The prediction of dynamic crack propagation in brittle materials is still an important issue in many engineering fields. The remeshing technique based on scaled boundary finite element method(SBFEM) is extended to pre...The prediction of dynamic crack propagation in brittle materials is still an important issue in many engineering fields. The remeshing technique based on scaled boundary finite element method(SBFEM) is extended to predict the dynamic crack propagation in brittle materials. The structure is firstly divided into a number of superelements, only the boundaries of which need to be discretized with line elements. In the SBFEM formulation, the stiffness and mass matrices of the super-elements can be coupled seamlessly with standard finite elements, thus the advantages of versatility and flexibility of the FEM are well maintained. The transient response of the structure can be calculated directly in the time domain using a standard time-integration scheme. Then the dynamic stress intensity factor(DSIF) during crack propagation can be solved analytically due to the semi-analytical nature of SBFEM. Only the fine mesh discretization for the crack-tip super-element is needed to ensure the required accuracy for the determination of stress intensity factor(SIF). According to the predicted crack-tip position, a simple remeshing algorithm with the minimum mesh changes is suggested to simulate the dynamic crack propagation. Numerical examples indicate that the proposed method can be effectively used to deal with the dynamic crack propagation in a finite sized rectangular plate including a central crack. Comparison is made with the results available in the literature, which shows good agreement between each other.展开更多
A new 2D Eu-BTB framework(1) with stratified gridding structure of about 14.6×16.9was synthesized and characterized.Compound 1 displays excellent water stability with the pH 2–12. The luminescent investigations ...A new 2D Eu-BTB framework(1) with stratified gridding structure of about 14.6×16.9was synthesized and characterized.Compound 1 displays excellent water stability with the pH 2–12. The luminescent investigations suggest that 1 could represent a chemical sensor of PO43. with high sensitivity and selectivity. Importantly, 1 as a sensor of PO_4^(3-) can be reused at least five times.On the other hand, the catalytic investigations of 1 were carried out, indicating that 1 could be demonstrated as a recyclable catalyst for CO_2 conversion with epoxides.展开更多
For the Poisson equation with Robin boundary conditions,by using a few techniques such as orthogonal expansion(M-type),separation of the main part and the finite element projection,we prove for the first time that the...For the Poisson equation with Robin boundary conditions,by using a few techniques such as orthogonal expansion(M-type),separation of the main part and the finite element projection,we prove for the first time that the asymptotic error expansions of bilinear finite element have the accuracy of O(h3)for u∈H3.Based on the obtained asymptotic error expansions for linear finite elements,extrapolation cascadic multigrid method(EXCMG)can be used to solve Robin problems effectively.Furthermore,by virtue of Richardson not only the accuracy of the approximation is improved,but also a posteriori error estimation is obtained.Finally,some numerical experiments that confirm the theoretical analysis are presented.展开更多
基金Supported by the Key Program of National Natural Science Foundation of China(No.51138001)the Science Fund for Creative Research Groups of National Natural Science Foundation of China(No.51121005)+2 种基金the Fundamental Research Funds for the Central Universities(DUT13LK16)the Young Scientists Fund of National Natural Science Foundation of China(No.51109134)China Postdoctoral Science Foundation(No.2011M500814)
文摘The prediction of dynamic crack propagation in brittle materials is still an important issue in many engineering fields. The remeshing technique based on scaled boundary finite element method(SBFEM) is extended to predict the dynamic crack propagation in brittle materials. The structure is firstly divided into a number of superelements, only the boundaries of which need to be discretized with line elements. In the SBFEM formulation, the stiffness and mass matrices of the super-elements can be coupled seamlessly with standard finite elements, thus the advantages of versatility and flexibility of the FEM are well maintained. The transient response of the structure can be calculated directly in the time domain using a standard time-integration scheme. Then the dynamic stress intensity factor(DSIF) during crack propagation can be solved analytically due to the semi-analytical nature of SBFEM. Only the fine mesh discretization for the crack-tip super-element is needed to ensure the required accuracy for the determination of stress intensity factor(SIF). According to the predicted crack-tip position, a simple remeshing algorithm with the minimum mesh changes is suggested to simulate the dynamic crack propagation. Numerical examples indicate that the proposed method can be effectively used to deal with the dynamic crack propagation in a finite sized rectangular plate including a central crack. Comparison is made with the results available in the literature, which shows good agreement between each other.
基金supported by the National Natural Science Foundation of China (21571123, 21571107, 21421001)the Natural Science Foundation of Tianjin (15JCZDJC37700)+1 种基金111 Project (B12015)MOE Innovation Team (IRT13022, IRT-13R30) of China
文摘A new 2D Eu-BTB framework(1) with stratified gridding structure of about 14.6×16.9was synthesized and characterized.Compound 1 displays excellent water stability with the pH 2–12. The luminescent investigations suggest that 1 could represent a chemical sensor of PO43. with high sensitivity and selectivity. Importantly, 1 as a sensor of PO_4^(3-) can be reused at least five times.On the other hand, the catalytic investigations of 1 were carried out, indicating that 1 could be demonstrated as a recyclable catalyst for CO_2 conversion with epoxides.
基金supported by National Natural Science Foundation of China(Grant Nos.11226332,41204082 and 11071067)the China Postdoctoral Science Foundation(Grant No.2011M501295)+1 种基金the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120162120036)the Construct Program of the Key Discipline in Hunan Province
文摘For the Poisson equation with Robin boundary conditions,by using a few techniques such as orthogonal expansion(M-type),separation of the main part and the finite element projection,we prove for the first time that the asymptotic error expansions of bilinear finite element have the accuracy of O(h3)for u∈H3.Based on the obtained asymptotic error expansions for linear finite elements,extrapolation cascadic multigrid method(EXCMG)can be used to solve Robin problems effectively.Furthermore,by virtue of Richardson not only the accuracy of the approximation is improved,but also a posteriori error estimation is obtained.Finally,some numerical experiments that confirm the theoretical analysis are presented.
