SHAPE DESIGN SENSITIVITY ANALYSIS AND OPTIMIZATION OF GENERAL SHAPE ARCHES

A method is presented for the shape design sensitivity analysis as app lied to general arches whose shapes cannot be mapped on one plane. The shape design sensitivity formulation with respect to the perturbation in the direction normal to the middle surface of the shallow arch cur ve is derived using the material derivative and the adjoint variable m ethod with the system variational equation expressed in a Cartesian co ordinate system. A general shape arch is subdivided into segments each of which can be considered as a shallow arch. On each subdivision of the arch, a Cartesian coordinate system is installed and the shape des ign sensitivity for the shallow arch is applied. For numerical impleme ntation, the finite element method is adopted and each finite element can be considered as such a subdivision. Numerical examples for sensit ivity analysis and optimization are presented to illustrate the finite element sensitivity method proposed.