International Journal for Numerical Methods in Engineering最新文献

{"title":"An Electro-Elastic Coupling Model for Piezoelectric Composites Based on the Voronoi Cell Finite Element Method","authors":"Huan Li,&nbsp;Nan Yang,&nbsp;Ran Guo","doi":"10.1002/nme.7631","DOIUrl":"https://doi.org/10.1002/nme.7631","url":null,"abstract":"<div>\u0000 \u0000 <p>The Voronoi cell finite element method (VCFEM) has successfully characterized the linear elastic behavior of the composites. This study is dedicated to develop an electro-elastic coupling VCFEM model mimicking the fully-coupled electro-elastic behavior of piezoelectric composites. For fiber-reinforced piezoelectric composites considering interfacial cracks, the interface traction reciprocity, the interface charge density reciprocity on bonded interfaces and the interface traction-free, the interface charge density-free on debonded interfaces are comprised in the new assumed stress and electric displacement hybrid variational functional. The new variational functional is derived on the base of the element multifield energy functionals. Independent stress/electric displacement fields are respectively assumed within the two-phase material domain. Several numerical examples considering perfectly-bonded interface and partially cracked interface were used to demonstrate the accuracy of the proposed method by comparing the piezoelectric Voronoi element model results with those obtained by ABAQUS. Then this model is used to study the effect of several microscopic details, such as the property ratio of fiber to matrix, volume fraction, interfacial crack length and polarization direction on macroscopic equivalent physical and mechanical properties, as well as local stress/electric displacement fields. It is clear that the proposed model is suitable for analyzing piezoelectric composites containing many microstructures with bonded interface or debonded interface.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142861666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An Improved Spectral Element Differential Method in Solving Nonlinear Thermoelastic Coupling Problems With Discontinuous Interfaces","authors":"Jianning Zhao,&nbsp;Dong Wei,&nbsp;Yuxi Wang,&nbsp;Donghuan Liu","doi":"10.1002/nme.7645","DOIUrl":"https://doi.org/10.1002/nme.7645","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, the spectral element differential method (SEDM) is improved to solve the nonlinear thermoelastic coupling problems with interface thermal resistance and interface gap in composite structures. The utilization of both Lobatto and Chebyshev node sets in SEDM significantly enhances solution efficiency by replacing integration with direct differential. Moreover, for strongly nonlinear problems caused by thermal radiation, unknown terms are incorporated into the stiffness matrix, and the relaxation iteration technique is also employed, the convergence has been improved compared to traditional methods. Importantly, the element format of the SEDM for 3D problems with discontinuous interfaces is given specifically in this paper, and element-by-element loop assembly of stiffness matrices is realized. Numerical examples confirm the effectiveness of the present method in efficiently and accurately solving 2D and 3D problems with discontinuous interfaces. The present method not only achieves faster convergence than the traditional finite element method, but also attains higher accuracy with fewer degrees of freedom and shorter computational time. Compared to the spectral element method (SEM), the proposed method significantly reduces the computation time of the stiffness matrix. Furthermore, by employing the coupled SEM-SEDM approach, computational efficiency is enhanced while maintaining high precision in sensitive regions.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142861667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modelling the effect of point forces and moments in plate bending with hybrid-Trefftz stress elements","authors":"J. A. Teixeira de Freitas,&nbsp;C. Tiago,&nbsp;E. M. B. R. Pereira","doi":"10.1002/nme.7587","DOIUrl":"https://doi.org/10.1002/nme.7587","url":null,"abstract":"<p>The formulation of the hybrid-Trefftz stress element for plate bending is extended to the modelling of concentrated forces and moments, either as prescribed loads or as reactions at point supports. As the bending, torsion and shear fields are hypersingular, the flexibility matrix of the element involves the use of the finite part integration concept. In addition, it requires the confirmation of the positive-definiteness of the flexibility under gross shape distortion. The tests illustrate the modelling of applied concentrated forces and moments and also the combination of boundary layer and point reaction effects. The results obtained are validated using converged solutions obtained with a stress-based hybrid-mixed element (HMS) and a displacement-based mixed element (MITC).</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"125 24","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142707980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On some energy-based variational principles in non-dissipative magneto-mechanics using a vector potential approach","authors":"Philipp Gebhart,&nbsp;Thomas Wallmersperger","doi":"10.1002/nme.7593","DOIUrl":"https://doi.org/10.1002/nme.7593","url":null,"abstract":"<p>This contribution covers the variational-based modeling of non-dissipative magneto-mechanical systems using a vector potential approach and the thorough analysis and discussion of corresponding conforming finite element methods. Since the construction of divergence-free finite element spaces explicitly enforcing the Coulomb gauge poses some major challenges, we propose some primal and mixed variational principles that ensure well posedness of the problem and allow to seek the vector potential in unconstrained function spaces. The performance of these methods is assessed in two comparative benchmark studies. The focus of both studies lies on the accurate approximation of field quantities in systems with material discontinuities and re-entrant corners.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"125 24","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7593","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142707756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Constitutive description of snow at finite strains by the modified cam-clay model and an implicit gradient damage formulation","authors":"Ahmad Moeineddin,&nbsp;Jakob Platen,&nbsp;Michael Kaliske","doi":"10.1002/nme.7595","DOIUrl":"https://doi.org/10.1002/nme.7595","url":null,"abstract":"<p>Snow, characterized as a unique granular and low-density material, exhibits intricate behavior influenced by the proximity to its melting point and its three-phase composition. This composition entails a structured ice skeleton surrounded by voids filled with air and spread with liquid water. Mechanically, snow experiences dynamic transformations, including bonding/degradation between its grains, significant inelastic deformations, and a distinct rate sensitivity. Given snow's varied structures and mechanical strengths in natural settings, a comprehensive constitutive model is necessary. Our study introduces a pioneering formulation grounded on the modified Cam-Clay model, extended to finite strains. This formulation is further enriched by an implicit gradient damage modeling, creating a synergistic blend that offers a detailed representation of snow behavior. The versatility of the framework is emphasized through the careful calibration of damage parameters. Such calibration allows the model to adeptly capture the effects of diverse strain rates, particularly at high magnitudes, highlighting its adaptability in replicating snow's unique mechanical responses across various conditions. Upon calibration against established experimental benchmarks, the model demonstrates a suitable alignment with observed behavior, underscoring its potential as a comprehensive tool for understanding and modeling snow behavior with precision and depth.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"125 24","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7595","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142707757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Partial-differential-algebraic equations of nonlinear dynamics by physics-informed neural-network: (I) Operator splitting and framework assessment","authors":"Loc Vu-Quoc,&nbsp;Alexander Humer","doi":"10.1002/nme.7586","DOIUrl":"https://doi.org/10.1002/nme.7586","url":null,"abstract":"<p>Several forms for constructing novel physics-informed neural-networks (PINNs) for the solution of partial-differential-algebraic equations (PDAEs) based on derivative operator splitting are proposed, using the nonlinear Kirchhoff rod as a prototype for demonstration. The present work is a natural extension of our review paper (Vu-Quoc and Humer, <i>CMES-Comput Modeling Eng Sci</i>, 137(2):1069–1343, 2023) aiming at both experts and first-time learners of both deep learning and PINN frameworks, among which the open-source DeepXDE (DDE; <i>SIAM Rev</i>, 63(1):208–228, 2021) is likely the most well documented framework with many examples. Yet, we encountered some pathological problems (time shift, amplification, static solutions) and proposed novel methods to resolve them. Among these novel methods are the PDE forms, which evolve from the lower-level form with fewer unknown dependent variables (e.g., displacements, slope, finite extension) to higher-level form with more dependent variables (e.g., forces, moments, momenta), in addition to those from lower-level forms. Traditionally, the highest-level form, the balance-of-momenta form, is the starting point for (hand) deriving the lowest-level form through a tedious (and error prone) process of successive substitutions. The next step in a finite element method is to discretize the lowest-level form upon forming a weak form and linearization with appropriate interpolation functions, followed by their implementation in a code and testing. The time-consuming tedium in all of these steps could be bypassed by applying the proposed novel PINN directly to the highest-level form. We also developed a script based on JAX, the High Performance Array Computing library. For the axial motion of elastic bar, while our JAX script did not show the pathological problems of DDE-T (DDE with TensorFlow backend), it is slower than DDE-T. Moreover, that DDE-T itself being more efficient in higher-level form than in lower-level form makes working directly with higher-level form even more attractive in addition to the advantages mentioned further above. Since coming up with an appropriate learning-rate schedule for a good solution is more art than science, we systematically codified in detail our experience running optimization (network training) through a normalization/standardization of the network-training process so readers can reproduce our results.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"125 24","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7586","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142707688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A two-way coupling approach for simulating bouncing droplets","authors":"Hui Wang,&nbsp;Yuwei Xiao,&nbsp;Yankai Mao,&nbsp;Shiying Xiong,&nbsp;Xubo Yang,&nbsp;Bo Zhu","doi":"10.1002/nme.7592","DOIUrl":"https://doi.org/10.1002/nme.7592","url":null,"abstract":"<p>This article presents a two-way coupling approach to simulate bouncing droplet phenomena by incorporating the lubricated thin aerodynamic gap between fluid volumes. At the heart of our framework lies a cut-cell representation of the thin air film between colliding liquid fluid volumes. The air pressures within the thin film, modeled using a reduced fluid model based on the lubrication theory, are coupled with the volumetric liquid pressures by the gradient across the liquid–air interfaces and solved in a monolithic two-way coupling system. Our method can accurately solve liquid–liquid interaction with air films without adaptive grid refinements, enabling accurate simulation of many novel surface-tension-driven phenomena such as droplet collisions, bouncing droplets, and promenading pairs.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"125 24","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7592","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142707635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A mixed hexahedral solid-shell finite element with self-equilibrated isostatic assumed stresses for geometrically nonlinear problems","authors":"Francesco S. Liguori,&nbsp;Giovanni Zucco,&nbsp;Antonio Madeo","doi":"10.1002/nme.7596","DOIUrl":"https://doi.org/10.1002/nme.7596","url":null,"abstract":"<p>Mixed Finite Elements (FEs) with assumed stresses and displacements provide many advantages in analysing shell structures. They ensure good results for coarse meshes and provide an accurate representation of the stress field. The shell FEs within the family designated by the acronym Mixed Isostatic Self-equilibrated Stresses (MISS) have demonstrated high performance in linear and nonlinear problems thanks to a self-equilibrated stress assumption. This article extends the MISS family by introducing an eight nodes solid-shell FE for the analysis of geometrically nonlinear structures. The element, named MISS-4S, features 24 displacement variables and an isostatic stress representation ruled by 18 parameters. The displacement field is described only by translations, eliminating the need for complex finite rotation treatments in large displacements problems. A total Lagrangian formulation is adopted with the Green–Lagrange strain tensor and the second Piola–Kirchhoff stress tensor. The numerical results concerning popular shell obstacle courses prove the accuracy and robustness of the proposed formulation when using regular or distorted meshes and demonstrate the absence of any locking phenomena. Finally, convergences for pointwise and energy quantities show the superior performance of MISS-4S compared to other elements in the literature, highlighting that an isostatic and self-equilibrated stress representation, already used in shell models, also gives advantages for solid-shell FEs.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"125 24","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7596","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142707480","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Reinforcement topology optimization considering the dynamic instability","authors":"Sol Ji Han,&nbsp;Gil Ho Yoon","doi":"10.1002/nme.7600","DOIUrl":"https://doi.org/10.1002/nme.7600","url":null,"abstract":"<p>The present study develops a new topology optimization scheme considering the dynamic instability caused by the unsymmetrical properties of system. From a mathematical point of view, the left and right eigenvectors of asymmetric system are observed with the complex eigenvalues. With the dynamic instability, the magnitudes of structural responses are increasing with respect to time and this phenomenon causes many engineering issues. As the dynamic instability is one of the serious problems, the suppression is desired from an engineering point of view. To systematically reduce this dynamic instability, the present study develops a new topology optimization scheme for the reinforcement design. To overcome the numerical difficulties of the mode conversion and the highly nonlinear behavior, this research proposes the summation of the first several complex eigenvalues. To show the issues of the dynamic instability and the validity of the present approach, several topological reinforcement problems are solved.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142859961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hybrid TBETI domain decomposition for huge 2D scalar variational inequalities","authors":"Zdeněk Dostál,&nbsp;Marie Sadowská,&nbsp;David Horák,&nbsp;Jakub Kružík","doi":"10.1002/nme.7597","DOIUrl":"https://doi.org/10.1002/nme.7597","url":null,"abstract":"<p>The unpreconditioned H-TFETI-DP (hybrid total finite element tearing and interconnecting dual-primal) domain decomposition method introduced by Klawonn and Rheinbach turned out to be an effective solver for variational inequalities discretized by huge structured grids. The basic idea is to decompose the domain into non-overlapping subdomains, interconnect some adjacent subdomains into clusters on a primal level, and enforce the continuity of the solution across both the subdomain and cluster interfaces by Lagrange multipliers. After eliminating the primal variables, we get a reasonably conditioned quadratic programming (QP) problem with bound and equality constraints. Here, we first reduce the continuous problem to the subdomains' boundaries, then discretize it using the boundary element method, and finally interconnect the subdomains by the averages of adjacent edges. The resulting QP problem in multipliers with a small coarse grid is solved by specialized QP algorithms with optimal complexity. The method can be considered as a three-level multigrid with the coarse grids split between primal and dual variables. Numerical experiments illustrate the efficiency of the presented H-TBETI-DP (hybrid total boundary element tearing and interconnecting dual-primal) method and nice spectral properties of the discretized Steklov–Poincaré operators as compared with their finite element counterparts.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"125 24","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142707554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}