## First Course in the Finite Element MethodA First Course in the Finite Element Analysis provides a simple, basic approach to the finite element method that can be understood by both undergraduate and graduate students. It does not have the usual prerequisites (such as structural analysis) require |

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Very apt for a under grad to start with the heavily conceptualized subject of FEM. The language in particular is the highlight of the book being very subtle and fluid. The questions and the explaination given in the solved example are of great help and serve as a quick exercise to the concepts.

### Contents

Introduction | 1 |

Introduction to the Stiffness Displacement Method | 28 |

Development of Truss Equations | 65 |

Development of Beam Equations | 151 |

Frame and Grid Equations | 214 |

Development of the Plane Stress and Plane Strain Stiffness Equations | 304 |

Practical Considerations in Modeling Interpreting Results and Examples of Plane StressStrain Analysis | 350 |

Development of the LinearStrain Triangle Equations | 398 |

Fluid Flow | 593 |

Thermal Stress | 617 |

Structural Dynamics and TimeDependent Heat Transfer | 647 |

Matrix Algebra | 708 |

Methods for Solution of Simultaneous Linear Equations | 722 |

Equations from Elasticity Theory | 744 |

Equivalent Nodal Forces | 752 |

Principle of Virtual Work | 755 |

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2007 Cengage Learning applied Assume axial axis axisymmetric beam element bending body forces boundary conditions Chapter coefficients computer program convection coordinates Copyright 2007 Cengage deflection degrees of freedom derive determine direct stiffness method displacement function distributed load element equations element shown element stiffness matrix equilibrium evaluate exact solution Example f ¼ Finite Element Analysis finite element method finite element model finite element solution fluid force matrix formulation Gaussian quadrature given by Eq global nodal global stiffness matrix heat transfer illustrate integration k-in Let E ¼ linear nodal displacements node obtain the global one-dimensional plane strain plane stress plate principal stresses problem Rights Reserved rotation Section shape functions shown in Figure Simplifying Eq Step sti¤ness structure Substituting Eq symmetry temperature thermal thickness three-dimensional triangular element truss two-dimensional von Mises stress yields zero