In recent years,finite element analysis is increasingly being proposed in slope stability problems as a competitive method to traditional limit equilibrium methods(LEMs)which are known for their inherent deficiencies....In recent years,finite element analysis is increasingly being proposed in slope stability problems as a competitive method to traditional limit equilibrium methods(LEMs)which are known for their inherent deficiencies.However,the application of finite element method(FEM)to slope stability as a strength reduction method(SRM)or as finite element limit analysis(FELA)is not always a success for the drawbacks that characterize both methods.To increase the performance of finite element analysis in this problem,a new approach is proposed in this paper.It consists in gradually expanding the mobilized stress Mohr’s circles until the soil failure occurs according to a prescribed non-convergence criterion.The present approach called stress deviator increasing method(SDIM)is considered rigorous for three main reasons.Firstly,it preserves the definition of the factor of safety(FOS)as the ratio of soil shear strength to the mobilized shear stress.Secondly,it maintains the progressive development of shear stress resulting from the increase in the principal stress deviator on the same plane,on which the shear strength takes place.Thirdly,by introducing the concept of equivalent stress loading,the resulting trial stresses are checked against the violation of the actual yield criterion formed with the real strength parameters rather than those reduced by a trial factor.The new numerical procedure was encoded in a Fortran computer code called S^(4)DINA and verified by several examples.Comparisons with other numerical methods such as the SRM,gravity increasing method(GIM)or even FELA by assessing both the FOS and contours of equivalent plastic strains showed promising results.展开更多
The finite cell method （FCM） combines the high-order finite element method （FEM） with the fictitious domain approach for the purpose of simple meshing. In the present study, the FCM is used to the Prandtl-Reuss fl...The finite cell method （FCM） combines the high-order finite element method （FEM） with the fictitious domain approach for the purpose of simple meshing. In the present study, the FCM is used to the Prandtl-Reuss flow theory of plasticity, and the results are compared with the h-version finite element method （h-FEM）. The numerical results show that the FCM is more efficient compared to the h-FEM for elasto-plastic problems, although the mesh does not conform to the boundary. It is also demonstrated that the FCM performs well for elasto-plastic loading and unloading.展开更多
In this work, a design procedure extending the B-spline based finite cell method into shape optimization is developed for axisymmetric solids involving the centrifugal force effect. We first replace the traditional co...In this work, a design procedure extending the B-spline based finite cell method into shape optimization is developed for axisymmetric solids involving the centrifugal force effect. We first replace the traditional conforming mesh in the finite element method with structured cells that are fixed during the whole design process with a view to avoid the sophisticated re-meshing and eventual mesh distortion.Then, B-spline shape functions are further implemented to yield a high-order continuity field along the cell boundary in stress analysis. By means of the implicit description of the shape boundary, stress sensitivity is analytically derived with respect to shape design variables. Finally, we illustrate the efficiency and accuracy of the proposed protocol by several numerical test cases as well as a whole design procedure carried out on an aeronautic turbine disk.展开更多
文摘In recent years,finite element analysis is increasingly being proposed in slope stability problems as a competitive method to traditional limit equilibrium methods(LEMs)which are known for their inherent deficiencies.However,the application of finite element method(FEM)to slope stability as a strength reduction method(SRM)or as finite element limit analysis(FELA)is not always a success for the drawbacks that characterize both methods.To increase the performance of finite element analysis in this problem,a new approach is proposed in this paper.It consists in gradually expanding the mobilized stress Mohr’s circles until the soil failure occurs according to a prescribed non-convergence criterion.The present approach called stress deviator increasing method(SDIM)is considered rigorous for three main reasons.Firstly,it preserves the definition of the factor of safety(FOS)as the ratio of soil shear strength to the mobilized shear stress.Secondly,it maintains the progressive development of shear stress resulting from the increase in the principal stress deviator on the same plane,on which the shear strength takes place.Thirdly,by introducing the concept of equivalent stress loading,the resulting trial stresses are checked against the violation of the actual yield criterion formed with the real strength parameters rather than those reduced by a trial factor.The new numerical procedure was encoded in a Fortran computer code called S^(4)DINA and verified by several examples.Comparisons with other numerical methods such as the SRM,gravity increasing method(GIM)or even FELA by assessing both the FOS and contours of equivalent plastic strains showed promising results.
基金supported by the Alexander von Humboldt Foundation
文摘The finite cell method （FCM） combines the high-order finite element method （FEM） with the fictitious domain approach for the purpose of simple meshing. In the present study, the FCM is used to the Prandtl-Reuss flow theory of plasticity, and the results are compared with the h-version finite element method （h-FEM）. The numerical results show that the FCM is more efficient compared to the h-FEM for elasto-plastic problems, although the mesh does not conform to the boundary. It is also demonstrated that the FCM performs well for elasto-plastic loading and unloading.
基金supported by the National Natura Science Foundation of China (Grant 51275424)973 Program (Gran2011CB610304)+1 种基金Research Fund for the Doctoral Program of Higher Education of China (Grant 20126102130003)the opening project (Grant KFJJ13-6M) of the State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology)
文摘In this work, a design procedure extending the B-spline based finite cell method into shape optimization is developed for axisymmetric solids involving the centrifugal force effect. We first replace the traditional conforming mesh in the finite element method with structured cells that are fixed during the whole design process with a view to avoid the sophisticated re-meshing and eventual mesh distortion.Then, B-spline shape functions are further implemented to yield a high-order continuity field along the cell boundary in stress analysis. By means of the implicit description of the shape boundary, stress sensitivity is analytically derived with respect to shape design variables. Finally, we illustrate the efficiency and accuracy of the proposed protocol by several numerical test cases as well as a whole design procedure carried out on an aeronautic turbine disk.
