Limit analysis of orthotropic plates

A nonlinear programming approach to limit analysis of non-associated plastic flow materials

“…where, with reference to the eth finite element, δ e is the nodal displacement column vector, N e is the interpolation function, and B e is the strain function. By means of the Gaussian integration technique, the objective function in equation ( 23) can be discretized and expressed in terms of the nodal displacement velocity as follows (26) where (ρ e ) i is the Gaussian integral weight at the ith Gaussian integral point in the element e, |J | i is the determinant of the Jacobian matrix at the ith Gaussian integral point, IG is the number of Gaussian integral points in the finite element e, and K e = B T e R q B e (27) H e = T f B e (28) G e = (Q f ) T (P f ) −1 B e (29) By introducing the transformation matrix of each element C e , the nodal displacement velocity vector δe for each element can be expressed by the global nodal displacement velocity vector δ for the structure aṡ…”

“…There are only a few results about anisotropic limit analysis because it is much more difficult to introduce an anisotropic yield criterion into limit analysis. An early work was from Kao et al [26], who theoretically studied the static and kinematic stability conditions of an orthotropic plate. Hill's yield criterion was used and the plane-stress model was assumed.…”