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The Knowledge Base series of articles has been running in BENCHmark magazine since October 2003. Each article gives a useful insight into some of the basic tools needed for a complete knowledge of FEA, and serves as an important reminder of the theory behind todays complex analyses.

The series is now available online to the analysis community in general, and will be updated each quarter with new articles to ensure you don't forget the basics.


Article Index

    The Importance of Mesh Convergence - Part 1

    This two-part article describes what might be one of the most overlooked issues that affect accuracy, namely; mesh convergence. This refers to the smallness of the elements required in a model to ensure that the results of an analysis are not affected by changing the size of the mesh. We have encountered occasions... more


    The Importance of Mesh Convergence - Part 2

    Extending the Convergence Study to Other Models If one model has been subject to a convergence study, as described in the first article, then it would be logical to argue that the corresponding region in a model of a ‘similar’ structure, with the same level of mesh refinement, would have the same... more

    Fundamentals of Numerical Techniques for Static, Dynamic and Transient Analyses - Part 1

    This, the first of two articles, compares the numerical aspects of dynamic and static solution types. The second article will discuss time varying (transient) problems and the pertinent features of implicit and explicit solutions. Statics For a linear static analysis, the system equations can be represented as... more


    Fundamentals of Numerical Techniques for Static, Dynamic and Transient Analyses – Part 2

    This article discusses linear buckling, transient vibration and the difference between explicit and implicit codes. Buckling Most textbooks on statics or strength of materials consider the simple strut (known as the ‘Euler’ strut). The buckling load is obtained by considering the beam bending... more


    Assessing Errors in Analysis Models

    This article discusses errors in analysis and methods to reduce or quantify them. The approach described in the SAFESA series of documents, published by NAFEMS (Ref. R0039 , R0040 , R0041 ) attempts to formalise the measurement and treatment of error in analysis. This article gives an interpretation of... more


    Commercial Analysis Validation

    This article discusses how it might be proved that a particular numerical analysis is ‘correct’. This is called analysis validation and can take many forms. Physical testing is the most obvious and convincing means of showing that an analysis is accurate. This is often not viable or cost-effective... more


    Concepts in Load Application and Stressing

    Some general concepts in structural assessment are described in this feature including categories of load, failure modes and uncertainty. The majority of structural assessments compare a peak predicted stress from a structural simulation, with an allowable stress obtained from material standards, design standards... more


    Probabilistic Analysis

    As mentioned in the last Knowledge Base article, conventional analysis techniques involve the use of safety factors as a way of accounting for variation in analysis input parameters. This can often result in overly conservative designs. By contrast, probabilistic analysis describes a process where the variation... more


    Analysis of Fabricated Structures

    The end of the last article on probabilistic analysis described one aspect of a typical technique for assessing fabricated structures under fatigue loading, accounting for failure probability of the welded joints. Most current approaches for assessing such structures do not employ the sort of probabilistic... more


    Nominal and Non-linear Stresses - Part 1

    International standards and codes of practice enable engineering design to draw on the best available data from a history of testing and service experience. The last Knowledge Base article discussed using FEA in conjunction with two standards for the fatigue design of steel and aluminium structures (BS 7608:1993... more


    Nominal and Non-linear Stresses - Part 2

    Cyclic Plasticity This article extends the introduction to modelling plastic or post-yield material behaviour introduced in the previous article. Plastic stresses first occur at stress concentrations or notches. These are termed secondary stresses in the context of the pressure vessel codes. Important concepts in... more


    Pressure Vessel Stresses

    The pressure vessel codes (including the ASME code and others) were originally intended to partner manual or hand calculation methods from which discrete values of stress can be obtained. Difficulties can arise when attempting to use them in conjunction with numerical analysis that produces a continuously varying... more


    Inelastic Analysis

    The last article discussed the distinction made between primary and secondary stresses in pressure vessel analysis. Primary stresses arise away from stress concentrations, whereas a secondary stress will be superimposed on the underlying primary stress within the region of a stress concentration. Figure 1... more


    Plastic Analysis

    The inelastic route in the pressure vessel codes distinguishes between two types of analysis: limit analysis and plastic analysis . These are associated respectively with the limit load and plastic collapse load of a vessel. Normally, the term ‘collapse’ has various dramatic connotations, but... more


    Plasticity, Collapse and Fatigue

    If loading causes regions in a structure to become plastic (i.e. exceed the yield stress) an analysis which includes a material with post-yield stiffness is required to evaluate the plastic stresses. A simple example is illustrated below. A linear analysis in which only the Young’s Modulus (E) is included... more


    Hysteresis in Fatigue

    If the yield stress is exceeded at notches in a structure, hysteresis loops of various sizes will be traversed at points around the notches. Providing the load is not too large, shakedown is achieved, in which the loops stabilise at all points, after a small number of cycles. But sustained repetition of this... more


    Fatigue Overview

    The previous article described the assumptions and method of forming discrete closed stress-strain hysteresis loops or cycles from a simplified general loading cycle. More complex random load histories can be similarly broken down into (often a very large number of) such discrete cycles, and this is achieved in... more



    About the Author

    Mark Chillery has over 15 years in analysis experience, and is currently general manager of Chalice Engineering Simulation Ltd ., an FEA consultancy based in Leeds, UK.