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A generalized Fourier transform by means of change of variables within multilinear approximation 在多元线性近似中采用变量变换的广义傅里叶变换
Q3 MECHANICS Pub Date : 2021-08-04 DOI: 10.1186/s40323-021-00202-8
Chevreuil, Mathilde, Slama, Myriam
The paper deals with approximations of periodic functions that play a significant role in harmonic analysis. The approach revisits the trigonometric polynomials, seen as combinations of functions, and proposes to extend the class of models of the combined functions to a wider class of functions. The key here is to use structured functions, that have low complexity, with suitable functional representation and adapted parametrizations for the approximation. Such representation enables to approximate multivariate functions with few eventually random samples. The new parametrization is determined automatically with a greedy procedure, and a low rank format is used for the approximation associated with each new parametrization. A supervised learning algorithm is used for the approximation of a function of multiple random variables in tree-based tensor format, here the particular Tensor Train format. Adaptive strategies using statistical error estimates are proposed for the selection of the underlying tensor bases and the ranks for the Tensor-Train format. The method is applied for the estimation of the wall pressure for a flow over a cylinder for a range of low to medium Reynolds numbers for which we observe two flow regimes: a laminar flow with periodic vortex shedding and a laminar boundary layer with a turbulent wake (sub-critic regime). The automatic re-parametrization enables here to take into account the specific periodic feature of the pressure.
本文讨论了在谐波分析中起重要作用的周期函数的近似。该方法重新审视了三角多项式,将其视为函数的组合,并提出将组合函数的模型类扩展到更广泛的函数类。这里的关键是使用结构化函数,它具有低复杂性,具有合适的函数表示和适合的参数化近似。这样的表示可以用很少的随机样本近似多元函数。通过贪心过程自动确定新的参数化,并使用低秩格式进行与每个新参数化相关的逼近。监督学习算法用于逼近树状张量格式的多个随机变量的函数,这里是特定的张量训练格式。提出了使用统计误差估计的自适应策略来选择底层张量基和张量-训练格式的秩。该方法用于估计在低至中等雷诺数范围内流过圆柱体的壁面压力,其中我们观察到两种流动形式:具有周期性涡脱落的层流和具有湍流尾迹的层流边界层(亚临界状态)。自动重新参数化使这里能够考虑到压力的特定周期性特征。
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引用次数: 0
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
Q3 MECHANICS 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
Q3 MECHANICS 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
Q3 MECHANICS 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
Q3 MECHANICS 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
Q3 MECHANICS 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
Q3 MECHANICS 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
Q3 MECHANICS 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
Q3 MECHANICS 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
Q3 MECHANICS 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
期刊
Advanced Modeling and Simulation in Engineering Sciences
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