该杂志报道了计算工程和科学领域学术价值的原创性研究。它侧重于涉及和丰富力学、数学和数值方法应用的领域。它涵盖了新方法和具有计算挑战性的技术。涵盖的领域包括固体、流体力学和材料模拟中的方法开发，以及在医学生物力学和力学、多物理场、断裂力学、多尺度力学、粒子和无网格方法中的应用。此外，鼓励包括材料系统合成的模拟和方法开发的手稿。报告使用既定方法获得的结果的手稿，除非它们涉及具有挑战性的计算，并且不鼓励使用商业软件包报告计算的手稿。

The journal "Computational Mechanics" publishes original research of academic value in the field of computational engineering and science. It focuses on areas that involve and enrich the applications of mechanics, mathematics, and numerical methods. The journal covers the development of methods in solid and fluid mechanics, as well as material simulations, and applications in biomedical mechanics, multiphysics, fracture mechanics, multiscale mechanics, particle methods, and meshless methods. Additionally, it encourages manuscripts that simulate and develop methods for material system synthesis. Manuscripts reporting results obtained using established methods are discouraged unless they involve challenging computations, and the use of commercial software packages for reporting computations is not encouraged.

《Computational Mechanics》是一本专注于计算工程和科学领域原创性研究的学术期刊。该期刊强调力学、数学和数值方法应用的相关领域，涵盖新方法和具有计算挑战性的技术。涉及的领域包括固体力学、流体力学和材料模拟中的方法开发，以及在医学生物力学、多物理场、断裂力学、多尺度力学、粒子和无网格方法中的应用。此外，期刊鼓励提交关于材料系统合成的模拟和方法开发的手稿。对于使用既定方法获得的结果的手稿，除非涉及具有挑战性的计算，否则不予鼓励使用商业软件包进行计算的报告。

Computational Mechanics

Damjan Lolić

Dejan Zupan

Miha Brojan

A consistent strain-based beam element with quaternion representation of rotations

基于四元数旋转表示的一致应变梁单元

Physics Informed Neural Networks (PINNs) are shown to be a promising method for the approximation of partial differential equations (PDEs). PINNs approximate the PDE solution by minimizing physics-based loss functions over a given domain. Despite substantial progress in the application of PINNs to a range of problem classes, investigation of error estimation and convergence properties of PINNs, which is important for establishing the rationale behind their good empirical performance, has been lacking. This paper presents convergence analysis and error estimates of PINNs for a multi-physics problem of thermally coupled incompressible Navier-Stokes equations. Through a model problem of Beltrami flow it is shown that a small training error implies a small generalization error. Posteriori convergence rates of total error with respect to the training residual and collocation points are presented. This is of practical significance in determining appropriate number of training parameters and training residual thresholds to get good PINNs prediction of thermally coupled steady state laminar flows. These convergence rates are then generalized to different spatial geometries as well as to different flow parameters that lie in the laminar regime. A pressure stabilization term in the form of pressure Poisson equation is added to the PDE residuals for PINNs. This physics informed augmentation is shown to improve accuracy of the pressure field by an order of magnitude as compared to the case without augmentation. Results from PINNs are compared to the ones obtained from stabilized finite element method and good properties of PINNs are highlighted.

Shoaib Goraya

Nahil Sobh

Arif Masud

Computational mechanics

Comput Mech

Error estimates and physics informed augmentation of neural networks for thermally coupled incompressible Navier Stokes equations.

热耦合不可压缩Navier-Stokes方程的神经网络误差估计与物理信息增强

Qiming Zhu

Zeliang Liu

Jinhui Yan

Machine learning for metal additive manufacturing: predicting temperature and melt pool fluid dynamics using physics-informed neural networks

金属增材制造的机器学习：利用物理信息神经网络预测温度和熔池流体动力学

M. Ambati

T. Gerasimov

L. De Lorenzis

Phase-field modeling of ductile fracture

韧性断裂的相场模拟

Lin Shi

Jing Li

Pai Liu

Yixiao Zhu

Zhan Kang

A multi-step relay implementation of the successive iteration of analysis and design method for large-scale natural frequency-related topology optimization

大规模自然频率相关拓扑优化分析与设计方法的多步接力实现

Rodrigo Silva-Valenzuela

Alejandro Ortiz-Bernardin

Edoardo Artioli

A node-based uniform strain virtual element method for elastoplastic solids

基于节点的均匀应变虚拟单元法在弹塑性固体中的应用

Abstract This work presents a semi-analytical solution of the Reynolds equation under Gümbel conditions for hydrodynamic bearings in rotordynamic simulations. The algorithm is based on the SBFEM (scaled boundary finite element method) in combination with eigenvalue problem derivatives. The pressure field is discretized by standard finite elements along the circumferential coordinate, while an exact analytical formulation is used in the axial direction. This transforms the partial differential equation into a system of ordinary differential equations and leads to an eigenvalue problem. The computation of the continuously changing eigenvalues and eigenvectors is achieved by accurate Taylor approximations so that the repeated call of a numerically expensive eigensolver can be avoided. The algorithm is incorporated into a time integration scheme for the dynamic analysis of a simple system, consisting of a rotor with two degrees of freedom in a hydrodynamic bearing. Thereby, the method is verified, and its numerical efficiency is demonstrated. For a bearing with a slenderness ratio (length-to-diameter ratio) of 1, the computational time is reduced to $$8.8\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>8.8</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> compared to a standard FVM (finite volume method) solution.

Simon Pfeil

Hauke Gravenkamp

Elmar Woschke

Efficient simulation of hydrodynamic bearings using the SBFEM with eigenvalue problem derivatives

使用SBFEM及特征值问题导数的流体动压轴承高效仿真

Abstract We use backward error analysis for differential equations to obtain modified or distorted equations describing the behaviour of the Newmark scheme applied to the transient structural dynamics equation. Based on the newly derived distorted equations, we give expressions for the numerically or algorithmically distorted stiffness and damping matrices of a system simulated using the Newmark scheme. Using these results, we show how to construct compensation terms from the original parameters of the system, which improve the performance of Newmark simulations. The required compensation terms turn out to be slight modifications to the original system parameters (e.g. the damping or stiffness matrices), and can be applied without changing the time step or modifying the scheme itself. Two such compensations are given: one eliminates numerical damping, while the other achieves fourth-order accurate calculations using the traditionally second-order Newmark method. The performance of both compensation methods is evaluated numerically to demonstrate their validity, and they are compared to the uncompensated Newmark method, the generalized- $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> method and the 4th-order Runge–Kutta scheme.

Donát M. Takács

Tamás Fülöp

Improving the accuracy of the Newmark method through backward error analysis

通过后向误差分析提高Newmark方法的精度

Abstract We present the Space–Time Isogeometric Analysis (ST-IGA) of wind turbine rotor and tower aerodynamics, with the rotor geometry of the NREL 5MW offshore baseline wind turbine. The computation is with a given wind speed and a specified rotor speed. The computational challenges include accurate representation of the rotor geometry, multiscale nature of the unsteady flow, the fast, rotational relative motion between the rotor and tower, and the IGA mesh generation for the complex geometry. In addressing the computational challenges, the ST-IGA is used together with the ST Variational Multiscale (ST-VMS) method, which is a core computational method, and the ST Slip Interface (ST-SI) and Complex-Geometry IGA Mesh Generation (CGIMG) methods, which are complementary general-purpose methods. These are the methods of the ST Computational Flow Analysis in this case. The ST-discretization feature provides higher-order accuracy compared to standard discretization methods. The VMS feature addresses the computational challenges associated with the multiscale nature of the unsteady flow. The moving-mesh feature of the ST framework enables high-resolution computation near the blades. The ST-SI enables high-fidelity moving-mesh computations even over meshes made of patches with nonmatching meshes at the interfaces between those patches. The mesh covering the rotor rotates with it, and the SI between the rotating mesh and the rest of the mesh accurately connects the two sides of the solution. The ST-IGA, with IGA basis functions in space, enables more accurate representation of the rotor geometry and increased accuracy in the flow solution. With IGA basis functions in time, it enables more accurate representation of the rotor and mesh rotations. The CGIMG makes it easier in IGA mesh generation to deal with the complex geometry. The computation presented shows that the ST-IGA and the accompanying methods are successful in addressing the challenges and bringing high-fidelity computational analysis to wind turbine rotor and tower aerodynamics.

Yang Liu

Yuto Otoguro

Kenji Takizawa

Tayfun E. Tezduyar

Space–Time Isogeometric Analysis of NREL 5MW wind turbine rotor and tower aerodynamics

NREL 5MW风力涡轮机转子和塔架气动学的时空等几何分析

Abstract Phase transition in porous materials is relevant within different engineering applications, such as freezing in saturated soil or pancake sea ice. Mathematical descriptions of such processes can be derived based on Biot’s consolidation theory or the Theory of Porous Media. Depending on parameters such as density ratio, permeability or compressibility of the solid matrix, either small or finite deformations occur. Numerical solution procedures for the general, finite deformation case, suffers from instabilities and high computational costs. Simplifications, assuming small deformations, increases stability and computational efficiency. Within this work shortcomings of simplified theories based on Biot and linearisations of the Theory of Porous Media (TPM) are systematically studied. In order to determine the interaction of the different model parameters a non-dimensional model for poro-elasticity is presented. Based on a characteristic test-case including phase-transition and consolidation, the simplified models are compared to the fully non-linear TPM, focusing on mass errors as well as the time behaviour of the solution. Taking further into account the efficiency of discretisation based on different primal variables and finite-element-spaces, a guideline for selecting an appropriate combination of model, kinematic assumption and discretisation scheme is presented.

Maximilian Brodbeck

Marlon Suditsch

Seyed Morteza Seyedpour

Tim Ricken

Phase transition in porous materials: effects of material parameters and deformation regime on mass conservativity

多孔材料中的相变：材料参数和变形模式对质量守恒的影响

Abbreviation	Comput Mech
Journal Impact	3.65
Quartiles(Global)	MECHANICS(Q1)

ISSN	0178-7675, 1432-0924
h-index	121

Publication Information	Publisher: Springer Verlag，Publishing cycle: Monthly，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 1986，Proportion of original research papers: 99.24%，Self Citation Rate:8.10%， Gold OA Rate: 41.87%
Average review cycle	网友分享经验：偏慢,4-8周
Average recruitment ratio	网友分享经验：较易

Computational Mechanics

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