Shape optimal design of an elastic solid of revolution under multiple constraints is treated. As a specific example, a device that seals a gun bore and transmits high in‐bore pressure to shear loading on the projectile, is considered. The design objective is minimum weight, with constraints on stress throughout the body, tractions on one surface of the boundary, and dimensions of the body. Methods of the calculus of variations and functional analysis are used to transform the variation of a functional over a variable region as a functional over a fixed region. An adjoint variable method of operator theory is then used to reduce this variation to an explicit function of only design variations. The resulting sensitivity coefficients are used in an iterative optimization algorithm. Numerical results are presented and show that the algorithm is stable and efficient.
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