Understanding Solid Mechanics

Duration:	2 - 3 hours per course
Delivery:	E-learning Onsite Classroom Virtual Classroom
Language:	English or Spanish
Level:	Introductory
Availability:	Worldwide
Tutor(s):	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.

Topics:

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.

Topics:

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.

Topics:

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.

Topics:

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.

Topics:

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.

Topics:

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.

Topics:

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.

Topics:

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.

Topics:

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

Materials

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

Manufacturing

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

Dynamics

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.

Topics:

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.

Topics:

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.

Interested?

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.

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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

•Plasticity

•Thermo-Mechanical Behaviour

•Buckling and Instability

•Composite Materials and Structures

•Creep and Time-Dependency