## Finite Elements: An Introduction for EngineersFirst published in 1983, this textbook introduces the finite-element method as an important general technique in engineering mathematics. It is written for students who have already completed a general course of vector calculus, matrix algebra and partial differential equations. The treatment introduced in this book will provide a secure foundation for more specialised work. Each chapter includes worked examples, many of which contain important applications and generalisations of the ideas in the main body of the text. The book is principally aimed at engineering students. |

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### Contents

The finiteelement method introduced | 33 |

Elastic stress analysis using linear triangular elements | 59 |

1 fixed element shapes | 78 |

2 generalising the element | 105 |

Axial symmetry and harmonic analysis | 121 |

The elastic analysis of beams plates and shells | 140 |

Problems for chapter 7 | 163 |

Programming the finiteelement method | 169 |

References | 190 |

### Common terms and phrases

approximating function axisymmetric bending boundary conditions chapter coefficients ct components constant coordinate system cubic defined deformation dependent variable derived described in section differential equation distribution eight-node square electrical network equivalent nodal loads essential boundary essential boundary conditions evaluation example expression finite-element analysis finite-element mesh finite-element method finite-element program Fortran four-node square Gauss Gauss integration Gauss points Gaussian elimination given gives higher-order elements inflows integrand inter-element boundaries knz/L left-hand side linear mapping mapping matrices Ky minimisation nodal displacements nodal equations nodal values nodal variables node numbers piecewise-linear plane stress plate Poisson problem Poisson's equation polynomial potential procedure quadratic function quadratic variation quadrilateral reduced integration replaced right-hand side Ritz method Ritz process satisfy scalar section 2.1 shape functions shape functions nt shear shown in Fig similar solution region solution to problem specified square element strain stress analysis symmetric tetrahedron three-dimensional triangle triangular element true solution two-dimensional vector written zero