In engineering practice, the parametric uncertainty and correlation may coexist in the powertrain mounting system (PMS). An effective robust-based design optimization approach is proposed for uncertain PMS based on full vehicle model, where both the parametric uncertainty and correlation are considered. The uncertain parameters of PMS are firstly treated as probabilistic variables, and the Unscented Transformation Inspired (UTI) transformation is introduced to quantify the correlation of uncertain parameters. Then, to perform the uncertainty and correlation analysis, the UTI-Monte Carlo (UMC) method is developed based on UTI transformation and Monte Carlo sampling to estimate the means, standard deviations, variation ranges and correlation coefficients of PMS responses. Meanwhile, an efficient method named UTI-Arbitrary Polynomial Chaos Expansion (UAPCE) method is derived for the uncertainty and correlation analysis of PMS responses by combining UTI transformation and arbitrary polynomial chaos expansion. Next, an optimization model considering parametric uncertainty and correlation is formulated to perform the robust-based design of PMS, in which the weight coefficients of optimization components are calculated by principal component analysis. Finally, the numerical example is investigated to verify the effectiveness of the proposed methods.

In engineering practice, some uncertain parameters of structures are usually independent while others might be correlated in the design problems of automotive engineering. This study introduces the multidimensional parallelepiped (MP) model to handle the independent and correlated parameters of an uncertain automotive powertrain mounting system (PMS) in a unified framework. Two uncertainty analysis methods, including the multidimensional parallelepiped-Monte Carlo method (MP-MCM) and the multidimensional parallelepiped-regularization-perturbation method (MP-RPM), are developed for the uncertainty analysis of the dynamic responses of PMS, in which independent and correlated parameters coexist. In the proposed MP-MCM, the uncertainty domain of all uncertain parameters is firstly established based on the MP model. Then, the correlated parameters are treated as independent uncertain variables and the traditional Monte Carlo simulation is applied to obtain random samples. Among the obtained samples, the ones satisfying the matrix inequality of MP model are selected and finally used to calculate the interval responses of PMS. In the proposed MP-RPM, the regularization method is firstly introduced to transform the parametric uncertainty domain into a standard multidimensional cube domain, where all uncertain parameters become independent with each other. And then, the perturbation analysis and central difference strategy are combined to efficiently calculate the interval responses of PMS. A numerical application is provided to demonstrate the effectiveness of the proposed methods on uncertainty analysis of the PMS with independent and correlated parameters. The influence of different parametric correlation on system dynamic responses, and the effect of the parametric correlation of different mounts on system responses are discussed in detail.

In the present paper, a numerical model, named smoothed particle hydrodynamics (SPH)-net model, is proposed for the coupled simulation of fixed net structures in currents and waves based on the coupling between the SPH method and screen model. The fluid is solved by the SPH method and the net structures are handled by the screen model, both of which are represented by a number of Lagrangian particles. A coupling algorithm between the SPH method and screen model is derived based on the momentum disturbance, which allows for accurate simulation of interactions between net structures and fluid. Thanks to the quasi-static assumption of the screen model, the proposed model can both handle the net structures in currents and waves. To validate the SPH-net model, numerical simulations were conducted on three distinct cases: fixed net panels in currents, a fixed net cage in currents, and a fixed net panel in the regular wave. The comparison of hydrodynamic forces on the net between the numerical results and experimental data demonstrates that the proposed SPH-net model has accuracy and reliability in predicting the hydrodynamic forces acting on fixed net structures in currents and regular waves.

The parametric uncertainty and correlation may coexist in the powertrain mounting system (PMS) in engineering practice. An effective approach is proposed for the multi-objective reliability-based robust design optimization of the PMS involving parametric uncertainty and correlation. In the proposed approach, the uncertain parameters of PMS with sufficient information are characterized as correlated random variables, whereas the uncertain parameters with discrete information are considered as discrete uncertain variables. Then, the Nataf-arbitrary polynomial chaos expansion (NAPCE) method is developed to estimate the means, standard deviations, and correlation coefficients of PMS responses. Meanwhile, the Nataf-Monte Carlo method is presented as a reference method to verify the NAPCE method. Next, the generalized maximum entropy principle and the correlation coefficient weighting method are respectively utilized to evaluate the reliabilities of PMS responses and the weight factors of optimization components. Afterwards, a multi-objective optimization model is established to explore the optimum design of the uncertain PMS considering both reliability and robustness simultaneously. Finally, the numerical application is provided to demonstrate the effectiveness of the proposed approach.

An effective subinterval analysis method is proposed to predict the response boundaries of uncertain problems with large uncertainty based on the positive and negative gradients. In the proposed method, the uncertain parameters with large uncertainty are described as interval variables. The variation intervals of interval variables are firstly divided into a series of uniform subintervals, and the original uncertainty domain with large uncertainty is thereby transformed into a series of subdomains with small uncertainty. Then, based on the gradient information of response function, the positive and negative gradients are employed as the search directions to identify the potential uncertainty subdomains which may contribute to the response boundaries. Next, the first-order Taylor expansion is used to precisely calculate the response boundaries of the uncertain problem on the potential uncertainty subdomains. Subsequently, the response boundaries on the original large uncertainty domain are further obtained through comparing the responses obtained on the uncertainty subdomains. Finally, several numerical examples and application examples are used to verify the effectiveness of the proposed method.

A three-dimensional smoothed-particle hydrodynamics (SPH) method is used to study the moving boundary problem of a swimming manta ray, focusing on Eulerian and Lagrangian coherent structures. The manta ray's boundary motion is predefined by a specific equation. The calculated hydrodynamic results and Eulerian coherent structures are compared with data from the literature. To improve computational stability and efficiency, the δ+-SPH model used in this study incorporates tensile instability control and an improved adaptive particle-refinement technique. By comparing and analyzing the Eulerian and Lagrangian coherent structures, the relationship between these vortex structures and hydrodynamic force generation is examined, revealing the jet mechanism in the manta ray's wake. The SPH method presented herein is robust and efficient for calculating biomimetic propulsion problems involving moving boundaries with large deformations, and it can accurately identify vortex structures. The approach of this study provides an effective simulation tool for investigating biomimetic propulsion problems such as bird flight and fish swimming.

Vehicle wading problems have received increasing attention from the automotive community in recent years because of the prosperous developments of electric vehicles, for which the performance of water tightness can be more important than conventional fuel vehicles. This paper presents an attempt to simulate vehicle wading problems based on an entirely meshless framework by using Smoothed Particle Hydrodynamics (SPH). First of all, an easy-to-implement but effective strategy is proposed to prevent the penetration between fluid particles and a wall boundary modeled by a set of solid particles when the distribution quality of the solid particles is poor. Subsequently, a comparative study is conducted to assess the feasibility and applicability of the SPH and Finite Volume (FV) methods in solving vehicle wading problems. Furthermore, the wading dynamics of a vehicle passing a puddle under different combinations of wading speeds and accumulating water depths is also investigated and discussed in detail by using the SPH method. It is suggested that the SPH method can be regarded as a potential candidate for solving vehicle wading problems, especially for those situations where the free-surface evolution during the wading process is particularly concerning.

The water-dropping (by water-dropping, we mean the phenomenon of water flow dispersing into droplets under the influence of airflows) of airtankers (by airtankers, we mean the aircraft carrying out firefighting missions) has always been a challenge in computational fluid dynamics simulation due to its complex mechanism and vast splashing space. Although the smoothed particle hydrodynamics (SPH) method has advantages in dealing with splashing problems, the multiphase flow SPH model faces the challenge of low computational efficiency in simulating splashing problems in the vast space. An efficient SPH model considering airflow resistance based on the single-phase coupling algorithm between fluid particles and airflows is proposed in this paper. The SPH model can calculate the airflow resistance of fluid particles based on their windward surface and surface normal and then simulate the splashing trajectory and pattern of SPH particles under the influence of high-speed airflows. In this article, two benchmark cases, including water jet and dropped water in the wind, are simulated based the SPH model. The simulation results are consistent with experimental results, verifying the computational accuracy and efficiency of the proposed SPH model. After that, the entire pattern of water-dropping about an airtanker is simulated, proving the feasibility of the algorithm for simulating large-scale water-dropping engineering problems.

The correlation analysis of the uncertain structures with multi-responses is carried out based on the multidimensional parallelepiped model in this research. Firstly, the multidi-mensional parallelepiped model is introduced to quantify the uncertainty and correlation of input parameters. Then, to deal with the large uncertainty of input parameters, the sub -parallelepiped perturbation analysis algorithm is designed to calculate the marginal inter-vals of output responses. Next, based on the Monte Carlo simulation and the second-order perturbation technique, the Monte Carlo correlation analysis algorithm and the second -order perturbation correlation analysis algorithm are respectively designed to obtain the correlation coefficients of output responses. Subsequently, two uncertainty domain anal-ysis algorithms based on the marginal intervals analysis and the correlation coefficients analysis, are presented to establish the uncertainty domains of output responses. Finally, the effectiveness of proposed algorithms is verified by three numerical examples.(c) 2023 Elsevier Inc. All rights reserved.

针对纯电动汽车动力总成悬置系统(Powertrain Mounting System,PMS)参数同时存在不确定性和相关性的情形,开展了纯电动汽车PMS固有特性的不确定性和相关性传播分析研究.利用多维平行六面体模型量化系统参数不确定性和相关性;基于多维平行六面体模型,将正则化法、泰勒展开法及中心差分法相结合,提出了一种PMS固有特性响应不确定性传播分析的MP摄动法.结合系统固有特性响应数据,基于蒙特卡罗法和置信度,提出了一种系统固有特性响应的相关性传播分析方法.以某纯电动汽车PMS算例验证了方法的有效性.分析结果表明:系统参数的不确定性会使得系统响应具有不确定性,而系统参数的相关性会使得系统响应具有一定的相关性.

Operating in extreme sea conditions, vessels often meet horrible wave impact which generates wave breaking and splashing at the bow and poses a great threat to staff safety and structural strength. Characterized with the ticklish issues e.g. multiphase interface and free surface large deformation, the study of slamming and splashing needs more reliable numerical tools. Smoothed particle hydrodynamics (SPH) method, benefiting from its Lagrangian meshless nature, shows superior performance in simulating slamming and splashing properties, which is employed in this paper to model the slamming process of the Sun Yat-sen University (SYSU) scientific research vessel. 2D wedges and 3D hemisphere water-entry benchmarks are simulated to validate the SPH model. After extending 2D to 3D simulation, SPH-based and finite volume method (FVM) -based solvers are exploited with various slamming cases for the SYSU scientific research vessel. Comparisons of the numerical results on dynamic response and bow slamming hydrodynamics of the SYSU vessel between SPH and FVM are performed in this paper. The numerical results demonstrate that except for precise prediction of hull dynamics, SPH is good at tracking the complex interface and splashing details, which possesses practical applicability in the simulation of violent fluid–structure interaction.

Uncertain structures may exhibit fuzzy uncertainty involving imprecise membership function (FuIMF). In this study, the uncertain parameters in FuIMF case are characterized as fuzzy variables, whereas the key parameters of their membership functions are treated as interval variables rather than exact values. Two ideas are put forward to handle FuIMF variables. First, the interval-boundary interval method (IBIM) is derived to conduct uncertainty propagation analysis, in which the [Formula: see text]-cut of FuIMF variables are considered as interval-boundary intervals. Second, the [Formula: see text]-cut of FuIMF variables are presented by the conservative and radical approximations, and the conservative and radical approximations method I (CRAM I) is proposed to conduct uncertainty propagation analysis. To further promote the computational efficiency, the conservative and radical approximations method II (CRAM II) is developed. Afterwards, a reference method based on Monte Carlo simulation is presented to verify the proposed methods. Finally, the effectiveness of proposed methods is demonstrated by numerical examples.

The fluid–soil interactions play a significant role in coastal and ocean engineering applications. However, there are still some complex mechanical problems with large deformations of water–soil interfaces to be solved. As a particle-based Lagrangian method, Smoothed Particle Hydrodynamics (SPH) is good at solving multiphase problems with large deformations of boundaries or interfaces. Therefore, in this work, the [Formula: see text]-SPH method is extended for the simulation of fluid–soil interacting problems. First, based on the weakly compressible assumption, the water is modeled as a viscous fluid while the soil is considered as a material with elastic–perfectly plastic behaviors. The [Formula: see text]-SPH method is implemented on the two phases separately, while the stress diffusive term only acts on the soil. The seepage force is introduced to model the interaction between two phases. After that, several numerical test cases with small to large interface deformations are presented. It is shown that the fluid–soil interacting model based on the [Formula: see text]-SPH model gives satisfying results compared with experimental data. Finally, the model is further extended for the simulation of vertical or oblique water jet scouring problems which demonstrates the potential applications of the SPH model for complex engineering problems.

为探讨复特征值分析(CEA)和瞬态动力学分析(TDA)在制动尖叫研究中的应用,将两种方法分别应用于同一汽车盘式制动器的尖叫不稳定性分析中,对其分析效率、分析特点和分析结果开展了对比研究.结果表明,两种方法均能对某制动器系统 7.5 kHz附近的潜在制动尖叫进行有效预测,但 CEA 预测的尖叫频率数目多于 TDA;CEA 的计算效率远高于TDA;CEA 可求解系统的不稳定特征值及不稳定模态,而 TDA 则可求解系统的振动加速度(速度或位移)、接触力和接触面积等;摩擦因数对系统的稳定性有显著影响,摩擦因数越大,尖叫不稳定性越突出.

This paper aims at presenting a general-purpose-oriented and fully parallelized meshless framework to simulate complex Fluid–Structure Interaction (FSI) problems in ocean engineering. In this framework, a Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) solver is combined with several advanced pre- and post-processing techniques. Based on the framework, we have been developing our in-house WCSPH-FSI package named SPHydro for solving hydrodynamic problems involving complex FSI processes in an accurate, efficient, and convenient manner. Three benchmarks are performed to qualitatively and quantitatively validate the accuracy and convergence of SPHydro. In addition, several practical applications are also provided to further highlight the generality and applicability of SPHydro in ocean engineering simulations. It is demonstrated that SPHydro holds satisfactory performance in solving complex FSI problems in ocean engineering and that the present framework can be further developed to tackle more complex FSI problems for general engineering applications due to its high flexibility and extensibility.

The bio-inspired propulsion facilitates the design of underwater vehicles because it benefits both the hydrodynamic performance and endurance of the underwater robots. This work is dedicated to investigating the fluid-structure interaction (FSI) of a three-dimensional (3D) self-propulsive anguilliform swimmer using the smoothed particle hydrodynamics (SPH) method. To this end, the δ + -SPH model incorporating with the techniques of tensile instability control (TIC) and adaptive particle refinement (APR) is adopted. Firstly, to validate the accuracy and stability of the present SPH model, viscous flows past 3D sphere are simulated and validated. After that, the 3D fish-liking swimming problem is simulated and the velocity of body center is compared with the reference result. Further, the comparison of the two-dimensional (2D) and 3D self-propulsive swimming problem shows that the longitudinal velocity and vorticity field are in large discrepancy. In addition, the vortex structure of the 3D fish’s wake is visualized and discussed in detail. It is demonstrated that the present 3D δ + -SPH model can be regarded as a reliable approach to investigate such bionic hydrodynamic problem close to a real fish.

This paper presents an improved smoothed particle hydrodynamics (SPH) model through a rigorous mathematical derivation based on the principle of virtual work, aiming at establishing a three-dimensional numerical wave tank overcoming excessive numerical dissipation that has been usually encountered in traditional SPH models in practical applications. In order to demonstrate the accuracy and convergence of the new scheme, the viscous damping of a standing wave is first investigated as a quantitative validation, with particular attention on emphasizing (1) its physical rationality with respect to energy conservation and (2) its ability to alleviate wave over-attenuation even using fewer neighbors compared with the traditional δ-SPH model. Subsequently, several fully three-dimensional engineering problems, with respect to water wave propagation and the interaction with structures, are investigated to demonstrate the effectiveness of the new scheme in alleviating wave over-attenuation. It is demonstrated that the present model can be performed with relatively few neighbors (i.e., higher computational efficiency) to obtain accurate and convergent numerical results for those SPH simulations involving long-term and long-distance water wave propagation.

针对电动汽车动力总成悬置系统(Powertrain Mounting System,PMS)参数可能被处理为不同类型概率变量的情形,提出了一种基于任意多项式混沌(Arbitrary Polynomial Chaos,APC)展开和最大熵原理(Maximum Entropy Principle,MEP)的电动汽车PMS固有特性不确定性分析方法.采用概率模型描述任意概率不确定情形下的PMS参数,通过APC展开获得任意概率不确定情形下PMS固有特性不确定性响应的前几阶统计矩,通过MEP拟合不确定性响应的概率密度函数(Probability Density Function,PDF)和累积分布函数(Cumulative Distribution Function,CDF)等信息,通过算例分析了5种概率不确定情形下的电动汽车PMS固有特性响应.分析结果表明,以蒙特卡洛法作为参考,所提出的方法可有效地分析不同概率不确定情形下的PMS固有特性响应,分析具有较高的计算精度和计算效率,能进一步获得响应满足设计要求的可靠度.

In recent years, forest fires and maritime accidents have occurred frequently, which have had a bad impact on human production and life. Thus, the development of seaplanes is an increasingly urgent demand. It is important to study the taxiing process of seaplanes for the development of seaplanes, which is a strong nonlinear fluid-structure interaction problem. In this paper, the Smoothed Particle Hydrodynamics (SPH) method based on the Lagrangian framework is utilized to simulate the taxiing process of seaplanes, and the SPH results are compared with those of the Finite Volume Method (FVM) based on the Eulerian method. The results show that the SPH method can not only give the same accuracy as the FVM but also have a strong ability to capture the splashing waves in the taxiing process, which is quite meaningful for the subsequent study of the effect of a splash on other parts of the seaplane.

采用无网格光滑粒子流体动力学(smooth particle hydrodynamics,SPH)方法,结合粒子体积自适应技术(volume adaptive scheme,VAS)构建高精度、高效率的新型轴对称SPH模型,实现水下爆炸冲击波和气泡运动模拟.在冲击波传播阶段,通过与经验公式及文献理论值对比,验证了该轴对称SPH模型的精度.针对气泡脉动模拟,选取典型的双气泡耦合问题,分析气泡形态和压力载荷的力学特性,讨论了两气泡之间的距离参数对气泡相互作用过程的影响.结果表明,该新型轴对称SPH模型可实现水下爆炸过程压力载荷和气泡形态演化的精确预报.