通过Adomian分解法求解二维Helmholtz方程

提出基于Adomian分解法求解二维Helmholtz方程。通过Adomian分解法可以把Helmholtz微分方程和边界条件分别转换成递归代数公式和适用符号计算的简单代数公式。利用边界条件可以很容易得到方程的解析解表达式。Adomian分解法的主要特点在于计算简单快速,并且不需要进行线性化或离散化。最后给出数值实例以验证Adomian分解法求解二维Helmholtz方程的有效性。通过数值计算可以发现,基于Adomian分解法的计算结果非常接近精确解,并且该方法具有良好的收敛性。这表明Adomian分解法能够快速有效求解Helmholtz方程。     

竖直下抛液体燃料爆炸抛撒的初步数值研究

对具有轴向初始速度即竖直下抛液体燃料的爆炸抛撒云雾形成过程进行了数值研究。近场的数据来自丁珏等的工作,以此数据作为远场初始参数。远场是燃料液滴与空气、燃料蒸汽、不同尺寸的液滴颗粒组成的多相体系之间的相互作用的过程。液滴的直径比较小,把液滴看成连续介质,且相互作用只考虑液滴的蒸发、破碎、碰撞聚合。轴向初速为0(静爆)时计算结果与实验结果相吻合。这说明本模型可以模拟爆炸抛撒云雾的形成过程,进而可以预估高速运动下云雾的形成过程。用以上模型计算了竖直下抛初速为100m/s、装填5kgPO的FAE装置的爆炸抛撒过程。所得的结果表明,100m/s的初速将影响云雾的最终形状及云雾内部的浓度分布。     

基于离散元的杆件断裂全过程数值模拟

杆件的断裂会涉及到大变形、非线性以及不连续等问题,通常的数值计算方法模拟这种复杂力学行为具有局限性。本文基于颗粒离散元法DEM,将接触粘结处的分布式弹簧用梁纤维进行等效,提出了一种适于结构弹塑性分析的DEM纤维梁模型,然后在此基础上构建了构件断裂模拟算法以及纤维破环准则。将该模型应用于悬臂梁结构,模拟了悬臂梁从弹性到弹塑性阶段,再到断裂破坏的全过程,数值模拟得到的结构响应和截面开裂破坏形态均较合理。最后将该方法应用于单层网壳倒塌破坏模拟,并与网壳振动台倒塌试验进行对比,结果表明,数值模拟得到的杆件断裂过程及结构倒塌模式与试验现象一致,验证了该模型的正确性和适用性。     

三维压裂缝网不稳定压力半解析求解方法

受地应力及压裂工艺影响, 大斜度井水力压裂缝网展布复杂, 缝网中存在不同倾斜方向、不同展布形态及不同贯穿程度的压裂缝. 本文通过将裂缝面离散为若干矩形微元实现裂缝形态有效表征, 将渗流过程划分为基质向裂缝流动及裂缝向井筒流动两阶段, 采用有限差分方法构建离散裂缝面内不稳定渗流数值解, 结合封闭边界面源函数及叠加原理构建基质内不稳定渗流解析解, 耦合裂缝内流动数值解与基质内流动解析解, 求解了三维压裂缝网不稳定压力. 基于积分中值定理提出了点源、特殊线源代替面源求解基质内渗流的求解方法, 分析了该方法的可行性及适用条件, 在保证模型精度的同时提升了计算效率. 研究表明, 在基质内采用点源函数面积分求解面源的方法可准确求解三维压裂缝网井底压力动态但计算效率极低, 基于积分中值定理的点源、特殊线源近似面源求解方法可大大提升计算效率, 且在裂缝微元划分较为精细(微元无因次边长小于0.15)时可取得较高精度, 基于该模型分析了裂缝导流能力、裂缝倾角、裂缝高度及裂缝段间距对压裂大斜度井典型试井曲线的影响.      

S型功能梯度扁球壳非线性屈曲的渐近分析

本文利用渐近迭代法获得了边界弹性支撑的功能梯度扁球壳的非线性屈曲问题的理论解．假设材料组分体积分数沿壳体厚度方向呈sigmoid幂函数变化,边界上考虑一般的弹性支撑约束．基于经典的薄壳理论和几何非线性关系,导出了S型功能梯度扁球壳的非线性屈曲问题的控制方程．采用渐近迭代法通过两次迭代得到了无量纲挠度和均布荷载之间的非线性特征关系．通过与已有有限元方法和其他数值方法的结果对比,验证了本文解的有效性和高精度．同时,通过计算阐述了缺陷因子、材料参数、边界约束系数及特征几何参数对壳体临界屈曲荷载的影响．     

Shock loading of a cylindrical shell filled with viscous compressible liquid

The effect of a uniformly distributed shock load on a thin-walled cylindrical shell filled with viscous compressible liquid is considered. An analytical method of inverse Laplace transformation of the general solution of the linearized Navier-Stokes equations is proposed. A numerical example is presented. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 11, pp. 55–61, November, 1999.     

Nonlinear Effects on Electrophoresis of a Soft Particle and Sustained Solute Release

A numerical study is made on the electrophoresis of a core-shell soft particle based on the first principle of electrophoresis. The soft particle consists of a charged rigid core coated with a polymer shell. Numerical computations for the electrophoretic velocity are obtained and compared with the existing analytical solution. The analytical solutions, based on the Boltzmann distribution of ions and the Debye–Huckel approximation, are valid for lower range of charge density, weak applied electric field and thin double layer. Discrepancy from the existing analytical solution is found when the Debye layer extends beyond the porous shell. This discrepancy becomes larger for higher values of the rigid core surface potential, fixed charge density of the soft shell and stronger imposed electric field. The double-layer polarization is found to have a strong impact when the shell thickness is lower than the Debye length. The electrophoretic velocity is found to vary nonlinearly with the imposed electric field when the imposed field strength is large enough to create a potential drop across the particle bigger than the thermal potential. We have also analyzed the mechanism of sustained solute release from the soft particle. Our results show that the rate of solute release is large compared to a pure diffusion dominated process.     

VIBRO-ACOUSTIC BEHAVIOR OF SUBMERGED CYLINDRICAL SHELLS: ANALYTICAL FORMULATION AND NUMERICAL MODEL

We propose both an analytical formulation and a numerical model to study the hydroelastic or vibroacoustic behaviour of cylindrical thin shells immersed in an unbounded, inviscid and heavy fluid. The analytical solution allows us to calculate the dynamic response and the pressure radiated in the far field by a baffled cylinder. This formulation uses the truncated modal basis of the dry structure to expand the displacements of the submerged shell. The analytical model is used as a reference in order to validate a numerical model which couples the finite element method (FEM) to the boundary element method (BEM). As opposed to the analytical formulation which is dedicated to baffled circular cylinders only, the numerical model allows us to treat any axisymmetric shell, such as cylindrical and spherical shells, or more complex shells of revolution. The structure is idealized by two-node ring finite elements and the boundary equation is solved using the method of singularities.     

不同起爆方式下炸药驱动柱壳膨胀断裂的数值模拟

采用数值模拟方法,研究不同起爆方式下内部炸药对金属柱壳的加载历程差别。计算结果表明,不同起爆方式下柱壳内表所经受的压力载荷、做功历史显著不同,分析了引起差异的原因。提出一种半解耦数值方法,使柱壳网格划分得更细,可以模拟不同起爆方式下柱壳的膨胀破坏过程,通过理论分析说明了这种方法的合理性。     

An Exact Analysis for Free Vibration of a Composite Shell Structure-Hermetic Capsule

ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｍｐｏｓｉｔｅｓｔｒｕｃｔｕｒｅｓｃｏｎｓｉｓｔｉｎｇｏｆｓｈｅｌｌｓｏｆｒｅｖｏｌｕｔｉｏｎｈａｖｅｗｉｄｅａｐｐｌｉｃａｔｉｏｎｓｉｎｖａｒｉｏｕｓｅｎｇｉｎｅｅｒｉｎｇｆｉｅｌｄｓｓｕｃｈａｓａｅｒｏｓｐａｃｅ ,ｃｈｅｍｉｃａｌ,ｃｉｖｉｌ,ｍｅｃｈａｎｉｃａｌ,ｍａｒｉｎｅｅｎｇｉｎｅｅｒｉｎｇ .Ｄｕｅｔｏｔｈｅｍａｔｈｅｍａｔｉｃａｌｃｏｍｐｌｅｘｉｔｙｏｆｓｈｅｌｌｅｑｕａｔｉｏｎｓａｎｄｔｈｅｄｉｆｆｉｃｕｌｔｙｔｏｍａｔｃｈｃｏｎｄｉｔｉｏｎｓｏｆｔｈｅ…     

Experimental and numerical analysis of spray-atomization characteristics of biodiesel fuel in various fuel and ambient temperatures conditions

The purpose of this work is to reveal the effects of fuel temperatures and ambient gas conditions on the spray-atomization behavior of soybean oil methyl ester (SME) fuel. The spray-atomization behavior was analyzed through spray parameters such as the axial distance from the nozzle tip, local and overall Sauter mean diameter (SMD). These parameters were obtained from a spray visualization system and a droplet measuring system. In addition, the experimental results were compared with the numerical results calculated by the KIVA-3V code. It was revealed that the increase of the fuel temperature (from 300 K to 360 K) little affects the spray liquid tip penetration. The increase of the ambient gas temperature (from 300 K to 450 K) caused a increase in the spray liquid tip penetration. Also, biodiesel fuel evaporation actively occurred due to the increase in the fuel temperature and the ambient gas temperature. Of special significance was that the highest vapor fuel mass concentration was observed at the center region of the spray axis. In the results of the microscopic characteristics, the detected local droplet size at the axial direction and overall droplet size at the axial and radial direction in a control volume increased when the fuel temperature increased. This is believed to be due to an increase in the number of small droplets that quickly evaporated. In addition, the increased fuel temperature caused the decrease of the number of droplets and the increase of the vapor fuel mass. The mean axial velocity of droplets decreased with increasing fuel temperature.     

Explosive projection of liquid from a thick-walled cylindrical container

The process of projection of a layer of an ideal liquid enclosed into a cylindrical elastoplastic shell by products of instantaneous detonation of a high explosive charge is studied numerically in a two-dimensional plane formulation. The processes of shell fracture and liquid exhaustion through the resultant slots are considered. Numerical results are analyzed, and analytical relations for angular distributions of radial velocity and mass of the liquid escaping through the slots are derived. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 56–63, May–June, 2009.     

Numerical simulation of liquefied fuel spills: II. Instantaneous and continuous LNG spills on an unconfined water surface

A simple numerical model based on the shallow water equations in radial symmetry is used to simulate both instantaneous and continuous spills of liquefied natural gas (LNG) onto a water surface. Using the computed results, a study is made of the similarities and differences in the pool structure resulting from the two types of spills. For instantaneous spills a relation linear on a logarithmic plot is suggested between the maximum pool size and the spill volume. The effects of shear forces and surface cohesivity on the evolution of the spill are also examined.     

Interaction between a submerged evacuated cylindrical shell and a shock wave—Part II: Numerical aspects of the solution

The interaction between a submerged elastic circular cylindrical shell and an external shock wave is addressed. A linear, two-dimensional formulation of the problem is considered. A semi-analytical solution is obtained using a combination of the classical analytical approach based on the use of the Laplace transform and separation of variables, and finite difference methodology. The study consists of two parts. Part I focuses on the simulation and analysis of the acoustic fields induced during the interaction. Both the diffraction (absolutely rigid cylinder) and complete diffraction–radiation (elastic shell) are considered. Special attention is paid to the lower-magnitude shell-induced waves representing radiation by the elastic waves circumnavigating the shell. The focus of Part II is on the numerical analysis of the solution. The convergence of the series solution and finite-difference scheme is analysed. The computation of the response functions of the problem is discussed as well, as is the effect of the bending stiffness on the acoustic field. The membrane model of the shell is considered to analyse such effect, which, in combination with the models addressed in Part I, allows for the analysis of the evolution of the acoustic field around the structure as its elastic properties change from an absolutely rigid cylinder to a membrane. The results of the numerical simulations are compared to available experimental data, and a good agreement is observed.     

厚壳三维分析的半解析解

本文对座标系三维弹性力学问题采用周向与径向解析,轴向离散的半解析数值方法。通过引入部分解析函数,将三维问题归结为一维离散化方程。这种方法能适应于一大类复杂的弹性力学问题,方法简单,计算工作量少。本文用这方法来分析厚壳的三维变形与应力规律,研究大厚跨比的强厚壳的三维弹性理论解,为建立可靠的强厚壳理论提供依据。     

基于二阶双渐近法的双层圆柱壳在水下爆炸作用下的鞭状运动

针对潜艇在水下爆炸载荷下的鞭状运动,从波动方程出发,推导了二阶双渐近法后期近似,并结合声固耦合法初步解决了双层圆柱壳的内域问题,然后将其与显式有限元耦合形成了圆柱壳结构水下爆炸流固耦合分析方法。通过简单算例验证了本文分析方法的有效性和精度。最后,基于此方法分析了双层圆柱壳结构在水下爆炸载荷下的总体响应特性以及周期比和爆距比对其影响规律。     

基于液体碳氢燃料的旋转爆轰燃烧特性研究

为了探索液体碳氢燃料参与旋转爆轰所产生的不完全燃烧现象,采用守恒元与求解元方法,开展柱坐标系下的汽油/空气两相旋转爆轰燃烧室三维数值模拟研究,针对燃料喷注压力和反应物当量比对旋转爆轰流场结构及燃烧室性能的影响进行分析。分析结果表明:保持总当量比为1.00,随着燃料喷注压力的上升,燃烧室内燃料不均匀分布增强,产生局部富燃区,燃料在燃烧室未能完全反应,导致燃烧室燃料比冲下降;保持喷注压力不变,减小当量比,在贫燃工况下依然存在局部富燃区,导致燃烧室内出现不完全燃烧现象,降低燃烧室比冲性能。由此可知,反应物喷注方案对气液两相旋转爆轰的不完全燃烧有显著影响。     

Interaction between a submerged evacuated cylindrical shell and a shock wave—Part I: Diffraction–radiation analysis

The interaction between a submerged elastic circular cylindrical shell and an external shock wave is addressed. A linear, two-dimensional formulation of the problem is considered. A semi-analytical solution is obtained using a combination of the classical analytical approach based on the use of the Laplace transform and separation of variables, and finite difference methodology. The study consists of two parts. Part I focuses on the simulation and analysis of the acoustic fields induced during the interaction. Both the diffraction (absolutely rigid cylinder) and complete diffraction–radiation (elastic shell) are considered. Special attention is paid to the lower-magnitude shell-induced waves representing radiation by the elastic waves circumnavigating the shell. The focus of Part II is on the numerical analysis of the solution. The convergence of the series solution and finite-difference scheme is analysed. The computation of the response functions of the problem is discussed as well, as is the effect of the bending stiffness on the acoustic field. The membrane model of the shell is considered to analyse such an effect, which, in combination with the models addressed in Part I, allows for the analysis of the evolution of the acoustic field around the structure as its elastic properties change from an absolutely rigid cylinder to a membrane. The results of the numerical simulations are compared to available experimental data, and a good agreement is observed.     

等几何壳体分析与形状优化

首先基于Reissner-Mindlin理论进行了三维壳体等几何分析,而后基于此对三维壳体进行形状优化,提出了形状优化中灵敏度的全解析计算方法,包括位移应变阵、雅克比阵和刚度阵等相对控制顶点位置的灵敏度解析计算公式;通过实例验证了壳体等几何分析和灵敏度全解析计算方法的有效性。与传统的基于网格的灵敏度半解析计算方法相比,基于NURBS的灵敏度全解析计算具有精确、计算效率高的特点,且可以避免优化迭代中的网格畸变。