A Practical Guide to Reliable Finite Element Modelling

Many books have been written about the finite element method; little however has been written about procedures that assist a practicing engineer in undertaking an analysis in such a way that errors and uncertainties can be controlled. In A Practical Guide to Reliable Finite Element Modelling, Morris addresses this important area. His book begins by introducing the reader to finite element analysis (FEA), covering the fundamental principles of the method, whilst also outlining the potential problems involved. He then establishes consistent methods for carrying out analyses and obtaining accurate and reliable results, concluding with a new method for undertaking error control led analyses which is illustrated by means of two case studies. The book addresses a number of topics that: Systematically cover an introduction to FEA, how computers build linear-static and linear-dynamic finite element models, the identification of error sources, error control methods and error-controlled analyses. Enable the reader to support the design of complex structures with reliable, repeatable analyses using the finite element method. Provide a basis for establishing good practice that could underpin a legal defence in the event of a claim for negligence. A Practical Guide to Reliable Finite Element Modelling will appeal to practising engineers engaged in conducting regular finite element analyses, particularly those new to the field. It will also be a resource for postgraduate students and researchers addressing problems associated with errors in the finite element method. This book is supported by an author maintained website at femec.co.uk

Many books have been written about the finite element method;little however has been written about procedures that assist apracticing engineer in undertaking an analysis in such a way thaterrors and uncertainties can be controlled. In A Practical Guide toReliable Finite Element Modelling, Morris addresses this importantarea. His book begins by introducing the reader to finite elementanalysis (FEA), covering the fundamental principles of the methodwhilst also outlining the potential problems involved. He thenestablishes consistent methods for carrying out analyses andobtaining accurate and reliable results, concluding with a newmethod for undertaking error control led analyses which isillustrated by means of two case studies.The book addresses a number of topics that:* Systematically cover anintroduction to FEA, how computers build linear-static andlinear-dynamic finite element models, the identification of errorsources, error control methods and error-controlled analyses.* Enable the reader tosupport the design of complex structures with reliable, repeatableanalyses using the finite element method.* Provide a basis forestablishing good practice that could underpin a legal defence inthe event of a claim for negligence.A Practical Guide to Reliable Finite Element Modelling willappeal to practising engineers engaged in conducting regular finiteelement analyses, particularly those new to the field. It will alsobe a resource for postgraduate students and researchers addressingproblems associated with errors in the finite element method.This book is supported by an author maintained website at href="femec.co.uk/">femec.co.uk

Preface.Chapter 1. Introduction.1.1 Aim of the book.1.2 Finite Element Types - a Brief Overview.1.3 Finite Element Analysis and Finite ElementRepresentations.1.4 Multi-Model Analyses.1.5 Consistency, Logic and Error Control.1.6 Chapter Contents.Chapter 2 Overview of Static Finite Element Analysis.2.1 Introduction.2.2 The Direct Method for Static Analyses.2.3 Reducing the Problem Size.Chapter 3: Overview of Dynamic Analysis3.1 Introduction3.2 Element Mass Matrix.3.3 Additional Information that can be Extracted to Support aDynamic Finite Element Analysis.3.4 Forced Responses.3.5 Damped Forced Responses.3.6 Reducing the Problem Size.Chapter 4: What's Energy Got to Do with It?4.1 Introduction .4.2 Strain Energy.4.3 Potential Energy.4.4 Simple Bar.4.5 General Case.4.6 Minimum Potential Energy.4.7 The Principle of Minimum Potential Energy Applied to aSimple Finite Element Problem.4.8 Finite Element Formulation.4.9 Direct Application to an Axial Bar Element.4.10 Convergence in Energy and Convergence in Stress.4.11 Results Interpretation.4.12 Kinetic Energy.4.13 Final Remark.Chapter 5. Preliminary Review of Errors and Error Control.5.1 Introduction.5.2 The Finite Element Process.5.3 Error and Uncertainty.5.4 Novelty, Complexity and Experience.5.5 Role of Testing.5.6 Initial Steps.5.7 Analysis Validation Plan (AVP).5.8 Applied Common Sense.5.9 The Process.Chapter 6. Discretisation: Elements and Meshes or Some Ways toAvoid Generated Error.6.1 Introduction.6.2 Element Delivery.6.3 Mesh Grading and Mesh Distortion.6.4 The Accuracy Ladder.Chapter 7. Idealisation Error Types and Sources.7.1 Design Reduction and Idealisation Errors.7.2 Analysis Features.7.3 The Domain.7.4 Levels of Abstraction.7.5 Boundary Conditions.7.6 Material Properties.7.7 Loads and Masses.Chapter 8. Error Control.8.1 Introduction.8.2 Approach and Techniques.8.3 Accumulation of Errors and Uncertainties.8.4 The Role of Testing.Chapter 9. Error Controlled Analyses.9.1 Introduction.9.2 Is the Finite Element System Fit for Purpose.9.3 Quality Report.9.4 The Error and Uncertainty Control Method.Chapter 10 FEMEC Walkthrough Example.10.1 Introduction.10.2 FEMEC Static Analysis Illustrative Problem.10.3 A Brief Look at the Dynamic FEMEC World.Index.