微分求积方法对于桩基大变形分析的应用

本文基于大变形的理论,采用弧坐标首先建立了具有初始位移的桩基的非线性数学模型,一组强非线性的微分-积分方程,其中,地基的抗力采用了Winkeler模型;其次,引入变数变换将微分-积分方程转化为一组非线性微分方程,并用微分求积方法离散了方程组,得到一组离散化的非线性代数方程;最后用Newton-Raphson迭代方法对离散化方程进行了求解,得到了桩基变形前后的构形、弯矩和剪力.计算中选取了两种不同类型的初始位移,并考察了它们对桩基大变形力学行为的影响.     

R型铁氧体BaFe4-xTi2+xO11的化学组态以及磁性行为的研究

本文通过传统的固相反应法制备了R型六角铁氧体BaFe_4-xTi_2+xO₁₁ (x= 0, 0.25, 0.5, 0.75, 1), 并且对它的原子价态以及磁性行为进行了研究. X 射线光电子能谱(XPS)结果显示了随着掺杂含量的增加, 体系中Fe³⁺离子逐渐减少而Fe²⁺离子逐渐增加. 由于具有非对称结构的阻挫晶格中存在各种关联作用的竞争, 使得BaFe_4-xTi_2+xO₁₁体系表现出了复杂的磁有序行为, 在T₁～250 K和T₂～83 K两处存在磁转变. 对这一系列掺杂样品, 在相变温度T₁之上表现顺磁行为, 而在相变温度T₂前后的磁化强度都表现出低场下随磁场的增加快速增加, 高场下则线性变化且在5×10⁴ Oe时还未达到饱和的行为, 表明这一系列掺杂样品是典型的倾斜反铁磁态(canted antiferromagnetic) 或者亚铁磁态.     

Phase transition and critical behavior of spin–orbital coupled spinel ZnV_2O_4

We present the temperature-dependent susceptibility and specific heat measurement of spinel ZnV_2O_4.The structural transition with orbital ordering and the antiferromagnetic transition with spin ordering were observed at 50 K and 37 K,respectively.By analysis of the hysteresis behavior between the specific heat curves obtained in warming and cooling processes,the structural transition was confirmed to be the first-order transition,while the antiferromagnetic transition was found to be of the second-order type.At the structural transition,the latent heat and entropy change were calculated from the excess specific heat,and the derivative of pressure with respect to temperature was obtained using the Clausius-Clapayron equation.At the magnetic transition,the width of the critical fluctuation region was obtained to be about 0.5 K by comparing with Gaussian fluctuations.In the critical region,the critical behavior was analyzed by using renormalization-group theory.The critical amplitude ratio A~+/A~- = 1.46,which deviates from the 3D Heisenburg model;while the critical exponent α is-0.011,which is close to the 3D XY model.We proposed that these abnormal critical behaviors can be attributed to strong spin-orbital coupling accompanied with the antiferromagnetic transition.Moreover,in the low temperature range(2-5 K),the Fermi energy,the density of states near the Fermi surface,and the low limit of Debye temperature were estimated to be2.42 eV,2.48 eV~(-1),and 240 K,respectively.     

具有初始构型的MEMS驱动器的跳跃和吸合现象研究

在曲梁变形后以弧长为参数的自然坐标系中,利用曲梁大变形分析理论,建立了具有任意初始构型的微电驱动器大变形电动力学分析的数学模型,并采用微分求积法(DQM)进行空间离散,得到了一组具有强非线性的微分-代数系统方程,运用Petzold-Gear BDF方法进行时间域内的求解。研究了MEMS驱动器在电场力作用下的瞬态动力学特性,包括跳跃(snap-through)和吸合(pull-in)现象,并与已有实验结果进行了比较。     

弹性或弹塑性土体中桩基的大变形分析

采用弧坐标,首先建立了位于弹性地基或弹塑性地基上并具有初始位移的桩基大变形行为的非线性微分方程组,并采用Winkeler模型来模拟地基对桩基的抗力;其次,应用微分求积方法离散非线性微分方程组,得到一组离散化的非线性代数方程,并给出了利用Newn-Raphson方法求解非线性代数方程的步骤;作为应用给出了数值算例,得到了桩顶受组合载荷作用时,变形后桩基的构形、弯矩和剪力,考察了土的弹性和弹塑性性质、桩基初始位移、荷载等参数对桩基力学行为的影响.最后将模型进行简化,得到了小变形理论的解析解,并比较了由大变形理论与小变形理论所得结果的差别.     

Analysis of nonlinear stability and post-buckling for Euler-type beam-column structure

Based on the assumption of finite deformation, the Hamilton variational principle is extended to a nonlinear elastic Euler-type beam-column structure located on a nonlinear elastic foundation. The corresponding three-dimensional (3D) mathematical model for anaiyzing the nonlinear mechanical behaviors of structures is established, in which the effects of the rotation inertia and the nonlinearity of material and geometry are considered. As an application, the nonlinear stability and the post-buckling for a linear elastic beam with the equal cross-section located on an elastic foundation are analyzed.One end of the beam is fully fixed, and the other end is partially fixed and subjected to an axial force. A new numerical technique is proposed to calculate the trivial solution,bifurcation points, and bifurcation solutions by the shooting method and the Newton-Raphson iterative method. The first and second bifurcation points and the corresponding bifurcation solutions are calculated successfully. The effects of the foundation resistances and the inertia moments on the bifurcation points are considered.     

桩基的稳定性:理论和最新进展

本文对桩基的稳定性分析的数学模型、分析计算方法以及离心机模拟试验的近期文献进行了一定的回顾.主要侧重于桩基的失稳模式和机理分析,包括基于Euler屈曲理论的桩基不稳定性、桩基的定向不稳定性、地震液化中桩基的不稳定性、桩基的动力不稳定性、桩基的后屈曲分析等.最后简单地提出了进一步需要开展的工作.     

粘弹性矩形板的稳定性分析

根据动力系统的观点研究了四边简支粘弹性矩形板的稳定性，利用Ｌａｐｌａｃｅ变换得到了蠕变临界载荷λｃｒ和瞬时临界载荷λｃｓ。同时采用Ｌａｐｌａｃｅ变换和Ｇａｌｒｋｉｎ方法计算了时间相关载荷λ（ｔ）的峰值λ满足条件λｅｒ〈λ〈λｃｓ时，线性和非线性问题的挠度随时间的变化规律。     

弹性地基上HDAJ接头桩的非线性稳定性分析

本文采用弧坐标首先建立了弹性地基中受轴向载荷作用的高柔性抗震拼接头桩(High Ductility Aseis-matic Joint Spliced Pile)的非线性数学模型，并假定土(基础)对桩基的反作用力服从Winkler模型；在此基础上对该模型进行了线性化，并得到HDAJ接头桩的临界载荷。最后根据分叉理论的观点和方法，讨论了HDAJ接头桩在临界载荷处的稳定性问题。研究结果表明HDAJ接头桩在临界载荷附近必发生分叉，且分叉解是唯一的，稳定的，并且给出了分叉解的渐近表达式。物理上，这表示HDAJ接头桩的平衡构形在临界载荷处必然发生改变，并且从一个稳定的平衡构形变化到另一个稳定的平衡构形。同时考察了土的液化对临界载荷的影响，说明液化的影响是非常明显的。当考虑土的液化时，桩基的临界载荷低于不考虑土的液化时桩基的临界载荷。     

无网格方法在平面粘弹性力学问题中的应用

本文综合应用无网格方法(EFGM)、线性粘弹性与弹性力学之间的对应原理,Laplace变换和逆变换等方法求解了拟静态平面弹性和粘弹性力学问题。首先,利用Laplace变换和逆变换推导了平面问题的粘弹性本构关系,建立了拟静态粘弹性平面问题的边值问题;其次,利用粘弹性与弹性力学之间的对应原理得到了Laplace变换域中平面问题的基本方程,在Laplace变换域中建立了相应的泛函,并得到了用无网格方法离散的控制方程;同时,求解了几个拟静态弹性和粘弹性平面问题,给出了它们的表达式和数值结果;最后,采用Laplace逆变换和数值逆变换,得到了粘弹性力学平面问题在物理空间中的解,并比较了由解析解和无网格数值方法所得到的数值结果,可以看到它们是非常吻合的。说明本文方法的正确性和有效性。