## Applied Finite Element AnalysisThis book is intended for presenting the basic concepts of Finite Element Analysis applied to several engineering applications. Salient Features: 1. Covers several modules of elasticity, heat conduction, eigenvalue and fluid flow analysis which are necessary for a student of Mechanical Engineering. 2. Finite Element formulations have been presented using both global and natural coordinates. It is important for providing smooth transition from formulation in global coordinates to natural coordinates. 3. Special focus has been given to heat conduction problems and fluid flows which are not sufficiently discussed in other textbooks. 4. Important factors affecting the formulation have been included as Miscellaneous Topics. 5. Many examples have been worked out in order to highlight the applications of Finite Element Analysis. |

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### Contents

Introduction | 1 |

Onedimensional Elasticity Problems | 9 |

AnalysisofTruss | 58 |

Analysis of Beams | 77 |

Contents | 108 |

Unsteady State Heat Condition | 151 |

Two Dimensional Problems of Elasticity | 168 |

High Order Elements | 208 |

SteadyInviscidIncompressibleFlowsandTorsionAnalysis | 230 |

EigenvalueProblems | 244 |

Three Dimensional Elasticity Problems | 261 |

MiscellaneousTopics | 277 |

291 | |

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### Common terms and phrases

beam element body force calculated convection deﬁned degrees of freedom diﬀerence direction cosines Discretization displacement vector dx du dy eigenvalue Eigenvector element equations element load vector Element matrices element shown element stiffness matrix element stresses essential boundary conditions evaluated expressed ﬁeld variable FIGURE ﬁn Finite Element Finite element method ﬁrst ﬂow force vector formulation global coordinate system global stiﬀness matrix heat conduction heat transfer Hence integral mass matrix material property matrix natural coordinate Nodal coordinates nodal degrees nodal displacement vector nodal temperatures number of elements number of nodes obtained One-dimensional linear element plane strain plane stress point load polynomial sampling points shape functions shear stresses shown in Fig solution solving speciﬁed stepped bar stream function surface system equations tetrahedron Thermal conductivity triangular element truss two-dimensional variation velocity potential