## A First Course in Finite Element AnalysisThe book endeavors to strike a balance between mathematical and numerical coverage of a wide range of topics in fi nite element analysis. It strives to provide an introduction, especially for undergraduates and graduates, to fi nite element analysis and its applications. Topics include advanced calculus, differential equations, vector analysis, calculus of variations, fi nite difference methods, fi nite element methods and time-stepping schemes. The book also emphasizes the application of important numerical methods with dozens of worked examples. The applied topics include elasticity, heat transfer, and pattern formation. A few self-explanatory Matlab programs provide a good start for readers to try some of the methods and to apply the methods and techniques to their own modelling problems with some modifi cations. The book will perfectly serve as a textbook in fi nite element analysis, computational mathematics, mathematical modelling, and engineering computations. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

ix | |

Vector and Matrix Algebra | 35 |

ODEs and Numerical Integration | 61 |

PDEs and Finite Diﬀerence | 77 |

Calculus of Variations | 93 |

Finite Element Method | 115 |

Elasticity | 139 |

Heat Conduction | 157 |

Transient Problems | 165 |

Finite Element Packages | 173 |

A Computer Programs | 187 |

### Common terms and phrases

analytic applications approximation beam becomes boundary conditions calculate calculus of variations coeﬃcients complex number computational constant coordinates curve deﬁned derivatives diﬀusion displacements domain dot product dx dy eigenvalue elastic engineering equivalent essential boundary essential boundary conditions Euler Euler-Lagrange equation example ﬁnd ﬁnite diﬀerence method Finite Element Finite element analysis ﬁnite element methods ﬁrst order ﬁxed formulation function f(x Gauss quadrature gradient heat conduction higher order index matrix initial inverse iteration mathematical Matlab matrix equation matrix exponentials mesh modulus nodes numerical integration ordinary diﬀerential equation partial diﬀerential equations pattern formation plane stress points polynomial potential energy Preprocessing problem quadratic form satisﬁes scalar scheme shading interp shown in Figure simple simulations solution solve square matrix stiﬀness matrix strain theorem time-stepping tion trapezium rule triangular element un+1 values variables vector wave equation written zero