The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identica...The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identical hybrid element. The Hilbert stress subspace of the assumed stress modes is established. So, it is easy to derive the equivalent orthogonal normal stress modes by Schmidt's method. Because of the resulting diagonal flexibility matrix, the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency, is improved greatly. The numerical examples show that the method is effective.展开更多
This paper describes the damage detection in framed structures due to thevertical support settlement and rotation of footing bases. The damage detection procedureproposed by Nobahari et al. [Nobahari and Seyedpoor (20...This paper describes the damage detection in framed structures due to thevertical support settlement and rotation of footing bases. The damage detection procedureproposed by Nobahari et al. [Nobahari and Seyedpoor (2013)] is used to detect thedamage in the members of the frame. In the present study, instead of using the flexibilitymatrix (referred here as original flexibility matrix) method, the generalized flexibilitymatrix is used in the same algorithm and the results are compared. The algorithm usesflexibility matrix and strain energy concept to detect the damage in the members. Thebehaviour of the frame is discussed through changes observed in flexibility in theassociated degree of freedom. Finally, the results indicate that, the damage indexdetermined by generalized flexibility matrix method is more reliable than using theoriginal flexibility matrix based method for the problem of settlement and rotation offooting base.展开更多
文摘The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identical hybrid element. The Hilbert stress subspace of the assumed stress modes is established. So, it is easy to derive the equivalent orthogonal normal stress modes by Schmidt's method. Because of the resulting diagonal flexibility matrix, the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency, is improved greatly. The numerical examples show that the method is effective.
文摘This paper describes the damage detection in framed structures due to thevertical support settlement and rotation of footing bases. The damage detection procedureproposed by Nobahari et al. [Nobahari and Seyedpoor (2013)] is used to detect thedamage in the members of the frame. In the present study, instead of using the flexibilitymatrix (referred here as original flexibility matrix) method, the generalized flexibilitymatrix is used in the same algorithm and the results are compared. The algorithm usesflexibility matrix and strain energy concept to detect the damage in the members. Thebehaviour of the frame is discussed through changes observed in flexibility in theassociated degree of freedom. Finally, the results indicate that, the damage indexdetermined by generalized flexibility matrix method is more reliable than using theoriginal flexibility matrix based method for the problem of settlement and rotation offooting base.
