Contents | |

Chapter 1 | Introduction |

Finite element technique; Shape functions and element stiffness matrix; Brief historical background; Basic relationships in engineering problems; Modified variational principles; The concept of T-complete solution; Comparison of T-elements with conventional finite elements; Comparison of T-elements with boundary elements. | |

Chapter 2 | Potential Problems |

Introduction; Statement of the problem; T-complete functions; Assumed fields; Generation of element matrix equation; Rank condition; Special purpose functions; Sensitivity to mesh distortion; Orthotropic case; The Helmholtz equation; HT-element with boundary ‘traction’ frame; Frameless T-elements. | |

Chapter 3 | Linear Elastostatics |

Introduction; Linear theory of elasticity; Assumed fields in plane elasticity; T-complete functions; Variational formulations; Element stiffness equation; Special-purpose elements; p-extension approach; Three-dimensional elasticity; Numerical examples. | |

Chapter 4 | Thin Plates |

Introduction; Thin plate theory; Assumed field; T-complete functions and particular solutions; Variational formulations for plate bending; Generation of element stiffness matrix; p-method elements; Special purpose functions; Extension to thin plates on elastic foundation; Two alternative plate bending p-elements; Numerical examples and assessment. | |

Chapter 5 | Thick Plates |

Introduction; Basic equations for Reissner-Mindlin plate theory; Assumed fields and particular solution; Variational formulation for HT thick plate elements; Implementation of the new family of HT elements; A 12 DOF quadrilateral element free of shear locking; Extension to thick plates on elastic foundation; Sensitivity to mesh distortion; Numerical assessment. | |

Chapter 6 | Transient Heat Conduction |

Introduction; Elements of heat conduction; Time step formula; Element matrix formulations; T-complete functions and particular solutions; Numerical examples. | |

Chapter 7 | Geometrically Nonlinear Analysis of Plate Bending Problems |

Introduction; Basic equations of nonlinear thin plate bending; Assumed fields and Trefftz functions; Particular solutions; Modified variational principle; Element matrix; Iterative scheme; Extension to post-buckling thin plates on elastic foundation; Geometrically nonlinear analysis of thick plates; Numerical examples. | |

Chapter 8 | Elastoplasticity |

Introduction; Time discretization; Basic relations; Assumed fields; Constraints on the approximation functions; Finite element equilibrium and compatibility equations; Finite element equations; Finite element governing system. | |

Chapter 9 | Dynamics of Plate Bending Problems |

Introduction; Basic equations; Time-stepping formulation; Numerical examples. | |

Chapter 10 | Trefftz Boundary Element Method |

Introduction; Potential problems; Plane elasticity; Thin plate bending; Moderately thick plates. |