## Foundations of the Mathematical Theory of Structures |

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### Contents

Introduction | 5 |

Basic Concepts of Functional Analysis | 18 |

The Convergence Theory for Variational Methods | 40 |

Copyright | |

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allowed fields approximate solution arbitrary constant assumed to vanish Banach space belonging body forces boundary conditions called classical theory compatibility equilibrium compatibilize compatible fields components contains continuous and bounded convergence theorem corresponding cosets couple-stresses defined denote differential discrete model displacement discontinuities displacement vector distance divergence theorem equa equilibrium conditions equilibrium equations exact solution finite element method force density functional F generalized-generating sense given Hilbert space initial strains inner product space inner-product Introducing isocompatible isoconstrained and isominimizing isoconstrained elements isoconstrained subset isominimizing subset linear space linear subspace magnitudes matrix ment metric space norm obtain orthogonal prescribed principal derivatives Ritz method rotations satisfied sequence simplified theory strain energy strain tensor strain-displacement equations strains and displacements strains stresses stress-strain equations subdomain tends to zero theory of shells theory of structures three-dimensional tions total potential complementary transverse displacement two-dimensional vanishing body forces variational theorems vector virtue