Static response analysis of structures with interval parameters using the second-order Taylor series expansion and the DCA for QB

Eigenvalue analysis of structures with interval parameters using the second-order Taylor series expansion and the DCA for QB

“…2, 3, 5 and 6 , when the uncertain factor is small enough, there is no fundamental difference between the bounds obtained by using FM and PM [16] . But with the increase of the uncertain factor β, the accuracy of the computational results obtained by using FM decreases quickly.…”

“…The DCA proposed by Tao [15] which only requires matrix-vector products is a dual method to solve these QB problems. Without requiring expensive computational time, the global optimal solution to the QB problems ( 16 ) could be found by the DCA [14] . The QB problem may be written as…”

“…Due to the property that the DCA converges to the global optimal solution of the QBA problem [14,29] quickly, the DCA for the QBA is chosen as an optimizer to determine the lower bound of the optimal objective of the QB problem [14,16,29] . Then taking advantage of the DCA and technique of the branch and bound [14,16] , without much computational cost, DCA could provide the global optimal solution. The procedure of DCA for QB was described below.…”

“…But with the increase of the uncertain factor β, the accuracy of the computational results obtained by using FM decreases quickly. As PM has taken into account for the effects of the second-order terms in the Taylor series expansion for the eigenvalues, PM would be more accurate than FM [16] . From Tables 3 and 6 , we can see that even if the uncertain factor is taken as a large value, PM yields results in good agreement with PVM or MCS.…”

“…Without requiring expensive computational time, the global optimal solution to the QB problem could be found by the DCA [14] . The similar methodology has been applied to the problem of the static response of structures with interval parameters [16] , but because the mathematical structure of the structural eigenvalue problem is different from the static response problem, the information of the partial derivatives of eigenvalues cannot directly obtained by differentiating the governing equation with respect to the uncertain parameters like the case of the static response problem. Alternatively, the information of the partial derivatives of eigenvalues could be determined by making use of the information of the eigenvectors and their associated eigenvalues of the structural eigenvalue problem.…”