International Journal for Numerical Methods in Engineering最新文献

{"title":"An Enriched Equilibrium Finite Element Method for Crack Problems With Direct Access to Stress Intensity Factors and Strict Error Estimation","authors":"Qisheng Zheng,&nbsp;Jike Liu,&nbsp;Li Wang","doi":"10.1002/nme.70097","DOIUrl":"https://doi.org/10.1002/nme.70097","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper proposes an enriched equilibrium finite element method (EFEM) for addressing crack problems within the framework of linear elastic fracture mechanics and complementary energy principle. The key ingredient of enriched EFEM is to construct the equilibrated stress field using equilibrated tractions along with asymptotic enrichment. Specifically, an auxiliary field is employed to capture the asymptotic singular behavior of the near-tip stress field, while the traction-based equilibrium finite element accounts for the residual terms. The remarkable property of the proposed enriched EFEM is that the stress intensity factors (SIFs) and the stress fields are directly obtained with high accuracy, even on a very coarse mesh. Moreover, in combination with the compatible solution acquired by the enriched finite element method (FEM), strict estimation of the discretization error is obtained for crack problems by dual analysis. Numerical examples are finally conducted to verify the performance of the proposed method on strict error estimation and accurate computation of the SIFs.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 15","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144751670","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 the Influence of the Fiber Curvature on the Stiffness of Long Fiber Reinforced Composites","authors":"Celine Lauff,&nbsp;Maximilian Krause,&nbsp;Matti Schneider,&nbsp;Thomas Böhlke","doi":"10.1002/nme.70094","DOIUrl":"https://doi.org/10.1002/nme.70094","url":null,"abstract":"<p>The degree of curvature of fiber inclusions in fiber-reinforced composites impacts the elastic properties of the composite, but numerical studies of this effect are limited by the lack of efficient microstructure generators with fiber curvature control. We propose an extension to the fused Sequential Addition and Migration algorithm (<i>Int. J. Numer. Methods Eng.</i>, 125(22), e7573, 2024) to allow for the direct control of the average fiber curvature. To this end, we prescribe an averaged curvature parameter for the entire microstructure, while also constraining local curvature for every fiber to a maximum value. While local curvature is unambiguously defined, the choice of the averaged curvature parameter is not obvious. We introduce as a novel curvature measure the deviation from straight curve (DSC), which computes as the trace of the local second-order fiber orientation tensor's covariance for a single fiber. Averaging this over all fibers leads to a scalar averaged curvature parameter. Using this parameter, we define an optimization procedure for generating curved-fiber reinforced microstructures. We compare the microstructure generation capabilities of the proposed extension with the prior algorithm without curvature control and find that the extended algorithm is capable of realizing a significantly wider spectrum of curvatures. Finally, we study the influence of fiber curvature on elastic properties, and find that for an example composite of glass-fiber reinforced polypropylene, increased fiber curvature leads to a reduction of the Young's modulus by as much as 10%.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 15","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70094","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144751671","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":"Gradient-Based Weight Minimization of Nonlinear Truss Structures With Displacement, Stress, and Stability Constraints","authors":"Ahmed Manguri,&nbsp;Domenico Magisano,&nbsp;Robert Jankowski","doi":"10.1002/nme.70096","DOIUrl":"https://doi.org/10.1002/nme.70096","url":null,"abstract":"<p>This paper presents an effective and robust computational method of gradient-based methodology for weight minimization of geometrically nonlinear structures, considering 3D trusses as exemplary case study. The optimization framework can accommodate multiple different constraints: (i) bounds on the cross-sectional area of each design element, (ii) prescribed ranges for displacements and stresses, and (iii) nonlinear stability for geometries such as arches and domes. For large structures, this results in numerous optimization variables and constraints, including the highly nonlinear (ii) and (iii). Such constraints are evaluated consistently and simultaneously by combining path-following finite element analysis and null vector method. Typically, the gradient of the nonlinear structural response is approximated numerically, which is computationally intensive and can introduce inaccuracies deteriorating the optimization process. In contrast, this work derives a fully analytical gradient evaluation for nonlinear deformation, stress, and stability constraints. This is implemented directly within the finite element solver, enhancing robustness and computational efficiency of the optimization. Validation examples range from simple benchmarks to large structures.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 14","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70096","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144716693","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":"Product of Exponentials (POE) Splines on Lie-Groups: Limitations, Extensions, and Application to \u0000 \u0000 \u0000 S\u0000 O\u0000 (\u0000 3\u0000 )\u0000 \u0000 $$ SO(3) $$\u0000 and \u0000 \u0000 \u0000 S\u0000 E\u0000 (\u0000 3\u0000 )\u0000 \u0000 $$ SE(3) $$","authors":"Andreas Müller","doi":"10.1002/nme.70088","DOIUrl":"https://doi.org/10.1002/nme.70088","url":null,"abstract":"&lt;p&gt;Existing methods for constructing splines and Bézier curves on a Lie group &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ G $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; involve repeated products of exponentials deduced from local geodesics, w.r.t. a Riemannian metric, or rely on general polynomials. Moreover, each of these local curves is supposed to start at the identity of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ G $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Both assumptions may not reflect the actual curve to be interpolated. This paper pursues a different approach to construct splines on &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ G $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Local curves are expressed as solutions of the Poisson equation on &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ G $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Therewith, the local interpolations satisfies the boundary conditions while respecting the geometry of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ G $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. A &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mtext&gt;th&lt;/mtext&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ kmathrm{th} $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-order approximation of the solutions gives rise to a &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mtext&gt;th&lt;/mtext&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ kmathrm{th} $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-order product of exponential (POE) spline. Algorithms for constructing 3rd- and 4th-order splines are derived from closed form expressions for the approximate solutions. Additionally, spline algorithms are introduced that allow prescribing a vector field the curve must follow at the interpolation points. It is shown that the established algorithms, where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mtext&gt;th&lt;/mtext&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ kmathrm{th} $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-order POE-splines are constructed by concatenating local curves starting at the identity, cannot exactly reconstruct a","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 14","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70088","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144705347","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 Dynamic Implicit 3D Material Point-To-Rigid Body Contact Approach for Large Deformation Analysis","authors":"Robert E. Bird,&nbsp;Giuliano Pretti,&nbsp;William M. Coombs,&nbsp;Charles E. Augarde,&nbsp;Yaseen U. Sharif,&nbsp;Michael J. Brown,&nbsp;Gareth Carter,&nbsp;Catriona Macdonald,&nbsp;Kirstin Johnson","doi":"10.1002/nme.70080","DOIUrl":"https://doi.org/10.1002/nme.70080","url":null,"abstract":"<p>Accurate and robust modeling of large deformation three-dimensional contact interaction is an important area of engineering, but it is also challenging from a computational mechanics perspective. This is particularly the case when there is significant interpenetration and evolution of the contact surfaces, such as the case of a relatively rigid body interacting with a highly deformable body. This paper provides a new three-dimensional large deformation contact approach where the Material Point Method (MPM) is used to represent the deformable material. A new contact detection approach is introduced that checks the interaction of the vertices of the domains associated with each material point with the discretized rigid body. This provides a general and consistent approach without requiring the reconstruction of an additional boundary representation of the deformable body. A new energy-consistent material point domain updating approach is also introduced that maintains stable simulations under large deformations. The dynamic governing equations allow the trajectory of the rigid body to evolve based on the interaction with the deformable body, and the governing equations are solved within an efficient implicit framework. The performance of the new contact approach is demonstrated on a number of benchmark problems with analytical solutions. The method is also applied to the specific case of soil-structure interaction, using geotechnical centrifuge experimental data that confirms the veracity of the proposed approach.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 14","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70080","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144705409","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":"Optimization of the Initial Post-Buckling Response of Trusses and Frames by an Asymptotic Approach","authors":"Federico Ferrari,&nbsp;Ole Sigmund","doi":"10.1002/nme.70082","DOIUrl":"https://doi.org/10.1002/nme.70082","url":null,"abstract":"<p>Asymptotic post-buckling theory is applied to sizing and topology optimization of trusses and frames, exploring its potential and current computational difficulties. We show that the designs' post-buckling response can be controlled by including the lowest two asymptotic coefficients, representing the initial post-buckling slope and curvature, in the optimization formulation. This also reduces the imperfection sensitivity of the optimized design. The asymptotic expansion can further be used to approximate the structural nonlinear response, and then to optimize for a given measure of the nonlinear mechanical performance, such as, e.g., end-compliance or complementary work. Examples of linear and nonlinear compliance minimization of trusses and frames show the effective use of the asymptotic method for including post-buckling constraints in structural optimization.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 14","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70082","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144647384","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":"Nonlinear Synthesis of Compliant Mechanisms With Selective Compliance","authors":"Stephanie Seltmann,&nbsp;Alexander Hasse","doi":"10.1002/nme.70084","DOIUrl":"https://doi.org/10.1002/nme.70084","url":null,"abstract":"<p>The synthesis of compliant mechanisms (CMs) is frequently achieved through topology optimization. Many synthesis approaches simplify implementation by assuming small distortions, but this limits their practical application since CMs typically undergo large deformations that include geometric and material nonlinearities. CMs designed to generate a desired deformation path at the output points under specific loads are known as path-generating CMs. However, these CMs face significant challenges in topology optimization, resulting in the development of only a few optimization methods. Existing approaches often include only certain load cases in the optimization process. Consequently, if a CM designed this way encounters different load cases in practice, its path-generating behavior cannot be guaranteed. The authors have previously contributed to the development of an approach suitable for synthesizing load case-insensitive CMs. This paper extends that approach to account for nonlinearities, enabling the synthesis of path-generating CMs. The effectiveness of this extended approach is demonstrated through appropriate design examples. Additionally, the paper presents, for the first time, a shape-adaptive path-generating CM.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 14","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70084","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144647385","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":"Influences of Porosity Distribution and Size-Dependent on Bending, Buckling, and Free Vibration of Bi-Directional FG Porous Microbeams With Variable Thickness and MLSPs Using the MSGT and IGA","authors":"Saeed Mirzaei,&nbsp;Mehrdad Hejazi,&nbsp;Reza Ansari","doi":"10.1002/nme.70069","DOIUrl":"https://doi.org/10.1002/nme.70069","url":null,"abstract":"<div>\u0000 \u0000 <p>In this study, the bending, buckling, and free vibration analysis of bi-directional functionally graded porous microbeams with variable thickness are investigated. By utilizing the modified strain gradient theory (MSGT) in conjunction with a sinusoidal shear deformation theory, governing equations are derived using Hamilton's principle within the framework of the non-uniform rational B-spline (NURBS)-based isogeometric analysis (IGA). In addition, the C²-continuity requirement can be easily achieved by increasing the order of the NURBS basis functions. The MLSPs and the material properties of microbeams vary along with both thickness and axial directions based on the rule of mixture scheme. To consider the effects of porosity, two even and uneven distributions are considered. After verifying the accuracy of the presented approach, the influence of the aspect ratio, gradient indices, different boundary conditions, porosity parameters, variable MLSPs, and thickness on the bending, buckling, and free vibration characteristics of microbeams are investigated.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 14","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144635582","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":"Transformed Tensor Decomposition Method for Topology Optimization","authors":"Jiayi Hu,&nbsp;Weisheng Zhang,&nbsp;Shaoqiang Tang","doi":"10.1002/nme.70061","DOIUrl":"https://doi.org/10.1002/nme.70061","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we propose a transformed tensor decomposition method for topology optimization. A transform is performed on the density variable to manipulate its range. The transformed variable is then decomposed as the sum of a number of modes, each in a variable-separated form. In this way, the number of design variables in discrete form and the optimization time used in each iteration are considerably reduced. Numerical tests are performed to illustrate the nice features of the proposed method with evidence for solving the problems of checkerboard and mesh-dependency.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 14","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144615288","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":"Spline-Based Framework for Microscopic Contact Zone Modeling in Lubricated Orthogonal Cutting","authors":"Jaewook Lee,&nbsp;Jannis Saelzer,&nbsp;Jacques Zwar,&nbsp;Florian Zwicke,&nbsp;Felipe Gonzalez,&nbsp;Thomas Spenke,&nbsp;Norbert Hosters,&nbsp;Gero Polus,&nbsp;Andreas Zabel,&nbsp;Stefanie Elgeti","doi":"10.1002/nme.70087","DOIUrl":"https://doi.org/10.1002/nme.70087","url":null,"abstract":"<p>Accurately predicting the coefficient of friction between tool, chip, and workpiece during machining is essential for a reliable and cost-effective process. In this context, current numerical methods are often based on homogenized approaches with friction models that use constant friction coefficients; thus, failing to capture local effects. In addition, often neither the effect of lubricants nor the local tool and chip topographies is accounted for. Towards improving the state of the art in both respects, in this paper, we present a micro-scale friction model that can be coupled with a meso-scale chip formation model. The micro model determines a local friction coefficient based on local temperature, contact pressure, cutting speed, and lubricant wetting. It also incorporates the experimentally determined tool and chip topography. A key assumption of the model is that the main contribution to the friction coefficient is the interlocking of local roughness peaks. Our numerical implementation uses a combination of isogeometric analysis (IGA) for the chip and finite elements with spline-based boundaries for the fluid. This approach ensures a smooth, conformal interface between the cooling fluid and the chip, allowing for direct spatial coupling. Temporally, a Robin–Neumann coupling is used, which is critical for handling fully enclosed fluid pockets. The direct contact between the tool and the chip is modeled using a mortar knot-to-surface approach. To ensure computational affordability in this multi-query FE² scenario, a surrogate model for the micro-scale model is created using Gaussian process regression.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 14","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70087","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144615096","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}