Based on the crack tip field expansion of the Reissner plate, a special high order bending crack tip element is developed, and the element stiffness matrix is given in the explicit form, which is especially convenien...Based on the crack tip field expansion of the Reissner plate, a special high order bending crack tip element is developed, and the element stiffness matrix is given in the explicit form, which is especially convenient for engineering analyses. A numerical example is presented and compared with previous results to demonstrate the efficiency and accuracy of the special element.展开更多
This article examines the interaction of multiple cracks in an infinite plate by using a numerical method. The numerical method consists of the non-singular displacement discontinuity element presented by Crouch and S...This article examines the interaction of multiple cracks in an infinite plate by using a numerical method. The numerical method consists of the non-singular displacement discontinuity element presented by Crouch and Startled and the crack tip displacement discontinuity elements proposed by the author. In the numerical method implementation, the left or the right crack tip element is placed locally at the corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. The numerical method is called a hybrid displacement discontinuity method. The following test examples of crack problems in an infinite plate under tension are included： “ center-inclined cracked plate”, “interaction of two collinear cracks with equal length”, “interaction of three collinear cracks with equal length”, “interaction of two parallel cracks with equal length”, and “interaction of one horizontal crack and one inclined crack”. The present numerical results show that the numerical method is simple yet very accurate for analyzing the interaction of multiple cracks in an infinite plate.展开更多
A simple and effective boundary element method for stress intensity factor calculation for crack problems in a plane elastic plate is presented. The boundary element method consists of the constant displacement discon...A simple and effective boundary element method for stress intensity factor calculation for crack problems in a plane elastic plate is presented. The boundary element method consists of the constant displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity elements proposed by YAN Xiangqiao. In the boundary element implementation the left or the right crack-tip displacement discontinuity element was placed locally at the corresponding left or right each crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. Test examples (i. e. , a center crack in an infinite plate under tension, a circular hole and a crack in an infinite plate under tension) are included to illustrate that the numerical approach is very simple and accurate for stress intensity factor calculation of plane elasticity crack problems. In addition, specifically, the stress intensity factors of branching cracks emanating from a square hole in a rectangular plate under biaxial loads were analysed. These numerical results indicate the present numerical approach is very effective for calculating stress intensity factors of complex cracks in a 2-D finite body, and are used to reveal the effect of the biaxial loads and the cracked body geometry on stress intensity factors.展开更多
This paper presents an extension of a displacement discontinuity method with cracktip elements （a boundary element method） proposed by the author for fatigue crack growth analysis in plane elastic media under mixed-...This paper presents an extension of a displacement discontinuity method with cracktip elements （a boundary element method） proposed by the author for fatigue crack growth analysis in plane elastic media under mixed-mode conditions. The boundary element method consists of the non-singular displacement discontinuity elements presented by Crouch and Starfield and the crack-tip displacement discontinuity elements due to the author. In the boundary element implementation the left or right crack-tip element is placed locally at the corresponding left or right crack tip on top of the non-singular displacement discontinuity elements that cover the entire crack surface and the other boundaries. Crack growth is simulated with an incremental crack extension analysis based on the maximum circumferential stress criterion. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not required because of an intrinsic feature of the numerical approach. Crack growth is modeled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characteristics of some related elements are adjusted according to the manner in which the boundary element method is implemented. As an example, the fatigue growth process of cracks emanating from a circular hole in a plane elastic plate is simulated using the numerical simulation approach.展开更多
In fracture simulation,how to model the pre-existing cracks and simulate their propagation without remeshing is an important topic.The newly developed triangular element partition method(TEPM)provides an efficient app...In fracture simulation,how to model the pre-existing cracks and simulate their propagation without remeshing is an important topic.The newly developed triangular element partition method(TEPM)provides an efficient approach to this problem.It firstly meshes the cracked body regardless of the geometry integrity of the interesting object with triangular elements.After the meshing procedure is completed,some elements are intersected by cracks.For the element intersected by a crack,the TEPM takes the element partition technique to incorporate the discontinuity into the numerical model without any interpolation enrichment.By this approach,the TEPM can simulate fracture without mesh modification.In the TEPM,all the cracked elements are treated as the usual partitioned elements in which the crack runs through.The virtual node pairs(the intersection points of crack faces and elements)at the opposite faces of the crack move independently.Their displacements are respectively determined by their neighbor real nodes(nodes formatted in the original mesh scheme)at the same side of the crack.However,among these cracked elements,the element containing a crack tip,referred to as the crack tip element thereafter,behaves differently from those cut through by the crack.Its influence on the singular field at the vicinity of the fracture tip becomes increasingly significant with the element size increasing.In the crack tip element,the virtual node pair at the crack tip move consistently before fracture occurs while the virtual node pair separate and each virtual node moves independently after the fracture propagates.Accordingly,the crack tip element is automatically transformed into the usual partitioned element.In the present paper,the crack tip element is introduced into the TEPM to account for the effect of the crack tip.Validation examples indicate that the present method is almost free from the element size effect.It can reach the same precision as the conventional finite element method under the same meshing scheme.But the TEPM is much more efficient and convenient than the conventional finite element method because the TEPM avoids the troubles that the conventional finite element method suffers,e.g.,the meshing problem of cracked body,modification of mesh scheme,etc.Though the extended finite element method can also avoid these troubles,it introduces extra degrees of freedom due to node interpolation enrichment.Due to the simplicity of the present TEPM,it is believed that its perspective should be highly inspiring.展开更多
文摘Based on the crack tip field expansion of the Reissner plate, a special high order bending crack tip element is developed, and the element stiffness matrix is given in the explicit form, which is especially convenient for engineering analyses. A numerical example is presented and compared with previous results to demonstrate the efficiency and accuracy of the special element.
文摘This article examines the interaction of multiple cracks in an infinite plate by using a numerical method. The numerical method consists of the non-singular displacement discontinuity element presented by Crouch and Startled and the crack tip displacement discontinuity elements proposed by the author. In the numerical method implementation, the left or the right crack tip element is placed locally at the corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. The numerical method is called a hybrid displacement discontinuity method. The following test examples of crack problems in an infinite plate under tension are included： “ center-inclined cracked plate”, “interaction of two collinear cracks with equal length”, “interaction of three collinear cracks with equal length”, “interaction of two parallel cracks with equal length”, and “interaction of one horizontal crack and one inclined crack”. The present numerical results show that the numerical method is simple yet very accurate for analyzing the interaction of multiple cracks in an infinite plate.
基金Project supported by the National Natural Science Foundation of China (No. 10272037)
文摘A simple and effective boundary element method for stress intensity factor calculation for crack problems in a plane elastic plate is presented. The boundary element method consists of the constant displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity elements proposed by YAN Xiangqiao. In the boundary element implementation the left or the right crack-tip displacement discontinuity element was placed locally at the corresponding left or right each crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. Test examples (i. e. , a center crack in an infinite plate under tension, a circular hole and a crack in an infinite plate under tension) are included to illustrate that the numerical approach is very simple and accurate for stress intensity factor calculation of plane elasticity crack problems. In addition, specifically, the stress intensity factors of branching cracks emanating from a square hole in a rectangular plate under biaxial loads were analysed. These numerical results indicate the present numerical approach is very effective for calculating stress intensity factors of complex cracks in a 2-D finite body, and are used to reveal the effect of the biaxial loads and the cracked body geometry on stress intensity factors.
基金Project supported by the National Natural Science Foundation of China (No. 10272037).
文摘This paper presents an extension of a displacement discontinuity method with cracktip elements （a boundary element method） proposed by the author for fatigue crack growth analysis in plane elastic media under mixed-mode conditions. The boundary element method consists of the non-singular displacement discontinuity elements presented by Crouch and Starfield and the crack-tip displacement discontinuity elements due to the author. In the boundary element implementation the left or right crack-tip element is placed locally at the corresponding left or right crack tip on top of the non-singular displacement discontinuity elements that cover the entire crack surface and the other boundaries. Crack growth is simulated with an incremental crack extension analysis based on the maximum circumferential stress criterion. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not required because of an intrinsic feature of the numerical approach. Crack growth is modeled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characteristics of some related elements are adjusted according to the manner in which the boundary element method is implemented. As an example, the fatigue growth process of cracks emanating from a circular hole in a plane elastic plate is simulated using the numerical simulation approach.
基金supported by the National Natural Science Foundation of China (Grant No. 11172172)the National Basic Research Program of China ("973" Project) (Grant No. 2011CB013505)
文摘In fracture simulation,how to model the pre-existing cracks and simulate their propagation without remeshing is an important topic.The newly developed triangular element partition method(TEPM)provides an efficient approach to this problem.It firstly meshes the cracked body regardless of the geometry integrity of the interesting object with triangular elements.After the meshing procedure is completed,some elements are intersected by cracks.For the element intersected by a crack,the TEPM takes the element partition technique to incorporate the discontinuity into the numerical model without any interpolation enrichment.By this approach,the TEPM can simulate fracture without mesh modification.In the TEPM,all the cracked elements are treated as the usual partitioned elements in which the crack runs through.The virtual node pairs(the intersection points of crack faces and elements)at the opposite faces of the crack move independently.Their displacements are respectively determined by their neighbor real nodes(nodes formatted in the original mesh scheme)at the same side of the crack.However,among these cracked elements,the element containing a crack tip,referred to as the crack tip element thereafter,behaves differently from those cut through by the crack.Its influence on the singular field at the vicinity of the fracture tip becomes increasingly significant with the element size increasing.In the crack tip element,the virtual node pair at the crack tip move consistently before fracture occurs while the virtual node pair separate and each virtual node moves independently after the fracture propagates.Accordingly,the crack tip element is automatically transformed into the usual partitioned element.In the present paper,the crack tip element is introduced into the TEPM to account for the effect of the crack tip.Validation examples indicate that the present method is almost free from the element size effect.It can reach the same precision as the conventional finite element method under the same meshing scheme.But the TEPM is much more efficient and convenient than the conventional finite element method because the TEPM avoids the troubles that the conventional finite element method suffers,e.g.,the meshing problem of cracked body,modification of mesh scheme,etc.Though the extended finite element method can also avoid these troubles,it introduces extra degrees of freedom due to node interpolation enrichment.Due to the simplicity of the present TEPM,it is believed that its perspective should be highly inspiring.
