## Mechanics of Structural Elements: Theory and ApplicationsThe presentment should be as simple as possible, but not a bit simpler. Albert Einstein Introduction The power of the variational approach in mechanics of solids and structures follows from its versatility: the approach is used both as a universal tool for describing physical relationships and as a basis for qualitative methods of analysis [1]. And there is yet another important advantage inherent in the variational approach – the latter is a crystal clear, pure and unsophisticated source of ideas that help build and establish numerical techniques for mechanics. This circumstance was realized thoroughly and became especially important after the advanced numerical techniques of structural mechanics, first of all the finite element method, had become a helpful tool of the modern engineer. Certainly, it took some time after pioneering works by Turner, Clough and Melos until the finite element method was understood as a numerical technique for solving mathematical physics problems; nowadays no one would attempt to question an eminent role played by the variational approach in the process of this understanding. It is a combination of intuitive engineer thinking and a thoroughly developed mathematical theory of variational calculus which gave the finite element method an impulse so strong that its influence can still be felt. It would be too rash to say that there are few publications or books on the subject matter discussed in this book. |

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### Contents

1 | |

References | 27 |

ADDITIONAL VARIATIONAL PRINCIPLES | 98 |

References | 132 |

PARTICULAR CLASSES OF PROBLEMS IN STRUCTURAL | 221 |

PARTICULAR CLASSES OF PROBLEMS IN STRUCTURAL | 312 |

PARTICULAR CLASSES OF PROBLEMS IN STRUCTURAL | 395 |

References | 456 |

compound profile | 482 |

References | 494 |

VARIATIONAL PRINCIPLES IN SPECTRAL PROBLEMS | 539 |

VARIATIONAL PRINCIPLES IN STABILITYBUCKLING | 605 |

CONCLUSION 701 | 700 |

Curvilinear coordinates on a plane associated with | 755 |

Crosssections of a combined profile | 776 |

783 | |

### Other editions - View all

Mechanics of Structural Elements: Theory and Applications Vladimir Slivker No preview available - 2006 |

Mechanics of Structural Elements: Theory and Applications Vladimir Slivker No preview available - 2010 |

### Common terms and phrases

admissible fields analysis arbitrary arc coordinate assume axes bar’s cross-section boundary conditions calculated Castigliano functional components constraints contour curvilinear bar curvilinear coordinates defined deformation denote derive displacement vector eigenvalues eigenvectors elastic equations of equilibrium equilibrium equations Euler equations expression external forces finite element finite element method formula geometric homogeneously kinematically admissible inertia kinematic boundary conditions Lagrange functional Lagrangian linear set load longitudinal mathematical mechanical system moment of inertia open-profile orthogonal parameter plane positive definite potential problem quadratic quadratic form Rayleigh Reissner functional relationships respect rigid displacements Ritz method Russian scalar product sectorial coordinate shear forces solution static boundary conditions statically admissible stationarity strain energy stress-and-strain field structural mechanics tangential stresses tensor theorem thin-walled bars Timoshenko torque torsion transform unit vector variational principle