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**Design sensitivity analysis of structural systems.**
*(English)*
Zbl 0618.73106

Mathematics in Science and Engineering, Vol. 177. Orlando etc.: Academic Press, Inc. (Harcourt Brace Jovanovich, Publishers) XVI, 381 p. Cloth: $ 60.00; Paper: $ 34.95 (1986).

The theory and numerical methods of structural design sensitivity analysis is the objective of the monograph. The text is organized into four chapters, which include: Finite-dimensional structural systems, Distributed parameter structural components, Structural components with shape as the design variable, Design sensitivity analysis of built-up structures.

In the case of finite-dimensional problems the structural state equations are matrix equations for static response, vibration and buckling of structures and matrix differential equations for transient dynamic response with design variables appearing in the coefficient matrices. For infinite-dimensional problems the state and design variables are functions of displacements and material distribution while the structural state equations are boundary-value problems of ordinary or partial differential equations. The material derivative idea is used to predict the effect of a change in shape of structural components on functionals that define structural response. In the final chapter built-up structures have been considered that are composed of the coupled components treated in the previous chapters.

Direct design differentiation and adjoint variable methods of design sensitivity analysis have been developed. Computational problems of implementing the methods have been considered in some detail making use of the finite-element technique. Many examples examined in the text include trusses, frames, beams, plates and other structural elements. They really illustrate the theoretical considerations well.

In the case of finite-dimensional problems the structural state equations are matrix equations for static response, vibration and buckling of structures and matrix differential equations for transient dynamic response with design variables appearing in the coefficient matrices. For infinite-dimensional problems the state and design variables are functions of displacements and material distribution while the structural state equations are boundary-value problems of ordinary or partial differential equations. The material derivative idea is used to predict the effect of a change in shape of structural components on functionals that define structural response. In the final chapter built-up structures have been considered that are composed of the coupled components treated in the previous chapters.

Direct design differentiation and adjoint variable methods of design sensitivity analysis have been developed. Computational problems of implementing the methods have been considered in some detail making use of the finite-element technique. Many examples examined in the text include trusses, frames, beams, plates and other structural elements. They really illustrate the theoretical considerations well.

Reviewer: Z.Dzygadło

### MSC:

74P99 | Optimization problems in solid mechanics |

74-02 | Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids |

74S05 | Finite element methods applied to problems in solid mechanics |

49J15 | Existence theories for optimal control problems involving ordinary differential equations |

49J20 | Existence theories for optimal control problems involving partial differential equations |

49J99 | Existence theories in calculus of variations and optimal control |