A differential geometrical method is for the first time used to calculate the effective moduli of a two-phase elastic composite materials with imperfect interface which the inclusions are assumed to be ellipsoidal of ...A differential geometrical method is for the first time used to calculate the effective moduli of a two-phase elastic composite materials with imperfect interface which the inclusions are assumed to be ellipsoidal of revolutions. All of the interface integral items participating in forming the potential and complementary energy functionals of the composite materials are expressed in terms of intrinsic quantities of the ellipsoidal of revolutions. Based on this, the upper and the lower bound for the effective elastic moduli of the composite materials with inclusions described above have been derived. Under three limiting conditions of sphere, disk and needle shaped inclusions, the results of this paper will return to the bounds obtained by Hashin([6]) (1992).展开更多
Sometimes boundary value problems have isolated regions where the solution changes rapidly.Therefore,when solving numerically,one needs a fine grid to capture the high activity.The fine grid can be implemented as a co...Sometimes boundary value problems have isolated regions where the solution changes rapidly.Therefore,when solving numerically,one needs a fine grid to capture the high activity.The fine grid can be implemented as a composite coarse-fine grid or as a global fine grid.One cheaper way of obtaining the composite grid solution is the use of the local defect correction technique.The technique is an algorithm that combines a global coarse grid solution and a local fine grid solution in an iterative way to estimate the solution on the corresponding composite grid.The algorithm is relatively new and its convergence properties have not been studied for the boundary element method.In this paper the objective is to determine convergence properties of the algorithm for the boundary element method.First,we formulate the algorithm as a fixed point iterative scheme,which has also not been done before for the boundary element method,and then study the properties of the iteration matrix.Results show that we can always expect convergence.Therefore,the algorithm opens up a real alternative for application in the boundary element method for problems with localised regions of high activity.展开更多
In this paper,the classical composite middle rectangle rule for the computation of Cauchy principal value integral(the singular kernel 1=(x-s))is discussed.With the density function approximated only while the singula...In this paper,the classical composite middle rectangle rule for the computation of Cauchy principal value integral(the singular kernel 1=(x-s))is discussed.With the density function approximated only while the singular kernel is calculated analysis,then the error functional of asymptotic expansion is obtained.We construct a series to approach the singular point.An extrapolation algorithm is presented and the convergence rate of extrapolation algorithm is proved.At last,some numerical results are presented to confirm the theoretical results and show the efficiency of the algorithms.展开更多
A composition method for constructing high order multisymplectic integrators is presented in this paper. The basic idea is to apply composition method to both the time and the space directions. We also obtain a genera...A composition method for constructing high order multisymplectic integrators is presented in this paper. The basic idea is to apply composition method to both the time and the space directions. We also obtain a general formula for composition method.展开更多
近年来,复合材料层合板结构被广泛地应用于航空航天、军工、建筑工程等领域。但是,由于其几何尺寸的不准确性、材料参数的分散性、载荷环境的波动性等不确定性因素的影响,可能会对复合材料层合板结构的可靠性和安全性,以及系统的输出响...近年来,复合材料层合板结构被广泛地应用于航空航天、军工、建筑工程等领域。但是,由于其几何尺寸的不准确性、材料参数的分散性、载荷环境的波动性等不确定性因素的影响,可能会对复合材料层合板结构的可靠性和安全性,以及系统的输出响应产生重大影响。由于复合材料层合板的层间黏结不良、外部应力集中等因素,当复合材料层合板结构的能量释放速率达到层间断裂韧性时,就会发生分层。因此对复合材料层合板结构的分层可靠性进行分析具有重要的意义。目前,对于复合材料层合板结构的可靠性分析主要是采用一阶可靠性方法(first order reliability method,FORM)、二阶可靠性方法(second order reliability method,SORM)和重要性抽样方法(importance sampling,IS)等传统可靠性分析方法,并将其和蒙特卡罗模拟(Monte Carlo simulation,MCS)对比。但是,当复合材料结构不确定性维度高且复杂时,这些方法不仅计算效率太低,而且不能保证其计算精度。相比于传统的可靠性分析方法,可以利用基于自适应Kriging模型集成策略和主动学习函数结合蒙特卡罗模拟(adaptive Kriging-based Monte Carlo simulation,AK-MCS)的方法,对复合材料层合板结构进行可靠性分析。而直接概率积分方法(direct probability integral method,DPIM)具有更高的计算效率和精度,特别是对于高维度和复杂的可靠性分析问题。所以,本文采用AK-MCS方法和DPIM对模式Ⅰ、模式Ⅱ和混合Ⅰ/Ⅱ模式下的复合材料层合板结构分层的可靠度进行了研究。结果表明:DPIM和AK-MCS与传统可靠性分析方法相比具有更高的计算精度和计算效率,但是DPIM以其高效的计算效率脱颖而出,尽管其精度略低于AK-MCS,但在处理随机变量更多、非线性程度更高的混合Ⅰ/Ⅱ模式下的层合板结构分层的可靠性时展现出明显优势。综合考虑精度与时效性的平衡,DPIM能够准确地评估复合材料结构的可靠度,保障其在航天航空装备等领域的安全运行。展开更多
文摘A differential geometrical method is for the first time used to calculate the effective moduli of a two-phase elastic composite materials with imperfect interface which the inclusions are assumed to be ellipsoidal of revolutions. All of the interface integral items participating in forming the potential and complementary energy functionals of the composite materials are expressed in terms of intrinsic quantities of the ellipsoidal of revolutions. Based on this, the upper and the lower bound for the effective elastic moduli of the composite materials with inclusions described above have been derived. Under three limiting conditions of sphere, disk and needle shaped inclusions, the results of this paper will return to the bounds obtained by Hashin([6]) (1992).
文摘Sometimes boundary value problems have isolated regions where the solution changes rapidly.Therefore,when solving numerically,one needs a fine grid to capture the high activity.The fine grid can be implemented as a composite coarse-fine grid or as a global fine grid.One cheaper way of obtaining the composite grid solution is the use of the local defect correction technique.The technique is an algorithm that combines a global coarse grid solution and a local fine grid solution in an iterative way to estimate the solution on the corresponding composite grid.The algorithm is relatively new and its convergence properties have not been studied for the boundary element method.In this paper the objective is to determine convergence properties of the algorithm for the boundary element method.First,we formulate the algorithm as a fixed point iterative scheme,which has also not been done before for the boundary element method,and then study the properties of the iteration matrix.Results show that we can always expect convergence.Therefore,the algorithm opens up a real alternative for application in the boundary element method for problems with localised regions of high activity.
基金The work of Jin Li was supported by National Natural Science Foundation of China(Grant No.11471195)China Postdoctoral Science Foundation(Grant No.2015T80703)+1 种基金Shan-dong Provincial Natural Science Foundation of China(Grant No.ZR2016JL006)Na-tional Natural Science Foundation of China(Grant No.11771398).
文摘In this paper,the classical composite middle rectangle rule for the computation of Cauchy principal value integral(the singular kernel 1=(x-s))is discussed.With the density function approximated only while the singular kernel is calculated analysis,then the error functional of asymptotic expansion is obtained.We construct a series to approach the singular point.An extrapolation algorithm is presented and the convergence rate of extrapolation algorithm is proved.At last,some numerical results are presented to confirm the theoretical results and show the efficiency of the algorithms.
基金This work is subsidized by the special funds for major state basic research projects (No.1999032800).
文摘A composition method for constructing high order multisymplectic integrators is presented in this paper. The basic idea is to apply composition method to both the time and the space directions. We also obtain a general formula for composition method.
文摘近年来,复合材料层合板结构被广泛地应用于航空航天、军工、建筑工程等领域。但是,由于其几何尺寸的不准确性、材料参数的分散性、载荷环境的波动性等不确定性因素的影响,可能会对复合材料层合板结构的可靠性和安全性,以及系统的输出响应产生重大影响。由于复合材料层合板的层间黏结不良、外部应力集中等因素,当复合材料层合板结构的能量释放速率达到层间断裂韧性时,就会发生分层。因此对复合材料层合板结构的分层可靠性进行分析具有重要的意义。目前,对于复合材料层合板结构的可靠性分析主要是采用一阶可靠性方法(first order reliability method,FORM)、二阶可靠性方法(second order reliability method,SORM)和重要性抽样方法(importance sampling,IS)等传统可靠性分析方法,并将其和蒙特卡罗模拟(Monte Carlo simulation,MCS)对比。但是,当复合材料结构不确定性维度高且复杂时,这些方法不仅计算效率太低,而且不能保证其计算精度。相比于传统的可靠性分析方法,可以利用基于自适应Kriging模型集成策略和主动学习函数结合蒙特卡罗模拟(adaptive Kriging-based Monte Carlo simulation,AK-MCS)的方法,对复合材料层合板结构进行可靠性分析。而直接概率积分方法(direct probability integral method,DPIM)具有更高的计算效率和精度,特别是对于高维度和复杂的可靠性分析问题。所以,本文采用AK-MCS方法和DPIM对模式Ⅰ、模式Ⅱ和混合Ⅰ/Ⅱ模式下的复合材料层合板结构分层的可靠度进行了研究。结果表明:DPIM和AK-MCS与传统可靠性分析方法相比具有更高的计算精度和计算效率,但是DPIM以其高效的计算效率脱颖而出,尽管其精度略低于AK-MCS,但在处理随机变量更多、非线性程度更高的混合Ⅰ/Ⅱ模式下的层合板结构分层的可靠性时展现出明显优势。综合考虑精度与时效性的平衡,DPIM能够准确地评估复合材料结构的可靠度,保障其在航天航空装备等领域的安全运行。
