@Article{Akgun2001,
    author      = {Mehmet A. Akg{\"u}n and Raphael T. Haftka and K. Chauncey Wu and Joanne L. Walsh and John H. Garcelon},
    title       = {Efficient Structural Optimization for Multiple Load Cases Using Adjoint Sensitivities},
    journal     = {AIAA Journal},
    keywords    = {structures, optimization, sensitivities},
    number      = {3},
    pages       = {511--516},
    volume      = {39},
    year        = {2001},
    abstract    = {Adjoint sensitivity calculation of stress, buckling,and displacement constraintsmay be much less expensive than direct sensitivity calculationwhen the number of load cases is large. In general, it is more dif? cult to implement the adjoint method than the direct method, but it is shown that the use of the continuum adjoint method, along with homogeneity conditions, can alleviate the problem. Expressions for vonMises stress and local buckling sensitivities for isotropic plate elements are derived. Computational ef? ciency of the adjointmethod is sensitive to the number of constraints, and, therefore, the adjoint method bene? ts from constraint lumping. A continuum version of the Kreisselmeier--Steinhauser functional is chosen to lumpconstraints. The adjoint and direct methods are compared for three examples: a truss structure, a small high-speed civil transport (HSCT) model, and a large HSCT model. These sensitivity derivatives are then used in optimization.}
}

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