## How To Use Beam Plate & Shell Elements

The main purpose of this book is to describe the essentials of how beam, plate and shell elements work and perform in actual use. An important theme is how they offer an efficient alternative compared to using 3D continuum elements, which are nowadays readily generated from modern CAD packages, often in large numbers.

Emphasis is placed on the more commonly used elements from these families, and which are available in commercial software. Many finite element users today do not have the opportunity to learn much of the underlining theory, which often inhibits their instincts into how well these elements perform, and how suitable meshes of these elements should be designed. This booklet is intended to fill in these gaps concerning the practicalities, but in order to economise on both complexity and volume, theoretical aspects are kept to a minimum.

The discussions and presentation of finite element theory involved are aimed at the level of the graduate in engineering or a related discipline, who is one year into a professional engineering career, but with a wide audience of practising and potential finite element users also in mind. Some basic knowledge of the finite element method is assumed.

## Contents

### 1. Introduction2. Scope of Use of Beam, Plate and Shell Elements

2.1 Introduction
2.2 Basic Beam Theory

2.2.1 Definition of Beams
2.2.2 Generalised Displacements and Forces
2.2.3 Constitutive Relations

2.3 Basic Plate Theory

2.3.1 Definition of Plates
2.3.2 Stresses and Moments
2.3.3 Displacement Assumptions
2.3.4 Constitutive Relations
2.3.5 Degrees of Freedom and Elastic Strain Energy

2.4 Basic Shell Theory

2.4.1 Definition of Shells

### 3. General Description of Beam, Plate and Shell Element Families

3.1 Introduction
3.2 Beam Elements

3.2.1 Geometric Considerations
3.2.2 Stiffness Matrices for Beam Elements
3.2.4 Results
3.2.5 Description of Some Important Beam Properties

3.3 Plate Elements

3.3.1 Stiffness Matrices for Plate Elements
3.3.3 Results Extraction for Plate Elements
3.3.4 Thin Plate Elements
3.3.5 Thick Plate Elements
3.3.6 Discrete Kirchhoff Elements
3.3.7 The Heterosis Element

3.4 Shell Elements
3.5 Shell Element Families

3.5.1 Flat Facet Shell Elements
3.5.2 Doubly Curved Triangular and Quadrilateral Shells
3.5.3 Isoparametric Shell Elements
3.5.4 Continuum Shell Elements
3.5.5 Shells of Revolution

### 4. Element Types Available in Practice

4.1 Introduction
4.2 Beam Elements

4.2.1 Two Noded Beams

4.2.2 The Albuquerque Semiloof Beam Element

4.3 Plate Elements
4.4 Shell Elements

4.4.1 Three Noded Facet Shell Elements
4.4.2 Doubly Curved Triangular and Quadrilateral Shells
4.4.3 Isoparametric Shell Elements
4.4.4 The Semiloof Thin Shell Element
4.4.5 Continuum Shell Elements
4.4.6 Shells of Revolution

### 5. Modelling Issues

5.1 Introduction
5.2 When to Use Beams and Shells
5.3 Sufficiency of Structure to be Analysed
5.4 Detailed Mesh Considerations

5.4.1 Definition of Normals
5.4.2 Section Properties and Offsets
5.4.3 Corners and Junctions
5.4.4 Joining Different Types of Elements

### 6. Examples of Use

6.1 Introduction
6.2 Benchmark Tests
6.3 Analysis of Welds
6.4 Analysis of Bridges
6.5 Analysis of Road Safety Barriers
6.6 Reinforcements for very Thin Torispherical Pressure Vessels

### Document Details

Reference HT34 Hellen. T English Analyst Publication 1st January 2006 Global