## Finite Deformation of an Elastic Solid |

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### Contents

VECTORS AND MATRICES | 1 |

The matrix element of arc and the element of area in the plane | 9 |

The canonical form of a linear operator | 17 |

Copyright | |

14 other sections not shown

### Common terms and phrases

3X1 matrix a-axis angle applied force arbitrary area dSx c-axis Cartesian reference frame coefficients column vector compatibility relations complex number compression cylinder deformable medium denote derivatives diagonal elements diagonal matrix differential elastically insensitive element of area element of volume energy of deformation equivalently Exercise final rectangular Cartesian follows force per unit formula given rotation Hence Hint hydrostatic pressure independent variables infinitesimal theory initial rectangular Cartesian initial stress isotropic Jacobian matrix linear combination linear function linear vector operator magnitude matrix element medium is elastically medium possesses multiplication non-singular obtain polar coordinates portion Vx principal axes R*TR rectangular Cartesian reference respect rotation matrix row vector second-order approximation second-order elastic constants shear Show simple shear square matrix strain matrix stress matrix symmetric matrix tension theory of elasticity third-order elastic constants transpose unit initial area unitary matrix virtual deformation zero