Derivatives of a statically reduced stiffness matrix with respect to sizing variables
An expression is obtained for the first derivatives with respect to the sizing variables of a statically reduced stiffness matrix that is a nonlinear function of the sizing variables, where the unreduced stiffness matrix is a linear function of the sizing variables. An accepted procedure to reduce the number of degrees of freedom is to eliminate a number of nodal displacements from the degrees of freedom such that the accuracy of the flutter analysis is not significantly affected. In a typical optimization procedure with flutter constraints, the derivative of the stiffness matrix may be used in a form that contains the characteristic vector of the flutter matrix equation and the transpose of the characteristic vector of the adjoint flutter matrix equation corresponding to a particular solution of the flutter equation.