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A novel physics-based and data-supported microstructure model for part-scale simulation of laser powder bed fusion of Ti-6Al-4V 基于物理和数据支持的Ti-6Al-4V激光粉末床熔合微观结构模型
Q1 Mathematics Pub Date : 2021-07-27 DOI: 10.1186/s40323-021-00201-9
J. Nitzler, C. Meier, K. W. Müller, W. Wall, N. Hodge
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引用次数: 1
A simple yet consistent constitutive law and mortar-based layer coupling schemes for thermomechanical macroscale simulations of metal additive manufacturing processes 一种简单而一致的本构定律和基于砂浆的层耦合方案,用于金属增材制造过程的热机械宏观模拟
Q1 Mathematics Pub Date : 2021-07-23 DOI: 10.1186/s40323-021-00209-1
Sebastian D. Proell, W. Wall, C. Meier
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引用次数: 10
Computational method for solving weakly singular Fredholm integral equations of the second kind using an advanced barycentric Lagrange interpolation formula 用改进的重心拉格朗日插值公式求解第二类弱奇异Fredholm积分方程的计算方法
Q1 Mathematics Pub Date : 2021-06-29 DOI: 10.21203/rs.3.rs-651030/v1
E. S. Shoukralla, Nermin Saber, A. Y. Sayed
In this study, we applied an advanced barycentric Lagrange interpolation formula to find the interpolate solutions of weakly singular Fredholm integral equations of the second kind. The kernel is interpolated twice concerning both variables and then is transformed into the product of five matrices; two of them are monomial basis matrices. To isolate the singularity of the kernel, we developed two techniques based on a good choice of different two sets of nodes to be distributed over the integration domain. Each set is specific to one of the kernel arguments so that the kernel values never become zero or imaginary. The significant advantage of thetwo presented techniques is the ability to gain access to an algebraic linear system equivalent to the interpolant solution without applying the collocation method. Moreover, the convergence in the mean of the interpolant solution and the maximum error norm estimation are studied. The interpolate solutions of the illustrated four examples are found strongly converging uniformly to the exact solutions.
在本研究中,我们应用一个先进的重心拉格朗日插值公式来寻找第二类弱奇异Fredholm积分方程的插值解。核在涉及两个变量的情况下被插值两次,然后被转换为五个矩阵的乘积;其中两个是单项基矩阵。为了隔离核的奇异性,我们开发了两种技术,这两种技术是基于对分布在积分域上的不同两组节点的良好选择。每个集合都特定于其中一个内核参数,因此内核值永远不会变为零或虚值。所提出的两种技术的显著优点是能够在不应用配置方法的情况下访问等价于插值解的代数线性系统。此外,还研究了插值解的均值收敛性和最大误差范数估计。发现所示四个例子的插值解强一致收敛于精确解。
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引用次数: 2
An SPH framework for fluid–solid and contact interaction problems including thermo-mechanical coupling and reversible phase transitions 流固和接触相互作用问题的SPH框架,包括热-机械耦合和可逆相变
Q1 Mathematics Pub Date : 2021-06-28 DOI: 10.1186/s40323-021-00200-w
Sebastian L. Fuchs, Christoph Meier, Wolfgang A. Wall, Christian J. Cyron
The present work proposes an approach for fluid–solid and contact interaction problems including thermo-mechanical coupling and reversible phase transitions. The solid field is assumed to consist of several arbitrarily-shaped, undeformable but mobile rigid bodies, that are evolved in time individually and allowed to get into mechanical contact with each other. The fluid field generally consists of multiple liquid or gas phases. All fields are spatially discretized using the method of smoothed particle hydrodynamics (SPH). This approach is especially suitable in the context of continually changing interface topologies and dynamic phase transitions without the need for additional methodological and computational effort for interface tracking as compared to mesh- or grid-based methods. Proposing a concept for the parallelization of the computational framework, in particular concerning a computationally efficient evaluation of rigid body motion, is an essential part of this work. Finally, the accuracy and robustness of the proposed framework is demonstrated by several numerical examples in two and three dimensions, involving multiple rigid bodies, two-phase flow, and reversible phase transitions, with a focus on two potential application scenarios in the fields of engineering and biomechanics: powder bed fusion additive manufacturing (PBFAM) and disintegration of food boluses in the human stomach. The efficiency of the parallel computational framework is demonstrated by a strong scaling analysis.
本工作提出了一种研究流固和接触相互作用问题的方法,包括热-机械耦合和可逆相变。假定固体场由几个任意形状、不可变形但可移动的刚体组成,这些刚体随时间单独演化,并允许彼此进行机械接触。流体场通常由多个液相或气相组成。采用光滑粒子流体力学(SPH)方法对所有场进行空间离散化。与基于网格或网格的方法相比,这种方法特别适用于不断变化的界面拓扑和动态相变,而不需要额外的方法和计算工作来进行界面跟踪。提出计算框架的并行化概念,特别是关于刚体运动的计算效率评估,是这项工作的重要组成部分。最后,通过二维和三维多刚体、两相流和可逆相变的数值实例证明了该框架的准确性和鲁棒性,并重点讨论了工程和生物力学领域的两种潜在应用场景:粉末床熔融增材制造(pbam)和食物丸在人胃中的分解。通过强尺度分析证明了并行计算框架的有效性。
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引用次数: 7
Non-intrusive nonlinear model reduction via machine learning approximations to low-dimensional operators 低维算子的机器学习近似非侵入非线性模型约简
Q1 Mathematics Pub Date : 2021-06-17 DOI: 10.1186/s40323-021-00213-5
Zhe Bai, Liqian Peng
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引用次数: 9
A semi-analytical coupled simulation approach for induction heating 感应加热半解析耦合模拟方法
Q1 Mathematics Pub Date : 2021-06-04 DOI: 10.1186/s40323-021-00199-0
Maialen Areitioaurtena, Unai Segurajauregi, Ville Akujärvi, Martin Fisk, Iker Urresti, Eneko Ukar
The numerical simulation of the induction heating process can be computationally expensive, especially if ferromagnetic materials are studied. There are several analytical models that describe the electromagnetic phenomena. However, these are very limited by the geometry of the coil and the workpiece. Thus, the usual method for computing more complex systems is to use the finite element method to solve the set of equations in the multiphysical system, but this easily becomes very time consuming. This paper deals with the problem of solving a coupled electromagnetic - thermal problem with higher computational efficiency. For this purpose, a semi-analytical modeling strategy is proposed, that is based on an initial finite element computation, followed by the use of analytical electromagnetic equations to solve the coupled electromagnetic-thermal problem. The usage of the simplified model is restricted to simple geometrical features such as flat or curved surfaces with great curvature to skin depth ratio. Numerical and experimental validation of the model show an average error between 0.9% and 4.1% in the prediction of the temperature evolution, reaching a greater accuracy than other analyzed commercial softwares. A 3D case of a double-row large size ball bearing is also presented, fully validating the proposed approach in terms of computational time and accuracy for complex industrial cases.
感应加热过程的数值模拟在计算上是非常昂贵的,特别是在研究铁磁性材料时。有几种描述电磁现象的分析模型。然而,这些是非常有限的几何线圈和工件。因此,计算更复杂系统的通常方法是使用有限元方法来求解多物理系统中的方程组,但这很容易变得非常耗时。本文研究了计算效率较高的电磁-热耦合问题的求解问题。为此,提出了一种半解析建模策略,即基于初始有限元计算,然后使用解析电磁方程来求解耦合的电磁-热问题。简化模型的使用仅限于曲率与蒙皮深度比大的平面或曲面等简单几何特征。数值和实验验证表明,该模型预测温度演变的平均误差在0.9% ~ 4.1%之间,比其他分析的商业软件具有更高的精度。最后给出了双列大尺寸滚珠轴承的三维算例,充分验证了该方法在计算时间和精度方面对复杂工业实例的适用性。
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引用次数: 10
Contact modeling from images using cut finite element solvers 使用切割有限元求解器从图像进行接触建模
Q1 Mathematics Pub Date : 2021-06-01 DOI: 10.1186/s40323-021-00197-2
F. Moshfeghifar, S. Darkner, K. Erleben, C. Wong
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引用次数: 9
Multivariate moment-matching for model order reduction of quadratic-bilinear systems using error bounds 基于误差界的二次双线性系统模型降阶的多变量矩匹配
Q1 Mathematics Pub Date : 2021-05-27 DOI: 10.1186/s40323-022-00236-6
Muhammad Altaf Khattak, M. I. Ahmad, Lihong Feng, P. Benner
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引用次数: 1
Numerical simulation of the experimental behavior of RC beams at elevated temperatures 高温下RC梁试验性能的数值模拟
Q1 Mathematics Pub Date : 2021-05-19 DOI: 10.1186/s40323-021-00198-1
C. Issa, R. Izadifard
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引用次数: 4
A multiscale model of terrain dynamics for real-time earthmoving simulation 用于实时土方模拟的多尺度地形动力学模型
Q1 Mathematics Pub Date : 2021-05-12 DOI: 10.1186/s40323-021-00196-3
Martin Servin, Tomas Berglund, Samuel Nystedt
A multiscale model for real-time simulation of terrain dynamics is explored. To represent the dynamics on different scales the model combines the description of soil as a continuous solid, as distinct particles and as rigid multibodies. The models are dynamically coupled to each other and to the earthmoving equipment. Agitated soil is represented by a hybrid of contacting particles and continuum solid, with the moving equipment and resting soil as geometric boundaries. Each zone of active soil is aggregated into distinct bodies, with the proper mass, momentum and frictional-cohesive properties, which constrain the equipment’s multibody dynamics. The particle model parameters are pre-calibrated to the bulk mechanical parameters for a wide range of different soils. The result is a computationally efficient model for earthmoving operations that resolve the motion of the soil, using a fast iterative solver, and provide realistic forces and dynamic for the equipment, using a direct solver for high numerical precision. Numerical simulations of excavation and bulldozing operations are performed to test the model and measure the computational performance. Reference data is produced using coupled discrete element and multibody dynamics simulations at relatively high resolution. The digging resistance and soil displacements with the real-time multiscale model agree with the reference model up to 10–25%, and run more than three orders of magnitude faster.
探讨了一种多尺度地形动力学实时仿真模型。为了表示不同尺度上的动力学,该模型将土壤描述为连续固体、不同颗粒和刚性多体。模型之间以及模型与土方设备之间是动态耦合的。搅拌土是一种接触颗粒和连续固体的混合体,以运动设备和静止土壤为几何边界。活跃土壤的每个区域都聚集成不同的体,具有适当的质量、动量和摩擦内聚性,这限制了设备的多体动力学。颗粒模型参数被预先校准为大范围不同土壤的体力学参数。结果是一个计算效率高的土方作业模型,它解决了土壤的运动,使用快速迭代求解器,并为设备提供了真实的力和动态,使用直接求解器,数值精度高。通过开挖和推土的数值模拟对模型进行了验证,并测量了模型的计算性能。参考数据的产生采用耦合离散元和多体动力学模拟在相对较高的分辨率。采用实时多尺度模型计算的开挖阻力和土体位移与参考模型的吻合度达到10 ~ 25%,运行速度提高3个数量级以上。
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引用次数: 11
期刊
Advanced Modeling and Simulation in Engineering Sciences
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