Article
Engineering, Multidisciplinary
Jianming Zhang, Chuanming Ju, Pihua Wen, Xiaomin Shu, Weicheng Lin, Baotao Chi
Summary: The recently proposed DiBFM has been successfully applied in solving various problems in two dimensions, with higher accuracy and computational efficiency compared to the traditional BEM. It is suitable for unifying conforming and nonconforming elements and approximating both continuous and discontinuous fields. The method has been extended to solve elasticity problems in three dimensions with detailed formulations, validated for accuracy and convergence rate through numerical examples.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Article
Mechanics
Suliman Khan, Rui He, Feroz Khan, M. Riaz Khan, Muhammad Arshad, Hasrat Hussain Shah
Summary: This paper introduces a new implementation of the dual reciprocity method in combination with the dual interpolation boundary face method for solving the Poisson equation. The method utilizes relationships between source nodes and virtual nodes for interpolation and boundary integration, showing superior performance for Poisson equations with various geometries.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2021)
Article
Engineering, Multidisciplinary
Le Yang, Jianming Zhang, Rui He, Weicheng Lin
Summary: This paper introduces a new numerical algorithm for solving the 2D transient heat conduction problem by combining the dual interpolation boundary face method with the precise integration method. The numerical algorithm has been successfully implemented and several numerical examples have been provided to illustrate its accuracy and stability compared to traditional methods.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Article
Engineering, Multidisciplinary
Fengxin Sun, Jufeng Wang, Qi Wei, Yong Wu
Summary: In this paper, an improved element-free Galerkin method (IEFGM) is proposed to solve two-dimensional elasticity problems. The IEFGM utilizes the dimension-splitting moving least squares (DS-MLS) method for constructing trial functions and the Galerkin variational weak form with integral coordinate transformation to obtain discrete equations for the elastic problems. The DS-MLS method, developed from dimensional splitting and moving least squares approximation, reduces the dimension and complexity of matrix operations, thus improving calculation efficiency. Several examples demonstrate the effectiveness of the improved meshless method in terms of reduced CPU time and higher accuracy solution compared to the EFG method.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Engineering, Multidisciplinary
Jianming Zhang, Pengfei Chai, Rui He, WeiCheng Lin, Chuangming Ju, Baotao Chi
Summary: In this paper, a dual interpolation boundary face method based on the Hermite-type moving-least-squares method is proposed for CAE analysis using discontinuous meshes. The method effectively avoids model repairing and simplification while ensuring a real automatic mesh division. The discontinuous meshes have strong geometric adaptability for arbitrarily complicated structures and provide the possibility for full-automatic CAE analysis.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2022)
Article
Mathematics, Applied
Eunjung Lee, Hyesun Na
Summary: The LL*-method is a least-squares finite element approach that solves a dual problem for approximation in partial differential equations. It has advantages for problems with low regularities and when L2-approximation is needed. However, piecewise polynomial approximation in LL* can generate artifacts such as spurious oscillations near shocks or discontinuities in the solution. This paper presents a stabilized LL*-method that aims to reduce these oscillations effectively. The consistency and error convergence of the proposed method are analyzed and numerical examinations are conducted.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Computer Science, Interdisciplinary Applications
Wenyuan Chen, Shufan Zou, Qingdong Cai, Yantao Yang
Summary: In this study, a new technique is proposed to improve the calculation of the volume force representing the body boundary based on the moving-least-squares immersed boundary method. The error between the desired volume force and the actual force given by the original method is theoretically analyzed for boundaries with simple geometry. A spatially uniform coefficient is introduced to correct the force, and it can be determined by the least-square method over all boundary markers. The new method shows promising results in reducing boundary velocity residual and can be combined with the iterative method for further improvement.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Engineering, Multidisciplinary
Pengfei Chai, Jianming Zhang, Rongxiong Xiao, Rui He, WeiCheng Lin
Summary: Based on the DiBFMHMLS method and the matrix condensation technique, this paper proposes a multi-domain method for solving 3D elasticity problems. This method accurately interpolates the boundary conditions in multi-domain models and has the potential for using a free mesh.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2022)
Article
Mathematics, Applied
Michael S. Floater
Summary: In this note, a solution is derived for the problem of finding a polynomial of degree at most $n$ that best approximates data at $n+2$ points in the $l_{p}$ norm. The solution can be expressed as a convex combination of Lagrange interpolants over subsets of $n+1$ points, and the error oscillates in sign.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2023)
Article
Engineering, Multidisciplinary
Sanpeng Zheng, Renzhong Feng, Aitong Huang
Summary: This paper proposes a new outlier detection and recovery method for data processing using the high accuracy of moving least squares quasi-interpolation scheme, its sensitivity to outliers, and the sparse distribution of outliers. The method constructs an l0-minimization problem with an inequality constraint and solves it efficiently using the classical orthogonal matching pursuit algorithm. The experiments demonstrate that the proposed method has high computational efficiency, very high detection accuracy, and high recovery accuracy for scattered data used for function approximation, making it practical.
APPLIED MATHEMATICAL MODELLING
(2023)
Article
Mathematics, Applied
Fleurianne Bertrand, Daniele Boffi
Summary: The study focuses on the approximation of the spectrum of least-squares operators in linear elasticity problems. By considering two different formulations and conducting numerical experiments, the theoretical results are confirmed.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Computer Science, Interdisciplinary Applications
Vahid Mohammadi, Mehdi Dehghan, Amirreza Khodadadian, Thomas Wick
Summary: This paper presents new numerical methods to solve the time-dependent transport equation in spherical coordinates, using generalized moving least squares and moving kriging least squares techniques. The methods are able to approximate the advection operator in spherical coordinates without singularities and do not rely on background mesh or triangulation. An implicit-explicit linear multistep method is used to discretize the time variable, resulting in a linear system of algebraic equations solved with the biconjugate gradient stabilized algorithm. Three test problems are solved to demonstrate the effectiveness of the methods.
ENGINEERING WITH COMPUTERS
(2021)
Article
Mathematics, Applied
Z. El Majouti, R. El Jid, A. Hajjaj
Summary: The article expands the three-dimensional modified moving least-square method for solving high-dimensional linear and nonlinear integral equations, without the need for mesh connectivity, with support size having a significant effect on maximum errors. The MMLS method with a non-singular moment matrix achieves better results than MLS approximation, and numerical experiments demonstrate the differences between the two methods for multidimensional problems.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
(2022)
Article
Mathematics, Applied
Rui Ding, Quan Shen, Yuan Yao
Summary: The translation discusses the use of the element-free Galerkin method for dynamic Signorini contact problems with friction in elastic materials, with Dirichlet boundary conditions and constrained conditions imposed using the penalty method. Error estimates indicate that the convergence order depends on various factors. The theoretical results are validated through numerical examples.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Computer Science, Interdisciplinary Applications
Ji Hee Kim, Naeun Choi, Seongmin Heo
Summary: This work proposes a novel iterative least squares method to approximate nonlinear functions using constrained least squares to ensure continuity. The method improves upon the existing continuous piecewise linear (CPWL) method by modifying the main steps and employing partitioned least squares and constrained least squares to reduce computational complexity. An iterative procedure with gradient descent using momentum is used for breakpoint updates to improve convergence characteristics.
COMPUTERS & CHEMICAL ENGINEERING
(2022)
Article
Mechanics
Alireza Enferadi, Majid Baniassadi, Mostafa Baghani
Summary: This study presents the design and analysis of an SMP microvalve, where the thermomechanical response of the SMP is investigated using a nonlinear constitutive model that incorporates hyperelasticity and viscoelasticity. The model accounts for fluid-solid interaction and heat transfer in both fluid and solid physics. Numerical simulations are carried out to examine the important characteristics of the SMP valve. The results demonstrate the significance of employing fluid-solid interaction conjugated heat transfer analysis for the efficient development of microvalves in diverse applications.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
Hridya P. Lal, B. R. Abhiram, Debraj Ghosh
Summary: Higher-order elasticity theories are used to model mechanics at the nanoscale, but the length-scale parameters in these theories need to be evaluated through experiments or MD simulations. This study shows that the length-scale parameter in the modified strain gradient theory varies with dimensions, boundary conditions, and deformation level for carbon and boron nitride nanotubes. To address this issue, a supervised ML-based framework is developed, combining MD simulations, continuum formulation, and ML to predict the length-scale parameter for a given material, dimension, and boundary condition. This predictive tool reduces the need for expensive MD simulations and opens up possibilities for applying non-classical continuum theories to nanoscale mechanics problems.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
Geng Chen, Shengzhen Xin, Lele Zhang, Min Chen, Christian Gebhardt
Summary: This paper develops a multiscale numerical approach to predict the failure probability of additive manufacturing (AM) structures subjected to time-varied loadings. The approach combines statistical homogenization, shakedown analyses, and reliability methods to consider the influence of microstructural features on load bearing capacity. Through case studies on exemplary structures and different material randomness assumptions, the robustness of the results is confirmed and the mechanism of how micropores influence structural reliability is explained.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
Guillaume Cadet, Manuel Paredes
Summary: This study proposes a comprehensive solution for calculating the stress field on the surface of a curved beam with a circular cross section, which is crucial for probabilistic fatigue life analysis.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
Hongshi Ruan, Xiaozhe Ju, Junjun Chen, Lihua Liang, Yangjian Xu
Summary: This paper proposes a data-driven approach to improve the efficiency of computational homogenization for nonlinear hyperelastic materials. By combining clustering analysis, Proper Orthogonal Decomposition (POD), and efficient sampling, a reduced order model is established to accurately predict elastoplasticity under monotonic loadings. The numerical results show a significant acceleration factor compared to a purely POD-based model, which greatly improves the applicability for structural analysis.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
Pep Espanol, Mark Thachuk, J. A. de la Torre
Summary: The motion of a rigid body, described by Euler's equations in Classical Mechanics, assumes that the distances between constituent particles are fixed. However, real bodies cannot meet this assumption due to thermal fluctuations. In order to incorporate dissipative and thermal fluctuation effects into the description, a generalization of Euler's equations is proposed. This theory explains the origin of these effects as internal, rather than caused by an external thermal bath, and derives the stochastic differential equations governing the body's orientation and central moments.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
Prateek Chandrakar, Narayan Sharma, Dipak Kumar Maiti
Summary: The current study focuses on the deterioration in thermal buckling performance of variable angle tow laminated (VATL) plates caused by damages in various composite and damage characteristics. Through numerical simulations and surrogate models, it was found that damages reduce the sensitivity of composite properties to buckling response, and a distinctive pattern of buckling response was observed when composite properties vary.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
Liangteng Guo, Shaoyu Zhao, Jie Yang, Sritawat Kitipornchai
Summary: This study introduces composites reinforced with graphene origami nanofillers into functionally graded multilayered phononic crystals. Numerical investigations reveal that these materials possess negative Poisson's ratio and offer unique mechanical properties, which can be tuned by adjusting the weight fraction and hydrogen coverage of the graphene fillers.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
Kai Li, Haiyang Wu, Yufeng Liu, Yuntong Dai, Yong Yu
Summary: This paper presents a novel self-oscillating liquid crystal elastomer fiber-beam system that can sway continuously and periodically under steady illumination. The governing equations of the system are established and the self-swaying process and motion mechanism are described in detail. Numerical results show the system undergoes supercritical Hopf bifurcation and the effects of system parameters on the self-swaying amplitude and frequency are discussed quantitatively.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
Lingkang Zhao, Peijun Wei, Yueqiu Li
Summary: This paper proposes a spatial-temporal fractional order model to study the dynamic behavior of thermoelastic nanoplates in a thermal environment. The model provides a flexible approach to describe the small-scale effects and complex history-dependent effects. Analytical and numerical methods verify the reliability of the model, and the effects of parameters on the dynamic response are discussed.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
A. N. O'Connor, P. G. Mongan, N. P. O'Dowd
Summary: This research presents an autonomous framework that combines Bayesian optimization and finite element analysis to identify ductile damage model parameters. The framework has been successfully applied to P91 material datasets and demonstrates the impact of algorithm hyperparameters on the resulting non-unique ductile damage parameters.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
S. V. Sorokin, S. Lenci
Summary: This paper reconsiders the nonlinear coupling between flexural and longitudinal vibrations of ideally straight elastic beams, using a nonlinear theory of curved beams and employing class-consistent boundary conditions. A paradoxical difference in the nonlinear parts of the Duffing equations obtained in the limit of vanishing curvature and in the case of an ideally straight beam is demonstrated and explained.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
C. Hari Manoj Simha
Summary: Dynamic Mode Decomposition (DMD) can be used to construct deformation fields for linear solids without making constitutive assumptions or knowing material properties. It operates on time-shifted data matrices and selects dominant modes using singular value decomposition. DMD can be used for reconstructing displacement states in elastic solids and identifying the onset of plasticity in elastic-plastic solids.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
C. Ren, K. F. Wang, B. L. Wang
Summary: An electromechanical model is established to investigate the characteristics of a bilayer structure consisting of a piezoelectric semiconductor film and an elastic substrate. The combined effects of piezoelectricity and flexoelectricity are considered, and closed-form expressions for the distributions of electron concentrations and relevant electromechanical fields are obtained. The effects of interfacial parameter, flexoelectricity, and initial carrier concentration are discussed. The research highlights the importance of the interfacial parameter and the weakening effect of flexoelectricity on the imperfect interface of the bilayer system.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
Yu Sun, Qiang Han, Chunlei Li
Summary: This paper presents the design of a tunable functionally graded metamaterial beam for flexural wave attenuation through the integration of a piezomagnetic shunt damping system and an inertial amplification mechanism. The proposed system demonstrates tunable and strong wave attenuation capability through local resonance and energy consumption. The theoretical and numerical results verify that the system can achieve significant wave attenuation at defined frequencies and also be optimized for maximal attenuation at various frequency ranges.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)