International Journal for Numerical Methods in Engineering最新文献

{"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":"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}

{"title":"Dynamic topology optimization considering the influence of the non-uniform temperature field","authors":"Li-hao Zhang,&nbsp;Jinze Li,&nbsp;Rui Zhao,&nbsp;Kaiping Yu","doi":"10.1002/nme.7594","DOIUrl":"https://doi.org/10.1002/nme.7594","url":null,"abstract":"<p>With the wide application of thermoelastic structures in industries such as the aerospace field, the problem of topology optimization of thermoelastic structures has become a very common and important research topic. It is well known that the thermal environment has a non-negligible influence on the dynamic performance of structures. However, few people consider the influence of the thermal environment on structural stiffness in thermoelastic dynamic topology optimization. In practical engineering applications, the influence of the environment on the structure performance should be considered to obtain the optimal structure. In this paper, we focus on the problem of dynamic topology optimization considering the effect of non-uniform temperature fields on structural stiffness. The influence of non-uniform temperature fields adds on structural stiffness to the topology optimization of thermoelastic dynamic for the first time, thereby comprehensively addressing its effects on structural stiffness in the context of dynamic topology optimization under harmonic vibration and transient load. The proposed method begins by computing the distribution of the non-uniform temperature field within the structure. Subsequently, thermal stresses in the structure are determined through the application of thermoelastic theory. The geometric stiffness matrix of the structure is then calculated using finite element theory. The dynamic topology optimization model, employing a variable density approach, is established in conjunction with the dynamic compliance design objective. Sensitivity analysis is conducted through the adjoint method, and the design variables are updated utilizing the method of moving asymptotes. Numerical examples are presented to validate the efficacy of the proposed method and obtain the influence of different factors on the optimization results. The results show that the dynamic compliance of the optimized structure increases with increasing heat flux. For the optimization under harmonic vibration, the optimization results obtained by different external excitation frequencies are significantly different. For transient optimization, the study discovers that the optimization present transient effect.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"125 24","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142707748","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":"DCEM: A deep complementary energy method for linear elasticity","authors":"Yizheng Wang,&nbsp;Jia Sun,&nbsp;Timon Rabczuk,&nbsp;Yinghua Liu","doi":"10.1002/nme.7585","DOIUrl":"10.1002/nme.7585","url":null,"abstract":"<p>In recent years, the rapid advancement of deep learning has significantly impacted various fields, particularly in solving partial differential equations (PDEs) in the realm of solid mechanics, benefiting greatly from the remarkable approximation capabilities of neural networks. In solving PDEs, physics-informed neural networks (PINNs) and the deep energy method (DEM) have garnered substantial attention. The principle of minimum potential energy and complementary energy are two important variational principles in solid mechanics. However, the well-known DEM is based on the principle of minimum potential energy, but it lacks the important form of minimum complementary energy. To bridge this gap, we propose the deep complementary energy method (DCEM) based on the principle of minimum complementary energy. The output function of DCEM is the stress function, which inherently satisfies the equilibrium equation. We present numerical results of classical linear elasticity using the Prandtl and Airy stress functions, and compare DCEM with existing PINNs and DEM algorithms when modeling representative mechanical problems. The results demonstrate that DCEM outperforms DEM in terms of stress accuracy and efficiency and has an advantage in dealing with complex displacement boundary conditions, which is supported by theoretical analyses and numerical simulations. We extend DCEM to DCEM-Plus (DCEM-P), adding terms that satisfy PDEs. Furthermore, we propose a deep complementary energy operator method (DCEM-O) by combining operator learning with physical equations. Initially, we train DCEM-O using high-fidelity numerical results and then incorporate complementary energy. DCEM-P and DCEM-O further enhance the accuracy and efficiency of DCEM.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"125 24","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142258238","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":"Featured Cover","authors":"Xueyan Hu,&nbsp;Zonghao Li,&nbsp;Ronghao Bao,&nbsp;Weiqiu Chen","doi":"10.1002/nme.7591","DOIUrl":"https://doi.org/10.1002/nme.7591","url":null,"abstract":"<p>The cover image is based on the article <i>Stabilized Time-Series Moving Morphable Components Method for Topology Optimization</i> by Xueyan Hu et al., https://doi.org/10.1002/nme.7562\u0000 \u0000 <figure>\u0000 <div><picture>\u0000 <source></source></picture><p></p>\u0000 </div>\u0000 </figure></p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"125 20","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7591","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142165261","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}