THE CONSTRUCTION OF WAVELET-BASED TRUNCATED CONICAL SHELL ELEMENT USING B-SPLINE WAVELET ON THE INTERVAL

Based on B-spline wavelet on the interval (BSWI), two classes of truncated conicalshell elements were constructed to solve axisymmetric problems, i.e. BSWI thin truncated conicalshell element and BSWI moderately thick truncated conical shell element with independent slope-deformation interpolation. In the construction of wavelet-based element, instead of traditionalpolynomial interpolation, the scaling functions of BSWI were employed to form the shape functionsthrough the constructed elemental transformation matrix,and then construct BSWI element viathe variational principle. Unlike the process of direct wavelets adding in the wavelet Galerkinmethod, the elemental displacement field represented by the coefficients of wavelets expansionwas transformed into edges and internal modes via the constructed transformation matrix. BSWIelement combines the accuracy of B-spline function approximation and various wavelet-basedelements for structural analysis. Some static and dynamic numerical examples of conical shellswere studied to demonstrate the present element with higher efficiency and precision than thetraditional element.     

CAE技术在井架设计中的应用

应用GAE技术，针对ZJ30／1700CZ钻机井架分别进行了静态分析及在自然状态和有钩载情况下的模态分析，为合理设计钻机井架结构提供了理论依据。通过分析计算，可以看出：所设计的井架的静态强度满足要求；经动力再设计后的井架固有频率与钻机的设计工作转速相差较大，达到工程要求，表明修改后的井架设计方案合理。     

高温封隔器胶筒与套管接触压力的实验研究

本文利用所研制的高温封隔器测试装置,应用高温电阻应变测试技术与有限元相结合的方法,研究了油井高温封隔器胶筒与石油套管内壁接触压力大小和分布规律,为优化高温封隔器的设计,提供有价值的数据。     

不可压缩二维流动Navier—Stokes方程的有限元解

对不可压缩流体沿二维后台阶流动的Ｎ－Ｓ方程的流函数－涡量式用有限元方法加以求解，固壁上的涡量用时间迭代法加以确定。分别计算Ｒｅ＝２００，４００，８００和１０００时流动区域的流函数和涡量值，并在Ｒｅ＝８００时与有关文献的结果相比较，基本吻合。且在此基础上讨论了出口条件对计算结果的影响。本文的方法对分析流经液压阀口等流动问题具有借鉴意义。     

Nodeless variable finite element method for heat transfer analysis by means of flux-based formulation and mesh adaptation

Based on flux-based formulation, a nodeless variable element method is developed to analyze two-dimensional steady-state and transient heat transfer problems. The nodeless variable element employs quadratic interpolation functions to provide higher solution accuracy without necessity to actually generate additional nodes. The flux-based formulation is applied to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method. The solution accuracy is further improved by implementing an adaptive meshing technique to generate finite element mesh that can adapt and move along corresponding to the solution behavior. The technique generates small elements in the regions of steep solution gradients to provide accurate solution, and meanwhile it generates larger elements in the other regions where the solution gradients are slight to reduce the computational time and the computer memory. The effectiveness of the combined procedure is demonstrated by heat transfer problems that have exact solutions. These problems are: (a) a steady-state heat conduction analysis in a square plate subjected to a highly localized surface heating, and (b) a transient heat conduction analysis in a long plate subjected to a moving heat source. The English text was polished by Yunming Chen.     

电磁波导的奇异元与对偶有限元分析

基于电磁波导的对偶变量变分原理以及Hamilton正则方程,将含有奇异性的电磁场问题导入Hamilton体系下进行分析,通过分离变量及共轭辛本征函数向量展开法,构造出可以表征电磁场奇异性的奇异解析元。奇异元的采用克服了普通单元处理含有导电劈和介质楔的波导问题的困难,同时能够方便地与电磁对偶元相结合,保持了有限元方法的灵活性,具有较高的精度。     

基于物理中面FGM板屈曲的有限元分析

基于物理中面的概念，根据最小势能原理推导了功能梯度材料FGM薄板屈曲的有限元控制方程，求得临界荷载的有限元解。利用FGM板的屈曲方程与参考均匀板的屈曲方程之间的相似性，建立了FGM板的临界荷载与参考均匀板的临界荷载之间的相似转换关系式，从而将FGM板临界荷载的计算转变为参考均匀板的临界荷载和材料不均匀系数的计算，极大地提高了计算效率，为FGM的推广起积极的推动作用。通过数值算例，将由有限元法和转换关系式得到的临界荷载进行了比较，并讨论了边界条件、荷载工况、材料组成和几何尺寸等对FGM板临界荷载的影响。     

Duffing系统的主--亚谐联合共振

以Duffing系统为研究对象,研究在多频激励下同时发生主共振和1/3次亚谐共振的动力学行为与稳定性.首先,通过多尺度法得到系统的近似解析解,利用数值方法检验近似程度,结果吻合良好,证明了求解过程和解析解的正确性.然后,从解析解中导出稳态响应的幅频方程和相频方程,从幅频曲线以及相频曲线中发现系统最多存在7个不同的周期解,这种多解现象可用于对系统状态进行切换.基于Lyapunov稳定性理论,得到联合共振定常解的稳定条件,利用该条件分析了系统的稳定性,并与Duffing系统的主共振和1/3次亚谐共振单独存在时比较.最后,通过数值方法分析了非线性项和外激励对系统动力学行为与稳定性的影响,发现了联合共振特有的现象:刚度软化时,非线性项不仅影响系统的响应幅值,同时还影响系统的多值性和稳定性;刚度硬化时,非线性项对系统的影响与单一频率下主共振和1/3次亚谐共振类似,仅影响系统的响应幅值.这些结果对Duffing系统动力学特性的研究具有重要意义.     

基于特征正交分解的一类瞬态非线性热传导问题的新型快速分析方法

提出了一种基于特征正交分解(POD)和有限元法的瞬态非线性热传导问题的模型降阶快速分析方法, 建立了导热系数随温度变化的一类瞬态非线性热传导问题有限元格式的POD降阶模型. 在隐式时间推进方法的基础上有效结合单元预转换方法和多级线性化方法发展了一种加速求解瞬态非线性热传导降阶模型的新型计算方法,并通过二维和三维算例验证了该方法的准确性和高效性. 研究结果表明: (1)降阶模型解的均方根误差在经过初始时段轻微的脉动后稳定于0.01%以下, 而其计算效率比有限元全阶模型提高2$\sim $3个数量级, 并且自由度数量(DOFs)愈大提高的幅度也愈加显著; (2)新型算法解决了常规算法在计算非线性降阶模型时加速性能差的问题, 即使是在DOFs比较小的时候也能够明显提高计算效率; (3)常数边界条件下得到的POD模态可以用来建立相同求解域在各种复杂时变边界条件下的瞬态非线性热传导降阶模型, 并对其传热过程和温度场进行快速准确的分析与预测, 具有很好的工程应用价值.