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Numerical Simulation of Fuzzy Volterra Integro-differential Equation using Improved Runge-Kutta Method 基于改进龙格-库塔法的模糊Volterra积分-微分方程数值模拟
Q4 Chemical Engineering Pub Date : 2021-11-09 DOI: 10.22055/JACM.2021.38381.3212
F. Rabiei, Fatin Abd Hamid, Mohammad Mehdi Rashidi, Zeeshan Ali, K. Shah, K. Hosseini, T. Khodadadi
In this research, fourth-order Improved Runge-Kutta method with three stages for solving fuzzy Volterra integro-differential (FVID) equations of the second kind under the concept of generalized Hukuhara differentiability is proposed. The advantage of the proposed method in this study compared with the same order classic Runge-Kutta method is, Improved Runge-Kutta (IRK) method uses a fewer number of stages in each step which causes less computational cost in total. Here, the integral part is approximated by applying the combination of Lagrange interpolation polynomials and Simpson’s rule. The numerical results are compared with some existing methods such as the fourth-order Runge-Kutta (RK) method, variational iteration method (VIM), and homotopy perturbation method (HPM) to prove the efficiency of IRK method. Based on the obtained results, it is clear that the fourth-order Improved Runge-Kutta method with higher accuracy and less number of stages which leads the less computational cost is more efficient than other existing methods for solving FVID equations.
在广义Hukuhara可微性的概念下,提出了求解第二类模糊Volterra积分微分方程的四阶改进三阶Runge-Kutta方法。与同阶的经典龙格-库塔方法相比,改进的龙格-库塔(IRK)方法的优点是每一步使用的阶段数更少,总体计算成本更低。在这里,积分部分用拉格朗日插值多项式和辛普森法则的组合来逼近。数值结果与现有的四阶龙格-库塔法(RK)、变分迭代法(VIM)和同伦摄动法(HPM)等方法进行了比较,证明了IRK方法的有效性。结果表明,四阶改进龙格-库塔法求解FVID方程的效率高于现有的求解FVID方程的方法,该方法具有精度高、阶数少、计算成本低的特点。
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引用次数: 2
Magneto Casson-Carreau Fluid Flow through a Circular Porous Cylinder with Partial Slip 磁流体在部分滑移多孔圆柱中的流动
Q4 Chemical Engineering Pub Date : 2021-11-08 DOI: 10.22055/JACM.2021.38390.3215
N. Nagendra, B. Venkateswarlu, Z. Boulahia, C. Amanulla, G. K. Ramesh
In the current study, a comparative analysis of two-dimensional heat transfer by the free convective flow of non-Newtonian Casson and Carreau fluid in electro-conductive polymer on the outside surface of a horizontal circular cylinder under slip and radial magnetic field effects is regarded. The Casson and Carreau fluid model formulation were first developed for the problem of the boundary layer of the horizontal circular cylinder and by using non-similarity transformations, the combined governing partial differential equations are translated into ordinary differential equations. The differential equations obtained are resolved by the Keller Box Method (KBM). The impact of the key parameters, the rate of heat transfer and skin friction is evaluated through graphs and tables. The result reveals that an increase in magnetic number decreases the velocity field of both Casson and Carreau fluid also Casson fluid is higher values when compared to Carreau fluid in variation of magnetic number.
本研究对比分析了滑移和径向磁场作用下导电聚合物中非牛顿卡森流体和卡罗流体在水平圆柱体外表面的自由对流换热。Casson和Carreau流体模型公式首先针对水平圆柱边界层问题提出,并通过非相似变换将组合的控制偏微分方程转化为常微分方程。得到的微分方程用凯勒盒法(KBM)求解。通过图形和表格评估了关键参数、传热速率和表面摩擦的影响。结果表明,随着磁数的增加,卡森流体和卡罗流体的速度场均减小,且卡森流体的磁数变化率高于卡罗流体。
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引用次数: 6
Calculation of Backscattered Ultrasonic Waves Field from a Copper-clad Steel Rod Immersing in Water and Effect of Clad Corrosion and Interfacial Disbond between Clad and Rod Defects on this Field using the Finite Element Method 用有限元法计算铜包钢棒在水中的后向散射超声波场及包层腐蚀和包层与棒间界面脱粘对该场的影响
Q4 Chemical Engineering Pub Date : 2021-11-04 DOI: 10.22055/JACM.2021.38098.3172
Omid Noormohammadi Arani, Mehdi Zeighami Salimabad, A. Yaghootian, M. Kari
Inspection and specificity of the intactness of multi-layer and small-size parts like copper-clad steel rod is a hard task and requires high accuracy. The intactness of these parts is crucial due to their importance. One of the inspection methods for these parts is using ultrasonic waves. The scattering phenomenon occurs when these waves impact curved shape bodies under a special condition. The ultrasonic scattering waves contain a lot of information from the physical conditions and mechanical properties of the part. However, using these waves requires high accuracy and attention due to their complexity. One result of the ultrasonic scattering waves is the far-field backscattered frequency spectrum, form function. For the first time in this research, the form function of a copper-clad steel rod that is immersed in water is calculated using the finite element method (FEM) available in the commercial ABAQUS software. For validating the proposed model, the simulation results are compared with analytical and experimental results in the normalized frequency range of 4 £ Ka £ 10. A good agreement is observed between the three methods at the resonance frequencies, and in the overall form of obtained form function. Furthermore, the effects of the two most common defects in these rods, i.e., the corrosion and interfacial disbond between the clad and steel rod, is studied. Results show that this method can properly specify the corrosion percentage and location, and also the length and location of the interfacial disbond defect.
铜包钢棒等多层小尺寸零件的完整性检测和鉴定是一项艰巨的任务,对精度要求很高。由于这些部件的重要性,它们的完整性至关重要。这些零件的检验方法之一是使用超声波。这些波在特殊条件下撞击弯曲体时,会产生散射现象。超声散射波包含了零件物理状况和力学性能的大量信息。然而,由于这些波的复杂性,使用它们需要很高的精度和注意力。超声散射波的一个结果是远场后向散射频谱,形式函数。本研究首次采用商用ABAQUS软件中的有限元法对浸在水中的铜包钢棒的形状函数进行了计算。为了验证所提出的模型,将仿真结果与归一化频率范围4 ~ 10的分析结果和实验结果进行了比较。三种方法在共振频率和得到的形式函数的总体形式上都有很好的一致性。此外,还研究了这些棒中最常见的两种缺陷的影响,即腐蚀和包层与钢棒之间的界面脱离。结果表明,该方法能较好地确定腐蚀的百分比和位置,以及界面脱离缺陷的长度和位置。
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引用次数: 1
Proportional Topology Optimization under Reliability-based Constraints 基于可靠性约束的比例拓扑优化
Q4 Chemical Engineering Pub Date : 2021-11-04 DOI: 10.22055/JACM.2021.38440.3226
R. R. Amaral, Julian Alves Borges, H. Gomes
Topology optimization is a methodology widely used in the design phase that has gained space in engineering. On the other hand, uncertainty is present in material properties, loads, and boundary conditions in practically any design. The main goal for this paper lies in the coupling of the two subjects to account for uncertainties in the topology optimization. The Proportional Topology Optimization method renders the possibility of treating the stress constraints in a unified way. This allows topologies that at the same time preserve structural reliability and optimize costs. The Proportional Topology Optimization method under the reliability constraint is presented for isostatic and hyperstatic beam examples with stress and displacement LSF.
拓扑优化是一种广泛应用于设计阶段的方法,在工程中获得了很大的发展空间。另一方面,在几乎任何设计中,材料特性、载荷和边界条件都存在不确定性。本文的主要目标在于将这两个主题耦合起来,以解释拓扑优化中的不确定性。比例拓扑优化方法为统一处理应力约束提供了可能。这使得拓扑结构可以同时保持结构可靠性和优化成本。针对具有应力和位移LSF的等静力和超静力梁实例,提出了可靠性约束下的比例拓扑优化方法。
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引用次数: 2
Mixed Convection Heat Transfer and Entropy Generation in a Water-Filled Square Cavity Partially Heated from Below: Effect of the Richardson and Prandtl numbers 部分从下加热的方形充水腔内的混合对流传热和熵生成:Richardson和Prandtl数的影响
Q4 Chemical Engineering Pub Date : 2021-10-17 DOI: 10.22055/JACM.2021.38614.3259
S. Boudebous, Nawal Ferroudj, H. Koten
In the present study, fluid flow, heat transfer, and entropy generation for mixed convection inside a water-filled square cavity were investigated numerically. The sidewalls of the cavity, which move upwards, are kept at low-temperature 𝑇𝑐 while only a part in the center of the bottom wall is kept at high-temperature 𝑇ℎ and the remaining parts are kept adiabatic. The governing equations, in stream function–vorticity form, are discretized and solved using the finite difference method. Particular attention was paid to the influence of the Prandtl numbers of 5.534, 3.045, and 2, corresponding respectively to the water temperatures of 303,15 K, 333,15 K, and 363,15 K. The numerical results are presented in the form of streamlines, isotherms, and entropy generation contours for different values of the Richardson numbers at an arbitrary Reynolds number Re=102. Besides this, the evolution of the average Nusselt number and the average entropy generation is also reported. The obtained results show interesting behaviors of the flow and thermal fields, which mainly involve stable symmetric and non-symmetric steady-state solutions, as well as unsteady regimes, depending on specific values of the Richardson and Prandtl numbers. It is additionally observed that the average Nusselt number increases and the average entropy generation decreases when both the Richardson and Prandtl numbers increase.
本文对充水方形腔内混合对流的流体流动、传热和熵产进行了数值模拟。向上移动的空腔侧壁保持低温𝑇𝑐,只有底部壁中心部分保持高温𝑇,其余部分保持绝热。对流函数涡量型控制方程进行离散化,并采用有限差分法进行求解。特别注意了分别对应于303、15 K、333、15 K和363,15 K水温的普朗特数5.534、3.045和2的影响。在任意雷诺数Re=102时,数值结果以流线、等温线和熵生成等高线的形式呈现。此外,还报道了平均努塞尔数和平均熵产的演变。得到的结果显示了流场和热场的有趣行为,主要涉及稳定对称和非对称稳态解,以及依赖于理查德森数和普朗特尔数特定值的非定常状态。当理查德森数和普朗特尔数增加时,平均努塞尔数增加,平均熵产减少。
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引用次数: 3
Investigation of Wood Properties at Elevated Temperature 高温下木材性能的研究
Q4 Chemical Engineering Pub Date : 2021-10-17 DOI: 10.22055/JACM.2021.38486.3239
A. Bragov, Tatiana Iuzhina, A. Lomunov, L. Igumnov, A. Belov, V. Eremeyev
The results of dynamic compression tests of aspen under elevated temperature up to +60°C are presented. The tests were carried out based on the Kolsky method using the split Hopkinson pressure bar. To study the anisotropy of properties, aspen samples were fabricated and tested by cutting along and across the fibers direction. Dynamic stress-strain curves were obtained as well as the average values of modulus of active loading sites. The greatest steepness of the loading branches and the highest breaking stresses are observed for the samples loaded along the fiber direction, while the smallest values are noted under loading across the fiber direction. Also the effect of elevated temperature on strength and deformation properties of aspen is estimated.
介绍了白杨在+60℃高温下的动态压缩试验结果。试验基于Kolsky法,采用分离式霍普金森压杆进行。为了研究其性能的各向异性,制备了杨木样品,并通过沿纤维方向和沿纤维方向切割进行了测试。得到了主动加载部位的动态应力-应变曲线和模量平均值。在沿纤维方向加载的试样中,观察到最大的陡峭度和最大的断裂应力,而在沿纤维方向加载的试样中,观察到最小的值。并分析了高温对杨木强度和变形性能的影响。
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引用次数: 2
Computational Enhancement of a Mixed 3D Beam Finite Element with Warping and Damage 具有翘曲和损伤的混合三维梁有限元的计算增强
Q4 Chemical Engineering Pub Date : 2021-10-16 DOI: 10.22055/JACM.2021.37948.3120
P. Re, D. Addessi
This paper describes the computational aspects of the beam Finite Element formulation recently developed by the authors to simulate the nonlinear response of structural members subjected to shear and torsion, accounting for cross-section warping. The paper focuses on an efficient consistent solution algorithm that by-passes the iterative procedure required in force-based and mixed Finite Elements and makes the model easy to be implemented in a standard code. Moreover, it proposes a new non-iterative technique to condense out the stress components derived by the three-dimensional constitutive response and not directly included in the fiber section formulation. The efficiency and accuracy of the proposed numerical model are validated by simulating the response of steel and reinforced concrete structural members.
本文描述了作者最近开发的梁有限元公式的计算方面,该公式用于模拟结构构件在剪切和扭转作用下的非线性响应,并考虑了截面翘曲。本文重点讨论了一种高效的一致解算法,该算法通过了基于力和混合有限元所需的迭代过程,使模型易于在标准代码中实现。此外,它提出了一种新的非迭代技术来浓缩由三维本构响应导出的、不直接包含在纤维截面公式中的应力分量。通过模拟钢和钢筋混凝土结构构件的响应,验证了所提出的数值模型的有效性和准确性。
{"title":"Computational Enhancement of a Mixed 3D Beam Finite Element with Warping and Damage","authors":"P. Re, D. Addessi","doi":"10.22055/JACM.2021.37948.3120","DOIUrl":"https://doi.org/10.22055/JACM.2021.37948.3120","url":null,"abstract":"This paper describes the computational aspects of the beam Finite Element formulation recently developed by the authors to simulate the nonlinear response of structural members subjected to shear and torsion, accounting for cross-section warping. The paper focuses on an efficient consistent solution algorithm that by-passes the iterative procedure required in force-based and mixed Finite Elements and makes the model easy to be implemented in a standard code. Moreover, it proposes a new non-iterative technique to condense out the stress components derived by the three-dimensional constitutive response and not directly included in the fiber section formulation. The efficiency and accuracy of the proposed numerical model are validated by simulating the response of steel and reinforced concrete structural members.","PeriodicalId":37801,"journal":{"name":"Applied and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44060125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Prediction Capabilities of a One-dimensional Wall-flow Particulate Filter Model 一维壁流颗粒过滤器模型的预测能力
Q4 Chemical Engineering Pub Date : 2021-10-15 DOI: 10.22055/JACM.2021.38708.3270
A. N. Impiombato, C. Biserni, M. Milani, L. Montorsi
This work is focused on the formulation of a numerical model for prediction of flow field inside a particulate filter. More specifically, a one-dimensional mathematical model of the gas flow in a particulate trap-cell is deduced and solved numerically. The results are given in terms of velocity, pressure, and filtration velocity. In addition, the dependence of the pressure drop on the main governing parameters has been investigated. More specifically, the permeability of the porous medium and the hydraulic diameter play a fundamental role in the pressure drop.
这项工作的重点是建立一个用于预测颗粒过滤器内部流场的数值模型。更具体地,推导并数值求解了颗粒捕集池中气体流动的一维数学模型。根据速度、压力和过滤速度给出了结果。此外,还研究了压降与主要调节参数的关系。更具体地说,多孔介质的渗透率和水力直径在压降中起着基本作用。
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引用次数: 0
Development of an Educational Code of Deriving Equations of Motion and Analyzing Dynamic Characteristics of Multibody Closed Chain Systems using GNU Octave for a Beginner 初学者用GNU八度曲推导运动方程及分析多体闭链系统动力学特性教学程序的开发
Q4 Chemical Engineering Pub Date : 2021-10-13 DOI: 10.22055/JACM.2021.38021.3132
Yonghui Park
In this study, an automatic GNU Octave code, a free high-level language, for the educational purposes was developed to derive equations of motion and constrain equations of a multibody closed chain system and to calculate the response of the system. The code for calculating the dynamic response was developed by formulating several equations in symbolic expression and extracting differential-algebraic equations in matrix form. The code has a similar structure to the previous code for the open chained system, but it deals with the constraint equation and different numerical integration. The examples of closed chain systems provide an additional procedure to derive the constraint equations by using Lagrangian multiplication theory and to solve the differential-algebraic equations using the Runge-Kutta method. The code was made to understand the theory of analysis and the structure of calculation easily. In addition, the code has an automatic process of the derivation of the Lagrange equation and the constraint equations in matrix form after inputting the number of symbolic information such as position and velocity coordinates and design variables of the system that the user wants to review. The code was validated by comparing the dynamic response of the four-bar linkage with the same design variables and initial conditions of the previous work. By using the code, the reader's ability to exchange information such as symbols and matrices will be expected to be improved.
在本研究中,开发了一种用于教育目的的自动GNU Octave代码,用于推导多体闭链系统的运动方程和约束方程,并计算系统的响应。通过建立若干符号表达式和提取矩阵形式的微分代数方程,编制了计算动力响应的程序。该代码与先前的开链系统代码结构相似,但处理了约束方程和不同的数值积分。闭链系统的例子为用拉格朗日乘法理论推导约束方程和用龙格-库塔法求解微分代数方程提供了一种新的方法。编写的代码便于理解分析理论和计算结构。此外,代码还具有在输入用户想要审阅的系统的位置、速度坐标、设计变量等符号信息的个数后,自动推导拉格朗日方程和矩阵形式的约束方程的过程。通过将四杆机构的动力响应与相同的设计变量和初始条件进行比较,验证了代码的有效性。通过使用这种代码,读者交换符号和矩阵等信息的能力有望得到提高。
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引用次数: 0
Magnetized Bi-convective Nanofluid Flow and Entropy Production Using Temperature-sensitive Base Fluid Properties: A Unique Approach 利用温度敏感基础流体特性的磁化双对流纳米流体流动和熵产生:一种独特的方法
Q4 Chemical Engineering Pub Date : 2021-10-05 DOI: 10.22055/JACM.2021.38204.3177
Tapas Barman, S. Roy, Ali J. Chamkha
The flow mechanism and entropy production of a bi-convective, magnetized, radiative nano-liquid flow for an inverted cone considering temperature-sensitive water properties is accomplished numerically. The functional nanomaterial comprises Copper, Alumina in the base liquid, water. The mathematical equations representing the system's physical characteristics are solved numerically by adopting a robust numerical approach for indulgencing non-similar solutions to understand numerous parameters' effect on temperature, velocity, salient gradients, and entropy production. The investigation summarizes that buoyancy force and injection heighten the velocity, and suction, particle percentage, radiation elevate the heat transfer. At the same time, the radiation and Brinkman number enhance the entropy generation. It is also detected from this investigation that the magnetic effect shows dual behaviour in entropy generation.
考虑温度敏感水的性质,用数值方法研究了双对流、磁化、辐射纳米液体在倒锥上的流动机理和熵产。该功能纳米材料由铜、氧化铝和水组成。代表系统物理特性的数学方程通过采用鲁棒的数值方法进行数值求解,以允许非相似解来理解众多参数对温度、速度、显著梯度和熵产生的影响。结果表明,浮力和喷注提高了速度,吸力、颗粒率、辐射提高了换热。同时,辐射和布林克曼数增强了熵的产生。本研究还发现,磁效应在熵的产生中表现出双重行为。
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引用次数: 0
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Applied and Computational Mechanics
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