## MATLAB Guide to Finite Elements: An Interactive ApproachThis book explores the numerical implementation of Finite Element Analysis using the computer program MATLAB, which is very popular today in engineering and engineering education. The book contains a short tutorial on MATLAB as well as a systematic strategy for the treatment of finite element methods. Useful to both students and researchers in engineering, it provides various examples and exercises from mechanical, civil and aerospace engineering, as well as from materials science. The book especially stresses the interactive use of MATLAB, with each example solved in an interactive manner. The accompanying CD-ROM includes more than fifty MATLAB functions specifically written to be used with this book in the form of a MATLAB Finite Element Toolbox. An extensive solutions manual is provided as well, which includes detailed solutions to all the problems in the book for classroom use. |

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### Contents

Introduction | 1 |

12 MATLAB Functions for Finite Element Analysis | 2 |

13 MATLAB Tutorial | 4 |

The Spring Element | 11 |

22 MATLAB Functions Used | 12 |

The Linear Bar Element | 27 |

32 MATLAB Functions Used | 28 |

The Quadratic Bar Element | 44 |

92 MATLAB Functions Used | 171 |

The Space Frame Element | 187 |

102 MATLAB Functions Used | 189 |

The Linear Triangular Element | 211 |

112 MATLAB Functions Used | 213 |

The Quadratic Triangular Element | 242 |

122 MATLAB Functions Used | 244 |

The Bilinear Quadrilateral Element | 267 |

42 MATLAB Functions Used | 45 |

The Plane Truss Element | 60 |

52 MATLAB Functions Used | 61 |

The Space Truss Element | 89 |

62 MATLAB Functions Used | 90 |

The Beam Element | 106 |

72 MATLAB Functions Used | 107 |

The Plane Frame Element | 133 |

82 MATLAB Functions Used | 135 |

The Grid Element | 170 |

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### Common terms and phrases

assemble one element assembles the element Assembling the Global backslash operator bending moment boundary conditions calculates the element centroid Columns Diagram for Element Discretizing the Domain displacements at nodes distributed load element connectivity element displacement vector element force vector element nodal displacement Element Number Node element stiffness matrix element with modulus elimination with MATLAB finite element Finite Element Analysis Finite Element Method function assembles function calculates function returns Gaussian elimination global nodal displacement global nodal force global stiffness matrix horizontal and vertical kN directed kN.m MATLAB as follows MATLAB calculations MATLAB commands MATLAB function matrix equation modulus of elasticity MPa tensile nodal displacement vector nodal force vector obtained using MATLAB plane frame element plane strain plane stress principal angle principal stresses reactions at nodes returns the element second node shear force diagram shown in Figure sigmal theta Thin Plate third node vector F vertical displacements zero matrix zeros(3