Monotone sequences are constructed that converge to the ex tremal solutions of second order three point boundary value problems when the functions involved do not possess any monotone properties.
This paper presents a further development of the Boundary Contour Method (BCM) for half-plane piezoelectric media. Firstly, the divergence free property of the integrand of the half-plane piezoelectric boundary elemen...This paper presents a further development of the Boundary Contour Method (BCM) for half-plane piezoelectric media. Firstly, the divergence free property of the integrand of the half-plane piezoelectric boundary element is proven. Secondly, the boundary contour method formulation is derived and potential functions are obtained by introducing linear shape functions and Green's functions[1] for half-plane piezoelectric media. Finally, numerical solutions for illustrative example are compared with exact ones and that of conventional boundary element method (BEM) ones. The numerical results of BCM coincide very well with exact solution, and the feasibility and efficiency of the method are verified.展开更多
An iterative direct-forcing immersed boundary method is extended and used to solve convection heat transfer problems.The pressure,momentum source,and heat source at immersed boundary points are calculated simultaneous...An iterative direct-forcing immersed boundary method is extended and used to solve convection heat transfer problems.The pressure,momentum source,and heat source at immersed boundary points are calculated simultaneously to achieve the best coupling.Solutions of convection heat transfer problems with both Dirichlet and Neumann boundary conditions are presented.Two approaches for the implementation of Neumann boundary condition,i.e.direct and indirect methods,are introduced and compared in terms of accuracy and computational efficiency.Validation test cases include forced convection on a heated cylinder in an unbounded flow field and mixed convection around a circular body in a lid-driven cavity.Furthermore,the proposed method is applied to study the mixed convection around a heated rotating cylinder in a square enclosure with both iso-heat flux and iso-thermal boundary conditions.Computational results show that the order of accuracy of the indirect method is less than the direct method.However,the indirect method takes less computational time both in terms of the implementation of the boundary condition and the post processing time required to compute the heat transfer variables such as the Nusselt number.It is concluded that the iterative direct-forcing immersed boundary method is a powerful technique for the solution of convection heat transfer problems with stationary/moving boundaries and various boundary conditions.展开更多
Marine structures are frequently subjected to repeated impact loadings,resulting in failure of the structures,even causing serious accidents.The analytical expressions of dimensionless permanent deflection and impact ...Marine structures are frequently subjected to repeated impact loadings,resulting in failure of the structures,even causing serious accidents.The analytical expressions of dimensionless permanent deflection and impact force of a metal beam based on maximal normal yield surface are derived by membrane factor method(MFM),then the results are compared with repeated impact tests.It can be found that the solutions based on MFM are between the upper and lower bounds,and very close to the results of the repeated impact tests,indicating the theoretical model proposed can predict the plastic responses of the metal beam accurately.What’s more,the influences of impact location and boundary condition on the dynamic responses of the beam subjected to repeated impacts are determined.Results show that,as the distance of impact location from the middle span of the beam increases,the permanent deflection decreases,while the impact force increases.Meanwhile,the influences of impact location enhance as the impact number increases.When the permanent deflection is smaller than the thickness,the effect of boundary condition on the plastic responses is significant.However,when the deflection is larger than the thickness,the beam will be like a string and only axial force works,resulting in little influence of boundary condition on the plastic responses of the beam.展开更多
In order to master the magnetic field distribution of submarines in the air completely and exactly and study the magnetic stealthy performance of submarine,a mathematic model of submarine magnetic field extrapolation ...In order to master the magnetic field distribution of submarines in the air completely and exactly and study the magnetic stealthy performance of submarine,a mathematic model of submarine magnetic field extrapolation is built based on the boundary element method(BEM).An experiment is designed to measure three components of magnetic field on the envelope surface surrounding a model submarine.The data in different heights above the model submarine are obtained by use of tri-axial magnetometers.The results show that this extrapolation model has good stabilities and high accuracies compared the measured data with the extrapolated data.Moreover,the model can reflect the submarine magnetic field distribution in the air exactly,and is valuable in practical engineering.展开更多
研究了复杂微细导线电容矩阵提取边界元法(boundary element method,BEM)的边界离散问题以及增强计算精度和数值稳定性的有效措施,分析了开阔边界尺寸、开阔边界离散、导线离散对计算精度的影响以及伪解、矩阵奇异性问题,提出了基于导...研究了复杂微细导线电容矩阵提取边界元法(boundary element method,BEM)的边界离散问题以及增强计算精度和数值稳定性的有效措施,分析了开阔边界尺寸、开阔边界离散、导线离散对计算精度的影响以及伪解、矩阵奇异性问题,提出了基于导线离散迭代和开阔边界迭代两阶段自动迭代边界元算法(automatic iterative boundary element method,AIBEM),并结合实例阐述了全域法和区域分解法两种多层介质问题系数矩阵生成方法。研究结果表明,边界环内生成的系数矩阵存在误差均衡协调问题,对复杂模型需合理选择各线段离散单元数及开阔边界尺寸,通过AIBEM可以获得经济的离散参数,有效避免矩阵奇异性,并提高收敛稳定性。将计算结果与有限元法、解析法、传输线法、矩量法进行了对比分析,证实了算法的可靠性。展开更多
传统有限元法对大坝-不规则地基-库水系统进行建模时存在一定的局限性。基于ABAQUS二次开发接口,实现了比例边界有限元方法(scaled boundary finite element method,SBFEM)与八叉树网格的结合,建立了一种考虑真实地形的高拱坝-不规则地...传统有限元法对大坝-不规则地基-库水系统进行建模时存在一定的局限性。基于ABAQUS二次开发接口,实现了比例边界有限元方法(scaled boundary finite element method,SBFEM)与八叉树网格的结合,建立了一种考虑真实地形的高拱坝-不规则地基-库水系统自动建模方法。利用构建的八叉树比例边界有限元法对某重力坝地震响应进行了数值验证。随后对NG5拱坝系统分别基于平整地基和不规则地基进行线弹性和非线性动力响应分析。结果表明:在地震作用下,相较于简化的平整地基拱坝系统,不规则地基拱坝系统坝顶与坝底横河向相对位移以及第一主应力峰值变化较大,分别增加了73.5%和103.6%;考虑拱坝横缝以及材料非线性的情况下,坝顶与坝底横河向相对位移以及顺河向相对位移和相对速度分别增加了43.9%、32.0%和56.6%,同时边缝的法向开度增加尤为显著,增加了388.9%和381.8%,开度峰值增加了105%,在应力和损伤方面,第一主应力峰值增加了81.6%,损伤较大的区域也沿着坝体底部进行了扩展。展开更多
It is not reasonable that one can only use the adjoint of model in data assimilation. The simulated numerical experiment shows that for the tidal model, the result of the adjoint of equation is almost the same as that...It is not reasonable that one can only use the adjoint of model in data assimilation. The simulated numerical experiment shows that for the tidal model, the result of the adjoint of equation is almost the same as that of the adjoint of model: the averaged absolute difference of the amplitude between observations and simulation is less than 5.0 cm and that of the phase-lag is less than 5.0°. The results are both in good agreement with the observed M2 tide in the Bohai Sea and the Yellow Sea. For comparison, the traditional methods also have been used to simulate M2 tide in the Bohai Sea and the Yellow Sea. The initial guess values of the boundary conditions are given first, and then are adjusted to acquire the simulated results that are as close as possible to the observations. As the boundary conditions contain 72 values, which should be adjusted and how to adjust them can only be partially solved by adjusting them many times. The satisfied results are hard to acquire even gigantic efforts are done. Here, the automation of the treatment of the open boundary conditions is realized. The method is unique and superior to the traditional methods. It is emphasized that if the adjoint of equation is used, tedious and complicated mathematical deduction can be avoided. Therefore the adjoint of equation should attract much attention.展开更多
文摘Monotone sequences are constructed that converge to the ex tremal solutions of second order three point boundary value problems when the functions involved do not possess any monotone properties.
文摘This paper presents a further development of the Boundary Contour Method (BCM) for half-plane piezoelectric media. Firstly, the divergence free property of the integrand of the half-plane piezoelectric boundary element is proven. Secondly, the boundary contour method formulation is derived and potential functions are obtained by introducing linear shape functions and Green's functions[1] for half-plane piezoelectric media. Finally, numerical solutions for illustrative example are compared with exact ones and that of conventional boundary element method (BEM) ones. The numerical results of BCM coincide very well with exact solution, and the feasibility and efficiency of the method are verified.
文摘An iterative direct-forcing immersed boundary method is extended and used to solve convection heat transfer problems.The pressure,momentum source,and heat source at immersed boundary points are calculated simultaneously to achieve the best coupling.Solutions of convection heat transfer problems with both Dirichlet and Neumann boundary conditions are presented.Two approaches for the implementation of Neumann boundary condition,i.e.direct and indirect methods,are introduced and compared in terms of accuracy and computational efficiency.Validation test cases include forced convection on a heated cylinder in an unbounded flow field and mixed convection around a circular body in a lid-driven cavity.Furthermore,the proposed method is applied to study the mixed convection around a heated rotating cylinder in a square enclosure with both iso-heat flux and iso-thermal boundary conditions.Computational results show that the order of accuracy of the indirect method is less than the direct method.However,the indirect method takes less computational time both in terms of the implementation of the boundary condition and the post processing time required to compute the heat transfer variables such as the Nusselt number.It is concluded that the iterative direct-forcing immersed boundary method is a powerful technique for the solution of convection heat transfer problems with stationary/moving boundaries and various boundary conditions.
文摘Marine structures are frequently subjected to repeated impact loadings,resulting in failure of the structures,even causing serious accidents.The analytical expressions of dimensionless permanent deflection and impact force of a metal beam based on maximal normal yield surface are derived by membrane factor method(MFM),then the results are compared with repeated impact tests.It can be found that the solutions based on MFM are between the upper and lower bounds,and very close to the results of the repeated impact tests,indicating the theoretical model proposed can predict the plastic responses of the metal beam accurately.What’s more,the influences of impact location and boundary condition on the dynamic responses of the beam subjected to repeated impacts are determined.Results show that,as the distance of impact location from the middle span of the beam increases,the permanent deflection decreases,while the impact force increases.Meanwhile,the influences of impact location enhance as the impact number increases.When the permanent deflection is smaller than the thickness,the effect of boundary condition on the plastic responses is significant.However,when the deflection is larger than the thickness,the beam will be like a string and only axial force works,resulting in little influence of boundary condition on the plastic responses of the beam.
文摘In order to master the magnetic field distribution of submarines in the air completely and exactly and study the magnetic stealthy performance of submarine,a mathematic model of submarine magnetic field extrapolation is built based on the boundary element method(BEM).An experiment is designed to measure three components of magnetic field on the envelope surface surrounding a model submarine.The data in different heights above the model submarine are obtained by use of tri-axial magnetometers.The results show that this extrapolation model has good stabilities and high accuracies compared the measured data with the extrapolated data.Moreover,the model can reflect the submarine magnetic field distribution in the air exactly,and is valuable in practical engineering.
文摘研究了复杂微细导线电容矩阵提取边界元法(boundary element method,BEM)的边界离散问题以及增强计算精度和数值稳定性的有效措施,分析了开阔边界尺寸、开阔边界离散、导线离散对计算精度的影响以及伪解、矩阵奇异性问题,提出了基于导线离散迭代和开阔边界迭代两阶段自动迭代边界元算法(automatic iterative boundary element method,AIBEM),并结合实例阐述了全域法和区域分解法两种多层介质问题系数矩阵生成方法。研究结果表明,边界环内生成的系数矩阵存在误差均衡协调问题,对复杂模型需合理选择各线段离散单元数及开阔边界尺寸,通过AIBEM可以获得经济的离散参数,有效避免矩阵奇异性,并提高收敛稳定性。将计算结果与有限元法、解析法、传输线法、矩量法进行了对比分析,证实了算法的可靠性。
文摘传统有限元法对大坝-不规则地基-库水系统进行建模时存在一定的局限性。基于ABAQUS二次开发接口,实现了比例边界有限元方法(scaled boundary finite element method,SBFEM)与八叉树网格的结合,建立了一种考虑真实地形的高拱坝-不规则地基-库水系统自动建模方法。利用构建的八叉树比例边界有限元法对某重力坝地震响应进行了数值验证。随后对NG5拱坝系统分别基于平整地基和不规则地基进行线弹性和非线性动力响应分析。结果表明:在地震作用下,相较于简化的平整地基拱坝系统,不规则地基拱坝系统坝顶与坝底横河向相对位移以及第一主应力峰值变化较大,分别增加了73.5%和103.6%;考虑拱坝横缝以及材料非线性的情况下,坝顶与坝底横河向相对位移以及顺河向相对位移和相对速度分别增加了43.9%、32.0%和56.6%,同时边缝的法向开度增加尤为显著,增加了388.9%和381.8%,开度峰值增加了105%,在应力和损伤方面,第一主应力峰值增加了81.6%,损伤较大的区域也沿着坝体底部进行了扩展。
文摘It is not reasonable that one can only use the adjoint of model in data assimilation. The simulated numerical experiment shows that for the tidal model, the result of the adjoint of equation is almost the same as that of the adjoint of model: the averaged absolute difference of the amplitude between observations and simulation is less than 5.0 cm and that of the phase-lag is less than 5.0°. The results are both in good agreement with the observed M2 tide in the Bohai Sea and the Yellow Sea. For comparison, the traditional methods also have been used to simulate M2 tide in the Bohai Sea and the Yellow Sea. The initial guess values of the boundary conditions are given first, and then are adjusted to acquire the simulated results that are as close as possible to the observations. As the boundary conditions contain 72 values, which should be adjusted and how to adjust them can only be partially solved by adjusting them many times. The satisfied results are hard to acquire even gigantic efforts are done. Here, the automation of the treatment of the open boundary conditions is realized. The method is unique and superior to the traditional methods. It is emphasized that if the adjoint of equation is used, tedious and complicated mathematical deduction can be avoided. Therefore the adjoint of equation should attract much attention.
