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Knowledge Base

Knowledge Base

BENCHMARK Article series

The Knowledge Base series of articles ran in BENCHMARK magazine. 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 below, for free, to the analysis community. You can also purchase the series as a book from the NAFEMS Resource Centre.

Article Index

The Importance of Mesh Convergence

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

Fundamentals of Numerical Techniques for Static, Dynamic and Transient Analyses

Part 1 This, the first part, compares the numerical aspects of dynamic and static solution types. The second part 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

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

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,

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,

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

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

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

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

Inelastic Analysis

The last article on Pressure Vessel Forces 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

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 in

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

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

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

About the Author

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


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