The finite element method (FEM) plays a valuable role in computer modeling and is beneficial to the mechanicaldesign of various structural parts. However, the elements produced by conventional FEM are easily inaccurat...The finite element method (FEM) plays a valuable role in computer modeling and is beneficial to the mechanicaldesign of various structural parts. However, the elements produced by conventional FEM are easily inaccurate andunstable when applied. Therefore, developing new elements within the framework of the generalized variationalprinciple is of great significance. In this paper, an 8-node plane hybrid finite element with 15 parameters (PHQ8-15β) is developed for structural mechanics problems based on the Hellinger-Reissner variational principle.According to the design principle of Pian, 15 unknown parameters are adopted in the selection of stress modes toavoid the zero energy modes.Meanwhile, the stress functions within each element satisfy both the equilibrium andthe compatibility relations of plane stress problems. Subsequently, numerical examples are presented to illustrate theeffectiveness and robustness of the proposed finite element. Numerical results show that various common lockingbehaviors of plane elements can be overcome. The PH-Q8-15β element has excellent performance in all benchmarkproblems, especially for structures with varying cross sections. Furthermore, in bending problems, the reasonablemesh shape of the new element for curved edge structures is analyzed in detail, which can be a useful means toimprove numerical accuracy.展开更多
The influence of the surface effect on the nanosized spherical void growth in a rigidperfectly plastic material is analyzed and the mechanism of the nanosized void growth with high triaxiality is given. Based on the R...The influence of the surface effect on the nanosized spherical void growth in a rigidperfectly plastic material is analyzed and the mechanism of the nanosized void growth with high triaxiality is given. Based on the Rice and Tracey model for a macro void growth, the present model is proposed to account for the nanosized void growth under a uniform remote strain rate field with consideration on the surface effect. It is concluded that the surface effect yields an evident resistant influence on the nanosized void growth. That is, this influence decays as the void radius increases. With high triaxiality, the nanosized void growth is divided into two stages： the initial stage and the mature stage. At the first stage, the void grows slowly and the influence of surface effect is relatively weak, whereas at the second stage, the influence is significant and the void grows drastically.展开更多
Sensitivity analysis of composite laminated plates with bonding imperfection is carried out based on the radial point interpolation method （RPIM） in a Hamilton system. A set of hybrid governing equations of response...Sensitivity analysis of composite laminated plates with bonding imperfection is carried out based on the radial point interpolation method （RPIM） in a Hamilton system. A set of hybrid governing equations of response and sensitivity quantities is reduced using the spring-layer model and the modified Hellinger-Reissner （H-R） variational principle. The analytical method （AM）, the semi-analytical method （SAM）, and the finite difference method （FDM） are used for sensitivity analysis based on the reduced set of hybrid governing equations. A major advantage of the hybrid governing equations is that the convolution algorithm is avoided in sensitivity analysis. In addition, sensitivity analysis using this set of hybrid governing equations can obtain response values and sensitivity coefficients simultaneously, and accounts for bonding imperfection of composite laminated plates.展开更多
基金the National Natural Science Foundation of China(No.11572210).
文摘The finite element method (FEM) plays a valuable role in computer modeling and is beneficial to the mechanicaldesign of various structural parts. However, the elements produced by conventional FEM are easily inaccurate andunstable when applied. Therefore, developing new elements within the framework of the generalized variationalprinciple is of great significance. In this paper, an 8-node plane hybrid finite element with 15 parameters (PHQ8-15β) is developed for structural mechanics problems based on the Hellinger-Reissner variational principle.According to the design principle of Pian, 15 unknown parameters are adopted in the selection of stress modes toavoid the zero energy modes.Meanwhile, the stress functions within each element satisfy both the equilibrium andthe compatibility relations of plane stress problems. Subsequently, numerical examples are presented to illustrate theeffectiveness and robustness of the proposed finite element. Numerical results show that various common lockingbehaviors of plane elements can be overcome. The PH-Q8-15β element has excellent performance in all benchmarkproblems, especially for structures with varying cross sections. Furthermore, in bending problems, the reasonablemesh shape of the new element for curved edge structures is analyzed in detail, which can be a useful means toimprove numerical accuracy.
基金the National Natural Science Foundation of China(No.10572110).
文摘The influence of the surface effect on the nanosized spherical void growth in a rigidperfectly plastic material is analyzed and the mechanism of the nanosized void growth with high triaxiality is given. Based on the Rice and Tracey model for a macro void growth, the present model is proposed to account for the nanosized void growth under a uniform remote strain rate field with consideration on the surface effect. It is concluded that the surface effect yields an evident resistant influence on the nanosized void growth. That is, this influence decays as the void radius increases. With high triaxiality, the nanosized void growth is divided into two stages： the initial stage and the mature stage. At the first stage, the void grows slowly and the influence of surface effect is relatively weak, whereas at the second stage, the influence is significant and the void grows drastically.
基金Project supported by the National Natural Science Foundation of China (No. 60979001)the Major Project of Civil Aviation University of China (No. CAUC2009ZD0101)
文摘Sensitivity analysis of composite laminated plates with bonding imperfection is carried out based on the radial point interpolation method （RPIM） in a Hamilton system. A set of hybrid governing equations of response and sensitivity quantities is reduced using the spring-layer model and the modified Hellinger-Reissner （H-R） variational principle. The analytical method （AM）, the semi-analytical method （SAM）, and the finite difference method （FDM） are used for sensitivity analysis based on the reduced set of hybrid governing equations. A major advantage of the hybrid governing equations is that the convolution algorithm is avoided in sensitivity analysis. In addition, sensitivity analysis using this set of hybrid governing equations can obtain response values and sensitivity coefficients simultaneously, and accounts for bonding imperfection of composite laminated plates.
