基于多重网格分层四边形单元有限元空间的预处理方法

用有限元方法解二阶问题时,常选用三角单元和四边形单元.对于基于三角形单元的有限元方程,采用多重网格分层函数的预处理方法,Yserentant,H.已作了详细的讨论.本文对基于四边形单元的有限元方程,采用类似于Yserentant,H.的多重网格分层函数的预处理方法,使得系数矩阵的条件数由原来的O((1/h)~2)缩小为O((log(1/h)~3).     

P2-阶子群X-ss-半置换的有限群

设G是有限群,X是G的一个非空子集,子群H称为在G中X-ss-半置换,若H在G中有补充子群T,对于T的任意Sylowp-子群P,只要(p,|H|)=1,就存在x∈X使得HP^x=P^xH。通过对p²-阶子群的X-ss-半置换性研究,得到了p-幂零群的新判断。     

镁合金空心螺钉内固定治疗股骨颈骨折的有限元分析研究

利用有限元分析方法探究镁合金空心螺钉内固定治疗股骨颈骨折的生物力学特性, 旨在为临床治疗股骨颈骨折提供一种新的思路. 选取一例青年健康志愿者的下肢CT数据建立股骨三维模型, 在Mimics插件3-matic中建立股骨网格并赋予网格材料属性, 利用Solidworks 17.0软件建立空心螺钉模型, 将上述2个三维模型导入Workbench 2020软件中, 分别赋予空心螺钉镁合金、钛合金材料属性, 进行对比分析, 记录股骨及空心螺钉的峰值、应力分布值和股骨位移. 结果表明, 钛合金螺钉内固定模型最大应力为357.27MPa, 最大位移为0.034mm; 镁合金螺钉内固定模型最大应力为311.27MPa, 最大位移为0.034mm; 2组不同材料的空心钉结果数值差异不大. 研究表明镁合金空心螺钉和传统钛合金空心螺钉力学性能相似, 且镁合金更加亲和人体, 在临床方面可以镁合金空心螺钉代替钛合金空心螺钉治疗股骨颈骨折.     

冲击荷载下C型G550冷弯钢的断裂机理研究

以C型G550薄壁冷弯钢构件为研究对象, 通过材料在不同应变率下的拉伸实验和数值模拟数据得到Johnson-Cook (J-C)本构模型和Johnson-Cook失效模型参数. 通过Abaqus软件模拟了不同冲击荷载作用下C型冷弯钢构件撕裂破坏的全过程, 利用落锤装置轴向冲击试验进行对比, 其实验结果与有限元数值模拟结果有良好的一致性. 此外, 对冲击试样撕裂断口进行微观形貌分析, 得到构件的断裂机理. 结果表明: 随着冲击速度的提高, 冲击力对构件的加载时间增加, 构件需要较大的塑性变形来吸收冲击能量; 冲击速度越高, 裂纹扩展功所占吸收冲击能量的比例越大, 显示出高速下裂纹扩展的能力越好; 冲击速度较高时, 以脆性断裂为主, 断口出现解理面, 甚至在高速变形时发生了绝热剪切破坏.     

基于GeoClaw海啸数值模拟程序对2011年日本东北大地震有限断层模型的验证

由于海啸波具有长周期、慢衰减的特征,对于能够激发海啸的海底地震,海啸波资料一定程度上可以作为利用地震波资料和大地测量资料反演得到的震源有限断层模型的补充数据,以验证该模型的合理性.本文以2011年日本东北大地震海啸期间反演的震源模型为例,利用Okada弹性半无限空间理论将震源有限断层模型转化为垂向海底变形;然后利用Ge...     

Linear Chemical Potential Dependence of Two-Quark Condensate

By differentiating the inverse dressed quark propagator at finite chemical potential μ with respect to μ, the linear response of the dressed quark propagator to the chemical potential can be obtained. From this we extract a modelindependent formula for the linear chemical potential dependence of the in-medium two-quark condensate and show by two independent methods (explicit calculation and Lorentz covariance arguments) that the first-order contribution in μto the in-medium two-quark condensate vanishes identically. Therefore if one wants to study the in-medium two-quark condensate one should expand to at least the second order in the chemical potential μ.     

Complex multiplication of exactly solvable Calabi–Yau varieties

We propose a conceptual framework that leads to an abstract characterization for the exact solvability of Calabi–Yau varieties in terms of abelian varieties with complex multiplication. The abelian manifolds are derived from the cohomology of the Calabi–Yau manifold, and the conformal field theoretic quantities of the underlying string emerge from the number theoretic structure induced on the varieties by the complex multiplication symmetry. The geometric structure that provides a conceptual interpretation of the relation between geometry and conformal field theory is discrete, and turns out to be given by the torsion points on the abelian varieties.     

永磁体空间磁场的分析计算及其在永磁磁力轴承中的应用

在介绍三种永磁体空间磁场计算模型的基础上,利用泛函理论分别推导出等效磁荷模型和等效电流模型对应的变分形式,并就等效磁荷模型详细地介绍了有限元法．由于等效磁荷模型使用仅有一个自由度的标量磁位,因而计算起来比具有三个自由度的矢量磁位的等效电流法更简便．从永磁磁力轴承磁场的计算算例中可以看出,用等效磁荷模型的有限元法计算永磁体空间磁场是非常简便和有效的．     

无限包层Bragg光纤的传输模式研究

分析得到了横向电场分量和磁场分量所满足的耦合方程,对于介质折射率的不连续处,采用严格的边界条件来处理。基于全矢量模型,使用有限差分法编写了复模式的求解器,并将其应用于Bragg光纤的模式求解和分析。绘制出了Bragg光纤模式谱图,分类分析了在无限包层情况下Bragg光纤模式的基本特性。     

Effect of size and indium-composition on linear and nonlinear optical absorption of InGaN/GaN lens-shaped quantum dot

Based on the Schr ¨odinger equation for envelope function in the effective mass approximation, linear and nonlinear optical absorption coefficients in a multi-subband lens quantum dot are investigated. The effects of quantum dot size on the interband and intraband transitions energy are also analyzed. The finite element method is used to calculate the eigenvalues and eigenfunctions. Strain and In-mole-fraction effects are also studied, and the results reveal that with the decrease of the In-mole fraction, the amplitudes of linear and nonlinear absorption coefficients increase. The present computed results show that the absorption coefficients of transitions between the first excited states are stronger than those of the ground states. In addition, it has been found that the quantum dot size affects the amplitudes and peak positions of linear and nonlinear absorption coefficients while the incident optical intensity strongly affects the nonlinear absorption coefficients.