit, but we believe that the courses comply with regulations in most US states (except Florida, North Carolina, Louisiana, and New York, where providors are required to be pre-approved)


Special Note(s):

Telephony surcharges may apply for attendees who are located outside of North America, South America and Europe. These surcharges are related to individuals who join the audio portion of the web-meeting by calling in to the provided toll/toll-free teleconferencing lines. We have made a VoIP option available so anyone attending the class can join using a headset (headphones) connected to the computer. There is no associated surcharge to utilize the VoIP option, and is actually encouraged to ensure NAFEMS is able to keep the e-Learning course fees as low as possible. Please send an email to the e-Learning coordinator (e-learning @ nafems.org ) to determine if these surcharges may apply to your specific case.

Just as with a live face-to-face training course, each registration only covers one person. If you plan to register a large group (10+), please send an email to e-learning @ nafems.org in advance for group discounts.

For NAFEMS cancellation and transfer policy, click here.