The sensitivity problem to mesh distortion and the low accuracy problem of the stress solutions are two inherent difficulties in the finite element method.By applying the fundamental analytical solutions (in global Cartesian coordinates) to the Airy stress function of the anisotropic materials,8-and 12-node plane quadrilateral hybrid stress-function (HS-F) elements are successfully developed based on the principle of the minimum complementary energy.Numerical results show that the present new elements exhibit much better and more robust performance in both displacement and stress solutions than those obtained from other models.They can still perform very well even when the element shapes degenerate into a triangle and a concave quadrangle.It is also demonstrated that the proposed construction procedure is an effective way for developing shape-free finite element models which can completely overcome the sensitivity problem to mesh distortion and can produce highly accurate stress solutions.
A novel hybrid-stress finite element method is proposed for constructing simple 4-node quadrilateral plane elements,and the new element is denoted as HH4-3β here.Firstly,the theoretical basis of the traditional hybrid-stress elements,i.e.,the Hellinger-Reissner variational principle,is replaced by the Hamilton variational principle,in which the number of the stress variables is reduced from 3 to 2.Secondly,three stress parameters and corresponding trial functions are introduced into the system equations.Thirdly,the displacement fields of the conventional bilinear isoparametric element are employed in the new models.Finally,from the stationary condition,the stress parameters can be expressed in terms of the displacement parameters,and thus the new element stiffness matrices can be obtained.Since the required number of stress variables in the Hamilton variational principle is less than that in the Hellinger-Reissner variational principle,and no additional incompatible displacement modes are considered,the new hybrid-stress element is simpler than the traditional ones.Furthermore,in order to improve the accuracy of the stress solutions,two enhanced post-processing schemes are also proposed for element HH4-3β.Numerical examples show that the proposed model exhibits great improvements in both displacement and stress solutions,implying that the proposed technique is an effective way for developing simple finite element models with high performance.
Song CenTao ZhangChen-Feng LiXiang-Rong FuYu-Qiu Long
