A technique for modelling of three-dimensional(3D)quasi-statically propagating cracks in elastic bodies by the displacement discontinuity method(DDM)was described.When the crack is closed,the Mohr-coulomb rule on the ...A technique for modelling of three-dimensional(3D)quasi-statically propagating cracks in elastic bodies by the displacement discontinuity method(DDM)was described.When the crack is closed,the Mohr-coulomb rule on the two contacted surfaces of the crack must be satisfied.A simple iterative method was adopted in order to consider three different states of cracks.Under the assumption that the advance of the point on the crack front would occur only in the normal plane which is through this edge point,the maximum energy release rate criterion is modified to be used as the criterion for the crack growth.With discretization,the process of crack propagation can be seen as the advance of the vertices of the crack front.The program MCP3D was developed based on these theories to simulate the 3D quasi-static crack propagation.A numerical example of a penny-shaped crack subject to tension and compression in an infinite elastic media was analyzed with MCP3D,and the results in comparison with others' show that the present method for 3D crack propagation is effective.展开更多
Dynamic simulation plays a fundamental role in security evaluation of distribution networks(DNs).However,the strong stiffness and non-linearity of distributed generation(DG)models in DNs bring about burdensome computa...Dynamic simulation plays a fundamental role in security evaluation of distribution networks(DNs).However,the strong stiffness and non-linearity of distributed generation(DG)models in DNs bring about burdensome computation and noteworthy instability on traditional methods which hampers the rapid response of simulation tool.Thus,a novel L-stable approximate analytical method with high accuracy is proposed to handle these problems.The method referred to as multistage discontinuous Galerkin method(MDGM),first derives approximate analytical solutions(AASs)of state variables which are explicit symbolic expressions concerning system states.Then,in each time window,it substitutes values for symbolic variables and trajectories of state variables are obtained subsequently.This paper applies MDGM to DG models to derive AASs.Local-truncation-error-based variable step size strategy is also developed to further improve simulation efficiency.In addition,this paper establishes detailed MDGM-based dynamic simulation procedure.From case studies on a numerical problem,a modified 33-bus system and a practical large-scale DN,it can be seen that proposed method demonstrates fast and dependable performance compared with the traditional trapezoidal method.展开更多
文摘A technique for modelling of three-dimensional(3D)quasi-statically propagating cracks in elastic bodies by the displacement discontinuity method(DDM)was described.When the crack is closed,the Mohr-coulomb rule on the two contacted surfaces of the crack must be satisfied.A simple iterative method was adopted in order to consider three different states of cracks.Under the assumption that the advance of the point on the crack front would occur only in the normal plane which is through this edge point,the maximum energy release rate criterion is modified to be used as the criterion for the crack growth.With discretization,the process of crack propagation can be seen as the advance of the vertices of the crack front.The program MCP3D was developed based on these theories to simulate the 3D quasi-static crack propagation.A numerical example of a penny-shaped crack subject to tension and compression in an infinite elastic media was analyzed with MCP3D,and the results in comparison with others' show that the present method for 3D crack propagation is effective.
文摘Dynamic simulation plays a fundamental role in security evaluation of distribution networks(DNs).However,the strong stiffness and non-linearity of distributed generation(DG)models in DNs bring about burdensome computation and noteworthy instability on traditional methods which hampers the rapid response of simulation tool.Thus,a novel L-stable approximate analytical method with high accuracy is proposed to handle these problems.The method referred to as multistage discontinuous Galerkin method(MDGM),first derives approximate analytical solutions(AASs)of state variables which are explicit symbolic expressions concerning system states.Then,in each time window,it substitutes values for symbolic variables and trajectories of state variables are obtained subsequently.This paper applies MDGM to DG models to derive AASs.Local-truncation-error-based variable step size strategy is also developed to further improve simulation efficiency.In addition,this paper establishes detailed MDGM-based dynamic simulation procedure.From case studies on a numerical problem,a modified 33-bus system and a practical large-scale DN,it can be seen that proposed method demonstrates fast and dependable performance compared with the traditional trapezoidal method.
