## Matrix-tensor Methods in Continuum MechanicsThe purposes of the text are: To introduce the engineer to the very important discipline in applied mathematics-tensor methods as well as to show the fundamental unity of the different fields in continuum mechanics-with the unifying material formed by the matrix-tensor theory and to present to the engineer modern engineering problems. |

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### Contents

MATHEMATICAL PRELIMINARIES | 1 |

TENSORS OR MATRICES OF ZERO FIRST | 35 |

CURVILINEAR COORDINATES | 64 |

CHAPTER PAGE | 88 |

APPLICATIONS OF THE THEORY OF ELASTICITY | 140 |

THE DEFLECTION TENSOR IN THE THEORY | 178 |

INTRODUCTION TO THE THEORY OF PLATES | 195 |

CHAPTER PACE | 203 |

EQUATIONS OF VISCOUS FLOW AND INTRODUCTION | 233 |

INTRODUCTORY THEORY OF PLASTICITY | 272 |

TENSOR ANALYSIS AS RELATED TO DIMENSIONAL | 293 |

CHAPTER PAGE | 296 |

306 | |

APPENDIX | 314 |

### Other editions - View all

Matrix-Tensor Methods in Continuum Mechanics: (Revised Second Printing) S F Borg Limited preview - 1990 |

### Common terms and phrases

analogy analysis applied assume axis beam bending Bernoulli-Euler body forces boundary conditions boundary layer Cauchy-Riemann equations Chapter column compatibility conditions complex number components consider constant coordinate system corresponding cross section curvilinear coordinates defined derived determine differential equation direction discussion dv dw dx dx dx dy dz dxdy dy dx dy dy elasticity theory elements engineering equilibrium equations example expression follows function fundamental given in terms Hence Hooke's Law independent indicial notation invariant large deflection linear mathematical matrix-tensor nonlinear notation Note obtained physical plane plane strain Prob quantity rectangular relations represents rigid virtual rotation satisfied scalar second order second-order tensor shear stresses shown in Fig single-valued small deflections small deformation solved strain tensor stress tensor stress-strain stresses and strains structure symmetric tensor Theorem theory of elasticity three-dimensional tion torque torsion problem two-dimensional u v w unit load vector velocity verify