【作者】 王刚；

【导师】 李光耀； 崔向阳；

【作者基本信息】 湖南大学 ， 机械工程， 2016， 博士

【摘要】 随着汽车工业的高速发展,汽车的振动噪声问题越来越受到消费者及从业人员的关注。为了缩短研发周期并降低成本,日渐成熟的CAE技术在整车开发的前期发挥着越来越重要的作用。以有限元、边界元和无网格法等为主体的数值计算方法作为目前商用CAE软件的核心,其在汽车刚度、模态、振动及噪声等分析中的作用不言而喻。传统边界元和无网格法在处理上述工程问题时,存在计算复杂、求解效率过低等缺陷。尽管基于三角形和四面体网格的低阶线性有限元方法在计算精度上的表现不尽人意,但由于其所依托的简单非结构网格可以精确地逼近复杂几何型面的边界并且网格生成成本较低,正逐步引起研究人员的关注。为了快速、高效地对汽车的振动噪声等问题进行模拟仿真,本文针对现有数值算法的不足,从广义梯度光滑技术和光滑伽辽金弱形式出发,提出了一套简单实用的、以非结构背景网格为载体的结构、声学及声子晶体节点积分计算方法。具体工作为:(1)构建了板壳结构的节点积分方法,并将其用于车身薄壁件的静力和自由振动分析。基于Reissner-Mindlin中厚板假设,通过将光滑势能泛函的二次残差项引入到系统平衡方程的构建并采用格林散度定理对应变梯度进行表征,构造了一种新型的节点积分中厚板单元数值模型,其有效地克服了传统节点积分中厚板单元的时域不稳定性并提高了其数值仿真的精度和效率。进一步基于Kirchhoff薄板壳假设,通过将域积分转换为边界积分并采用格林散度定理降低试函数的连续性要求,使线性插值求解四阶偏微分方程成为可能;同时,提出了节点随动坐标系的概念,并给出了非同面内的梯度光滑操作实现方案;以上述理论为基准,分别构造了节点积分轴对称薄板壳单元和节点积分广义薄板壳单元的数值模型,从而为车身薄壁件的刚度、模态等力学特性仿真提供了高效高精度的计算工具。(2)提出了声学问题的节点积分方法,并将之用于汽车内声场噪声预测的数值模拟。进一步发展了围绕单元节点构造积分域的理念,对问题域离散模型内的每一单元构造了其梯度场的相关支持域,在此基础上采用Shepard全局插值函数实现了单元内梯度场的加权重构,进而在国际上首创了声学梯度加权有限元法的数值模型。此外,为克服传统节点积分方法因时域不稳定而不能用于声学等工程问题计算的业界难题,基于等效积分与泰勒中值定理,构造了一种以增加虚拟积分点数目为特征、以考虑积分域内声压梯度项变化为特色的新型声学节点积分有限元法模型。上述两种单元构造方式弥补了当前低阶有限元法无法模拟中高频声学问题及数值色散误差增长过快的缺陷,提高了线性单元的计算效率和精度。(3)开发了基于非结构网格的高精度结构-声场耦合算法,并将其用于车身结构的声固耦合分析计算。以三角形和四面体两类简单非结构背景网格为载体,引入了基于单元边的随动坐标系,给出了空间壳体结构的边光滑有限元法动力学方程构造方案,并将其与三维内声场问题数值模拟的面光滑有限元法相结合,进而开发了一种新型的低阶高精度边光滑/面光滑有限元法声固耦合数值模型。与此同时,基于已开展的研究工作,充分发掘无转角节点积分薄板壳单元和声学梯度加权有限元法的各自优势,通过车身结构件振动与车内声场声压之间位移和力的连续性条件,构建了二者之间耦合分析的计算模型。以上两种方案拓宽了传统线性单元在汽车结构-声耦合分析中可计算的频率范围,为三角形和四面体单元在工程中的进一步应用研究奠定了基础。(4)提出了声子晶体带隙特性仿真的节点积分方法,并将之用于声子晶体的能带结构和振动传输特性仿真计算。针对声子晶体等声学超材料带隙特性仿真中现有数值模型收敛速度慢及对材料弹性常数差敏感的缺陷,通过将节点积分思想与梯度光滑技术引入到原胞动力学方程的构建,并结合周期结构中弹性波传播的Bloch定理,开发了二、三维无限周期声子晶体能带结构计算的节点积分有限元法数值模型。由于采用了非结构网格对原胞内的不同介质进行了离散,因此可以减小界面间的模型离散误差、提高数值仿真的精度。同时,构建了有限周期声子晶体振动传输特性计算的节点积分有限元法方程,并设计了相关实验对仿真结果进行了验证,从而进一步证实了节点积分方法的实用性和有效性,为声子晶体等声学超材料在汽车上的减振降噪应用研究提供了有力的技术支撑。更多还原

【Abstract】 With the rapid development of automobile industry,the vibration and noise level of the vehicle has attract more and more people’s concern during the past several decades.In order to shorten the research period and reduce the cost,the maturing CAE technology plays a significant role in the conceptual phase of car design.As the core module of the commercial software,the numerical methods,which include the finite element method,the boundary element method and the meshfree method,affect significantly the accuracy and efficiency of the vehicle’s performance simulation.The boundary element method and the meshfree method suffer from the low computational efficiency deficiency when dealing with these practical engineering problems.Although the low-order finite element method with three-node triangular and four-node tetrahedral elements encounter the poor computational accuracy shortage,it attracting more and more researcher ’s attention in recent years for its simplicity and efficiency.In order to simulate the vehicle’s NVH characteristics in an effective and efficient way,this thesis present several simple plate and shell elements,acoustic elements and phononic crystal computational methods based on the gradient smoothing technique and the generalized Galerkin weak form using the unstructured mesh and the nodal integration method.The dissertation includes:(1)Plate and shell nodal integration methods are proposed for the static and free vibration analyses of vehicle body structure.Based on the Reissner-Mindlin hypothesis,a novel nodal integration method is first proposed to cure the temporal instability and improve the accuracy and efficiency of the original nodal integration.By expressing the strain gradient through the divergence theorem,a stabilization item is added into the smoothed potential energy functional of the original nodal integration,consisting of squared-residual of equilibrium equations.With the framework of Kirchhoff hypothesis,a novel computational theory,namely,solving the fourth order boundary value problem with linear interpolation functions,is further proposed in this work,which consists of relaxing the continuity requirement of trial function with the Green’s theorem and converting the domain integration into boundary integration.Based on these theoretic achievements,two nodal integration methods are thus proposed to simulate the thin shell and the axisymmetric shell problems.These numerical models can be seen as good alternatives for the mechanical property simulation of vehicle structural components.(2)A class of acoustic nodal integration methods are proposed for the numerical simulation of vehicle noise prediction.The concept of constructing the integration domain based on the nodes of element is expanded in this work.For each independent element,a compacted support domain,which will be further used to reconstruct the acoustic gradient field,is established based on the element itself and its adjacent elements sharing common edges/faces.With the aid of Shepard interpolation method,a gradient-weighted finite element method is first proposed to reduce the dispersion error in computational acoustics.In order to cure the temporal instability of the original integration method and reduce the pollution error in numerical acoustics,a novel nodal integration method by considering the gradient variance items over the smoothing domain based on the Taylor mid-value theorem is proposed in this study.Both the two computational models eliminated the numerical dispersion error in computational acoustics successfully and improved the computing accuracy and efficiency of low order linear elements.(3)A series of fluid-structure interaction algorithms based on the unstructured mesh are presented for the structural-acoustic analysis of vehicle body.An edge-based smoothed triangular shell element is presented to discretize the kinematic equation for shell structure by introducing an edge local coordinate system when performing the strain smoothing operation.After combining the face-based smoothed finite element method used in three-dimensional acoustic simulation,a coupled edge-/face-based smoothed finite element model is further proposed to analyze the structural-acoustic problems in this study.At the same time,based on the previous work,a coupled structural-acoustic numerical model is constructed using the rotation-free nodal integration thin shell formulation and the gradient-weighted finite element method.The coupled equation is established through the continuity requirement between the structural displacement and the acoustic pressure on the coupling surface.These coupling numerical models can provide much more accurate results than the traditional computational methods,which laid the foundation for their further engineering application.(4)Proposed a nodal integration method for the computation of band structure and vibration transmission character of phononic crystals.As the conventional numerical methods suffer from the slower convergence speed and higher sensitivity for large contrast between two elastic parameters,a nodal integration method that combines the gradient smoothing technique and the Bloch theorem is further proposed in this work to study the propagation of elastic waves in two-and three-dimensionalinfinite periodic phononic crystals.Because the unstructured meshes are employed here to discretize the cell consisting of different materials,the discretization error can be reduced to the minimum.Besides,the vibration transmission formula for finite periodic phononic crystals using the nodal integration method is also constructed in this work.In order to further demonstrate the effectiveness of the present method for band structure calculation,some experiment are also designed in this work.The excellent results validate that the proposed algorithm can be seen as a good technical support for the application research of phononic crystals in vibration and noise reduction.更多还原