OVERVIEW

Various solution procedures that can be viewed as particular cases of the CA method are summarized in this chapter. As noted earlier, the accuracy of the results and the efficiency of the calculations are usually two conflicting factors. That is, better accuracy can be achieved at the expense of more computational effort by considering additional information. The CA method is most effective in cases where highly accurate approximations can be achieved by considering only a small number of basis vectors. Moreover, simplified procedures, such as the Binomial Approximations (BA) and the Scaled Approximations (SA), are often sufficiently accurate.

Some low-order approximations used in structural optimization and in the analysis of damaged structures are demonstrated in Sections 8.1.1 and 8.1.2. These include the first- and second-order approximations of the BA, SA and CA methods. Efficiency considerations are discussed in Section 8.1.3. It is shown that the number of algebraic operations and the computational cost involved in solution by the CA method are significantly smaller than those required for complete analysis. Limitations on design changes, intended to limit the errors occurring in low-order approximations, are presented in Section 8.1.4. The common design variable limits, often used for local approximations (such as the Taylor series and the BA), are not suitable for the SA and the CA methods. More rational limitations on the design changes are demonstrated for these methods.

A procedure to obtain exact solutions by the CA method for simultaneous rank-one changes in the stiffness matrix is demonstrated in Section...