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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000010153776 | TA347.F5 M67 2007 | Open Access Book | Book | Searching... |
Searching... | 30000010191578 | TA347.F5 M67 2008 | Open Access Book | Book | Searching... |
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Summary
Summary
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 http://www.femec.co.uk
Author Notes
Alan Morris has recently retired from his post at Cranfield University in the UK as Professor of Structural Analysis. His range of expertise covers the development and application of optimal design and analysis systems, with special emphasis on the finite element methods and structural optimisation programs. Previously, he was a Principal Research Officer in the Royal Aircraft Establishment (now QinetiQ) at Farnborough and was head of the Structures and Optimization Sections at the Advanced Concepts Section.
Table of Contents
| 1 |
| Chapter 1 Introduction and Overview |
| 1.1 Purpose of the book |
| 1.2 Finite Element Types - a Brief Overview |
| 1.3 Finite Element Analysis and Finite Element Representations |
| 1.4 Multi-Model Analyses |
| 1.5 Consistency, Logic and Error Control |
| 1.6 Chapter Contents |
| 1.6.1 |
| Chapter 2 Overview of Static Finite Element Analysis |
| 1.6.2 |
| Chapter 3 Overview of Dynamic Analysis |
| 1.6.3 |
| Chapter 4 What's Energy Got to Do with It? |
| Purpose of the chapter |
| 1.6.4 |
| Chapter 5 Preliminary Review of Errors and Error Control |
| 1.6.5 |
| Chapter 6 Discretisation: Elements and Meshes or Some Ways to Avoid Generated Error |
| Purpose of the chapter |
| 1.6.6 |
| Chapter 7 Idealisation Error Types and Sources |
| 1.6.7 |
| Chapter 8 Error Control |
| 1.6.8 |
| Chapter 9 Error Control led Analyses |
| 1.6.9 |
| Chapter 10 FEMEC Walkthrough Example |
| 1.7 References |
| 2 |
| Chapter 2 Overview of Static Finite Element Analysis |
| 2.1 Introduction |
| 2.2 The Direct Method for Static Analyses |
| 2.2.1 Element Matrices |
| 2.2.2 Assembled Global Stiffness Matrix for Static Analyses |
| 2.2.3 Global Coordinates |
| 2.2.4 Some Typical Elements |
| 2.2.5 The Analysis Loop |
| 2.3 Reducing the Problem Size |
| 2.3.1 Symmetry |
| 2.3.2 Condensation and Superelements |
| 2.3.2.1 The Condensation Process |
| 2.3.2.2 Temptations |
| 2.3.3 Sub-structures |
| 3 |
| Chapter 3 Overview of Dynamic Analysis |
| 3.1 Introduction |
| 3.2 Element Mass Matrix |
| 3.2.1 Free Undamped Vibrations |
| 3.3 Additional Information that can be Extracted to Support a Dynamic Finite Element Analysis |
| 3.3.1 Sturm Property Check |
| 3.3.2 Rayleigh Quotient |
| 3.4 Forced Responses |
| 3.4.1 Modal Analysis |
| 3.4.2 Direct Integration |
| 3.5 Damped Forced Responses |
| 3.5.1 Modal Analysis with Damping |
| 3.5.2 Modal Damping Ratio |
| 3.5.3 Direct Integration |
| 3.6 Reducing the Problem Size |
| 3.6.1 Symmetry |
| 3.6.2 Reducing the Number of Variables |
| 3.6.3 Sub-structure Analysis (Component Mode Synthesis)|21 Sub-structure Analysis (Component Mode Synthesis)|21 |
| 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 a Simple 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 |
| 4.10.1 Single Element Bar Model |
| 4.10.2 2-Elements Bar Model |
| 4.10.3 4-Bar Element Model |
| 4.10.4 8-Bar Element Model |
| 4.10.5 16-Bar Element Model |
| 4.11 Results Interpretation |
| 4.11.1 Potential Energy Convergence |
| 4.11.2 Stress Improvement |
| 4.11.3 Displacement Convergence |
| 4.12 Kinetic Energy |
| 4.13 Final Remark |
| 5 |
| 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 |
| 5.4.1 Analysis Novelty |
| 5.4.1.1 Low Level |
| 5.4.1.2 Medium Level |
| 5.4.1.3 High Level |
| 5.4.2 Degree of Complexity |
| 5.4.3 Experience |
| 5.5 Role of Testing |
| 5.6 Initial Steps |
| 5.6.1 Qualification Process |
| 5.6.2 Acceptable Magnitude of Error or Uncertainty |
| 5.7 Analysis Validation Plan (AVP) |
| 5.8 Applied Common Sense |
| 5.9 The Process |
| 6 |
| Chapter 6 Discretisation: Elements and Meshes or Some Ways to Avoid Generated Error |
| 6.1 Introduction |
| 6.2 Element Delivery |
| 6.2.1 2 Dimensional Elements |
| 6.2.2 3 Dimensional Elements |
| 6.2.3 Why do this? |
| 6.2.4 Optimal Stress Points and Making the Most of Them |
| 6.3 Mesh Grading and Mesh Distortion |
| 6.3.1 Mesh Grading |
