## Optimum design of structures: with special reference to alternative loads using geometric programmingThis book presents the integrated approach of analysis and optimal design of structures. This approach, which is more convenient than the so-called nested approach, has the difficulty of generating a large optimization problem. To overcome this problem a methodology of decomposition by multilevel is developed. This technique, which is also suitable for implementation on parallel processing computers, has the advantage of reducing the size of the optimization problem generated. The geometric programming for both equality and inequality constraints is used in the optimization. |

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### Contents

INTRODUCTION | 1 |

GEOMETRIC PROGRAMMING WITH EQUALITY CONSTRAINTS | 24 |

DECOMPOSITION AND REDUCTION TECHNIQUES FOR LARGE | 40 |

Copyright | |

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### Common terms and phrases

2,Three Bar 25-Member Truss alternative loads analysis equations Area of bar Area of Members ava ao vaav awmoA bar element Bar Truss Example base vectors basis reduction condensation Constraints Algorithm convergence convex functions coordinate system coordinating constraints coordinating variables cross-sectional areas cycle Cyclic Iteration History design areas design shape variables developed equality constraints Example 1 Algorithm Example 1,Three Bar feasible final design finite element finite element method first-level problem formulation fully stressed Function for Subproblem global coordinate system global optimization global solution goal coordination method inequality constraints initial design initial relaxation integrated optimum structural interaction variables linear program load condition Minimize move coordination method multilevel nodal displacements node nonlinear programming objective function obtained optimal design optimum structural design posynomial reduced response variables Schmit second level solve the following stiffness equation straints stress in bar structural design variables subsystem technique Three Bar Truss tion values variable linking

### References from web pages

Chibani, L., Optimum Design of Structures. With Special Reference **...**

Rook. Reviews. 157. Sanchez Hubert, J.; Sanchez Palencia, E., Vibrations and. Coupling of Con ti nu o us S ys tems. Asymptotic Methods. ...

doi.wiley.com/ 10.1002/ zamm.19920720220