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 Ca...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.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.10872108,10876100)the Program for New Century Excellent Talents in University(Grant No. NCET-07-0477)+1 种基金the National Basic Research Program of China(Grant No. 2010CB832701)ASFC
文摘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.
