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Understanding Solid Mechanics

This training course has been accredited by the NAFEMS Education & Training Working Group

Understanding Solid Mechanics


Duration:2 - 3 hours per course
Onsite Classroom
Virtual Classroom
Language:English or Spanish

Gino Duffett
Adib Becker

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Get to grips with Solid Mechanics in a concise, practical, and modular way.

Understanding Solid Mechanics is a set of 30 stand-alone courses addressing all aspects of solid mechanics that are important for designers and engineers who wish to gain a good understanding of the main theories underlying solid mechanics.

The courses cover solid mechanics topics in a concise and practical manner. Unlike traditional university courses, these courses avoid lengthy mathematical derivations and highlight many practical examples to illustrate the application of solid mechanics 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.

These courses can be taken in a number of ways:

  • individual 2 to 3 hour courses with an additional 30 minutes for live Q&A,
  • individual courses that could be added as specific topics to enrich in-house company courses,
  • courses that could be bundled together according to specific topics,
  • courses that could be bundled together as required for contracted in-house company courses,
  • courses may be personalised or new courses may be added on request.

Attendees will learn about the solid mechanics and basic theories that are widely used in engineering design, analysis and simulation. All courses are designed as stand-alone sessions but these can be grouped for a particular focus.

All you need as a pre-requisite is a working knowledge of engineering design and simulation. All of the modular courses are independent of any finite element software code.

The courses are loosely grouped in the following themes:

Stress Analysis Approaches

This course will provide an overview of basic mechanics concepts such as forces, statics and equilibrium, etc., and will give delegates a good understanding of force, static and equilibrium and how to utilise free body diagrams.


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

This course will provide a full overview of fundamental stress and strains analysis, and give delegates a good understanding of stress and strain components and evaluating stress and strain at a material point.


  • 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.

This course will provide an overview of some of the most well-known material relationships used in engineering analysis, and the various material relationships that define the calculation of stress from strain.


  • 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

This course will provide an overview of hand calculations used in engineering analysis that help engineers/designers carry out strength of component calculations without a detailed understanding of the basic solid mechanics theories. It will show delegates how to carry out hand calculations using established equations and tables that are useful in design and analysis.


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

This course will provide a detailed overview of how boundary conditions and external loads can be expressed to enable the analysis of engineering structures. Delegates will get a good understanding of how boundary conditions and applied loads on the surface of a structure can be described and checked.


  • 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

Applied Stress Analysis

The course will cover the analysis of stresses arising in beam-like structures.


  • Definition of a beam
  • Assumptions in modelling beam bending
  • Shear forces and bending moments
  • Bending stresses in beam cross-sections
  • Shear behaviour in beams
  • Deflections of beams
  • Overloading a beam

The course will cover the analysis of stresses arising in thick cylinders under pressure.


  • Thin and thick cylinders
  • Hoop and longitudinal stresses in thick cylinders
  • Plasticity in thick cylinders
  • Modelling end conditions in cylinders
  • Heat conduction through cylinder walls
  • Thermal stresses in cylinders
  • Shrink-fitting of cylinders

The course will provide an overview of determining forces and stresses in shells, membranes and plates. Both thin and thick shells will be included as well as standard configurations such as cylinders and spheres where specific equations can be developed.


  • Shells, membranes, plates
  • Forces and Stresses in shells
  • Through thickness shear in shells
  • Edge conditions on shells

The course will provide an overview of shear stress and twisting or torsion in circular bars and shafts, including those of non-circular cross section.


  • Shear stresses
  • Circular bars
  • Polar moment of inertia
  • Torque and twist
  • Non-circular sections



  • Uniaxial tensile test (steels)
  • Biaxial testing (steels)
  • Compression test (stone, concrete, etc.)
  • Hardness tests
  • Bending test
  • Shear test
  • Torsion test
  • Creep and Fatigue tests
  • Metals
  • Ceramics
  • Polymers
  • Composites
  • Mechanical and thermal properties
  • Suitability of materials
  • Manufacturing processes
  • Metal material properties
  • Atomic and crystalline structures
  • Iron-carbon phase diagrams
  • Phase transformations
  • Alloying elements
  • Recrystallization and grain growth
  • Dislocations
  • Metal manufacturing processes
  • Metal welding
  • Structure and Materials
  • Applications and Uses
  • Ceramic matrix
  • Fibreglass and Carbon fibre
  • Metal matrix
  • Sandwich layups
  • Other composite types
  • Modelling concepts
  • Composition, Micro-structure, types
  • Material macro-behaviour
  • Polymer constitutive models
  • Examples
  • Behaviour and Properties of rock and soils
  • Soil constitutive models
  • Rock constitutive models
  • Failure, Critical state
  • Cohesion, Partial saturation, etc.
  • Examples


Strength of Materials

  • Yielding in tensile tests
  • Metallurgical changes in plasticity
  • Multiaxial yielding
  • Yield criteria used in engineering design
  • Post-yielding plasticity
  • Plasticity under cyclic loading
  • Plasticity in beams and thick cylinders
  • Residual stresses and springback
  • Plasticity around cracks
  • Uniaxial creep testing
  • Metallurgical changes in creep
  • Creep material properties
  • Time and temperature dependency
  • Creep in engineering structures
  • Creep fracture
  • Creep-fatigue interaction
  • Cyclic loading
  • Fatigue S-N Curves
  • Low cycle and high cycle fatigue
  • Fatigue design approaches
  • Effects of mean stress
  • Fatigue life prediction
  • Fatigue failure
  • Crack initiation and crack growth
  • Designing against fatigue
  • Brittle and ductile fracture
  • Linear Elastic Fracture mechanics
  • Determination of Stress intensity factors
  • Crack initiation
  • Crack propagation
  • Crack tip yielding
  • Fatigue cracks
  • Creep cracks
  • Classification of contact problems
  • Frictional contact
  • Hertzian contact problems
  • Plasticity in contact problems
  • Contact of wedges and punches
  • Receding contact problems
  • Cyclic contact behaviour
  • Difficulties in analysing contact problems
  • Stability, Instability, Buckling, Bifurcation
  • Local, global, elastic, plastic buckling
  • Column buckling
  • Euler critical load
  • Panel buckling
  • Eigenvalue analysis, buckling modes
  • Post buckling behaviour


    • Sheet metal forming (pressing, hydroforming, etc.)
    • Bulk metal forming (forging, casting, etc.)
    • Plastic forming (injection and blow moulding, etc.)
    • Composite forming (pressure, curing, RTM, etc.)
    • How simulation can help
    • Residual stresses due to plasticity
    • Residual stresses in beams and cylinders
    • Residual stresses due to welding
    • Residual stresses in manufacturing
    • Distortions due to residual stresses
    • Reducing residual stresses
    • Experimental measurement of residual stresses
    • The welding process
    • Fusion welding
    • Solid state welding
    • Advantages and disadvantages of welding processes
    • Metallurgical changes during welding
    • Residual stresses caused by welding
    • Relieving residual stresses in welds
    • Cracks in welds



    • Statics and dynamics
    • Laws of motion
    • Velocity and acceleration
    • Linear and rotational motion
    • Gear systems
    • Impact
    • Undamped vibrations
    • Damping
    • Natural frequency
    • Forced vibrations
    • Mass-spring systems
    • Multi-degrees of freedom vibrations
    • Model shapes
    • Dynamic equations for high speed impact
    • Limitations
    • Material behaviour
    • Contact behaviour
    • FEA considerations.

      Thermal Analysis

    • Modes of heat transfer
    • Heat conduction, convection and radiation
    • Thermal material properties
    • Transient heat transfer
    • Thermal boundary conditions
    • Themo-mechanical problems
    • Examples

      Numerical Methods

      The course will provide an overview (but not every little detail) of the internal finite element mathematical steps and calculations that are carried out when a linear static analysis is carried out.


      • Basic FEA steps
      • Element stiffness matrix, shape functions, integration rules, reduced integration
      • Global F=Ku equation, global stiffness, singular/non-singular matrix, direct solver basics, iterative solver basics, reactions, rounding error
      • Stress, strain calculations, element nodal stresses, average stresses, errors
      • Problems of shear stiffening, hourglassing
      • Compatibility, constitutive, equilibrium equations, approximation

      The course will provide an overview (but not every little detail) of many numerical techniques used in finite element software.


      • Interpolation
      • Integration
      • Transformation (Jacobian)
      • Determinants
      • Finding roots/solutions
      • Systems of equations (direct and iterative)
      • Least-squares approximations
      • Eigen-solutions
      • Non-linear solvers (Newton-Raphson, Riks, others)
      • Time stepping schemes (Euler, Newmark, etc.)


        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.


        Get in touch to discuss your next steps with our experienced training team. We can work closely with you to understand your specific requirements, cater for your specific industry sector or analysis type, and produce a truly personalised training solution for your organisation.

        All NAFEMS training courses are entirely code independent, meaning they are suitable for users of any software package.

        Courses are available to both members and non-members of NAFEMS, although member organisations will enjoy a significant discount on all fees.

        NAFEMS course tutors enjoy a world-class reputation in the engineering analysis community, and with decades of experience between them, will deliver tangible benefits to you, your analysis team, and your wider organisation.

        Find out more

        PSE Competencies addressed by this training course

        The solid mechanics modular courses are designed to cover many of the topics covered in the NAFEMS PSE competencies. However, it should be noted that the modular courses will be focused on the understanding of solid mechanics theories used in engineering and design, rather than topics that address FE simulations.


        The relevant PSE competency Technical Areas partially covered by the solid Mechanics courses are:

        •Core Finite Element Analysis

        •Mechanics, Elasticity and Strength of Materials

        •Materials for Analysis and Simulation

        •Flaw Assessment and Fracture Mechanics

        •Nonlinear Geometric Effects and Contact

        •Beams, Membranes, Plates and Shells

        •Dynamics and Vibration


        •Thermo-Mechanical Behaviour

        •Buckling and Instability

        •Composite Materials and Structures

        •Creep and Time-Dependency