International Journal for Numerical Methods in Engineering最新文献

{"title":"Interface-Filtering Structural Optimization","authors":"Tianye Wang,&nbsp;Xiaoping Qian","doi":"10.1002/nme.7669","DOIUrl":"https://doi.org/10.1002/nme.7669","url":null,"abstract":"<p>In this paper, we present an interface-filtering structural optimization method that optimizes structural shape and topology through successive interface movements. This interface filtering is achieved via the combination of the variable-radius-based partial-differential-equation (PDE) filtering and the Heaviside projection on a density representation. In the proposed method, designs are represented by a density field with sharp interface and no internal grey features, and a filter radius field is used as the design variable in the optimization process. With this method, any density distribution with sharp interfaces can be used as initial designs, and sharp density contrast in density distribution is preserved throughout the optimization process. An analytical relation between the maximum movements of interfaces and the maximum filter radius is given, so that the interface movement can be controlled during the optimization process. Sensitivities with respect to filter radius variables are derived. Two numerical treatments, involving the density update scheme and the radius re-initialization scheme, are developed to achieve smooth successive shape updates and avoid artificial local minima. Numerical examples, including geometric deformation problem, structural compliance minimization, thermal compliance minimization, and negative Poisson ratio problem, are presented to demonstrate the capabilities of the proposed method.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7669","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143118416","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":"Volume and Mass Conservation in Lagrangian Meshfree Methods","authors":"Pratik Suchde,&nbsp;Christian Leithäuser,&nbsp;Jörg Kuhnert,&nbsp;Stéphane P. A. Bordas","doi":"10.1002/nme.7657","DOIUrl":"https://doi.org/10.1002/nme.7657","url":null,"abstract":"<p>Meshfree Lagrangian frameworks for free surface flow simulations do not conserve fluid volume. Meshfree particle methods like SPH are not mimetic, in the sense that discrete mass conservation does not imply discrete volume conservation. On the other hand, meshfree collocation methods typically do not use any notion of mass. As a result, they are neither mass conservative nor volume conservative at the discrete level. In this paper, we give an overview of various sources of conservation errors across different meshfree methods. The present work focuses on one specific issue: inconsistent volume and mass definitions. We introduce the concept of representative masses and densities, which are essential for accurate post-processing in meshfree collocation methods. Using these, we introduce an artificial compressibility in the fluid to reduce errors in volume conservation. Numerical experiments show that the introduced frameworks significantly improve volume conservation behaviour in meshfree collocation methods, even for complex industrial test cases such as automotive water crossing.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7657","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143118415","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":"Topology Optimization of Contact-Aided Thermo-Mechanical Regulators","authors":"Anna Dalklint,&nbsp;Joe Alexandersen,&nbsp;Andreas Henrik Frederiksen,&nbsp;Konstantinos Poulios,&nbsp;Ole Sigmund","doi":"10.1002/nme.7661","DOIUrl":"https://doi.org/10.1002/nme.7661","url":null,"abstract":"<p>Topology optimization is used to systematically design contact-aided thermo-mechanical regulators, i.e., components whose effective thermal conductivity is tunable by mechanical deformation and contact. The thermo-mechanical interactions are modeled using a fully coupled non-linear thermo-mechanical finite element framework. To obtain the intricate heat transfer response, the components leverage self-contact, which is modeled using a third medium contact method. The effective heat transfer properties of the regulators are tuned by solving a topology optimization problem using a traditional gradient-based algorithm. Several designs of thermo-mechanical regulators in the form of switches, diodes, and triodes are presented.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7661","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143118030","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 Computationally Efficient Technique for Dynamic Sensitivity Filtering in Topology Optimization","authors":"Hongbin Huang,&nbsp;Yiming Wang,&nbsp;Haoyin Wang,&nbsp;Bo Wu,&nbsp;Youmin Hu","doi":"10.1002/nme.7643","DOIUrl":"https://doi.org/10.1002/nme.7643","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we present a novel approach: a dynamic sensitivity filtering technique designed for density-based topology optimization. Sensitivity filtering methods have found extensive utility in mitigating numerical instabilities. Nevertheless, conventional sensitivity filtering can introduce numerous gray elements along the topology's boundaries, thereby impeding practical manufacturing within real-world engineering applications. To address this challenge, we propose a dynamic sensitivity filter that adjusts the sensitivity at each iterative step based on the optimization outcomes of the preceding iteration. Through diverse test examples, our method demonstrates the capacity to effectively solve the numerical instability problem while concurrently achieving a nearly pure black and white design, characterized by significantly reduced computational expense and improved structural stiffness.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143117701","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":"A Crack-Length Control Technique for Phase-Field Fracture in FFT Homogenization","authors":"Pedro Aranda,&nbsp;Javier Segurado","doi":"10.1002/nme.7664","DOIUrl":"https://doi.org/10.1002/nme.7664","url":null,"abstract":"<p>Modeling the propagation of cracks at the microscopic level is fundamental to understand the effect of the microstructure on the fracture process. Nevertheless, microscopic propagation is often unstable and when using phase-field fracture poor convergence is found or, in the case of using staggered algorithms, leads to the presence of <i>jumps</i> in the evolution of the cracks. In this work, a novel method is proposed to perform micromechanical simulations with phase-field fracture imposing monotonic increases of crack length and allowing the use of monolithic implementations, being able to resolve all the snap-backs during the unstable propagation phases. The method is derived for FFT-based solvers in order to exploit its very high numerical performance in micromechanical problems, but an equivalent method is also developed for Finite Elements (FE) showing the equivalence of both implementations. It is shown that the stress-strain curves and the crack paths obtained using the crack control method are superposed in stable propagation regimes to those obtained using strain control with a staggered scheme. J-integral calculations confirm that during the propagation process in the crack control method, the energy release rate remains constant and equal to an effective fracture energy that has been determined as a function of the concretization for FFT simulations. Finally, to show the potential of the method, the technique is applied to simulate crack propagation through the microstructure of composites and porous materials providing an estimation of the effective fracture toughness.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7664","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143117045","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 Generalized Single-Step Multi-Stage Time Integration Formulation and Novel Designs With Improved Stability and Accuracy","authors":"Yazhou Wang,&nbsp;Nikolaus A. Adams,&nbsp;Kumar K. Tamma","doi":"10.1002/nme.7658","DOIUrl":"https://doi.org/10.1002/nme.7658","url":null,"abstract":"<p>This paper focuses upon the single-step multi-stage time integration methods for second-order time-dependent systems. Firstly, a new and novel generalization of the Runge-Kutta (RK) and Runge-Kutta-Nyström (RKN) methods is proposed, featuring an advanced Butcher table for designing new and optimal algorithms. It encompasses not only the classical multi-stage methods as subsets, but also introduces novel designs with enhanced accuracy, stability, and numerical dissipation/dispersion properties. Secondly, to sharpen the focus on the present developments, several existing multi-stage explicit time integration methods (which are of interest and the focus of this paper) are revisited within the proposed unified mathematical framework, such that it highlights the differences, advantages, and disadvantages of various existing methods. Thirdly, the consistency analysis is rigorously demonstrated using both single-step and multi-step local truncation errors, addressing the order reduction problem observed in existing methods when applied to nonlinear dynamics problems. Finally, two sets of single-step, two-stage, third-order time-accurate schemes with controllable numerical dissipation/dispersion at the bifurcation point are presented. In contrast to existing methods, these newly proposed schemes preserve third-order time accuracy in nonlinear dynamics applications and exhibit improved stability in cases involving physical damping. Numerical examples are demonstrated to verify the theoretical analysis and the superior performance of the proposed schemes compared to existing methods.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7658","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143117039","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":"Scalar Auxiliary Variable (SAV) Stabilization of Implicit-Explicit (IMEX) Time Integration Schemes for Non-Linear Structural Dynamics","authors":"Sun-Beom Kwon,&nbsp;Arun Prakash","doi":"10.1002/nme.7660","DOIUrl":"https://doi.org/10.1002/nme.7660","url":null,"abstract":"<p>Implicit-explicit (IMEX) time integration schemes are well suited for non-linear structural dynamics because of their low computational cost and high accuracy. However, the stability of IMEX schemes cannot be guaranteed for general non-linear problems. In this article, we present a scalar auxiliary variable (SAV) stabilization of high-order IMEX time integration schemes that leads to unconditional stability. The proposed IMEX-BDF<i>k</i>-SAV schemes treat linear terms implicitly using <i>k</i>th-order backward difference formulas (BDF<i>k</i>) and non-linear terms explicitly. This eliminates the need for iterations in non-linear problems and leads to low computational costs. Truncation error analysis of the proposed IMEX-BDF<i>k</i>-SAV schemes confirms that up to <i>k</i>th-order accuracy can be achieved and this is verified through a series of convergence tests. Unlike existing SAV schemes for first-order ordinary differential equations (ODEs), we introduce a novel SAV for the proposed schemes that allows direct solution of the second-order ODEs without transforming them into a system of first-order ODEs. Finally, we demonstrate the performance of the proposed schemes by solving several non-linear problems in structural dynamics and show that the proposed schemes can achieve high accuracy at a low computational cost while maintaining unconditional stability.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7660","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143117047","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":"Global Length and Overhang Control for Level Set and Density Approaches via Perimeter Minimization","authors":"Jose Torres,&nbsp;Fermin Otero,&nbsp;Alex Ferrer","doi":"10.1002/nme.7662","DOIUrl":"https://doi.org/10.1002/nme.7662","url":null,"abstract":"<div>\u0000 \u0000 <p>Topology optimization is probably one of the most efficient techniques for structural design. However, running topology optimization without geometry control provides complex designs, which often are manufactured with additive manufacturing methods. Consequently, a fundamental aspect in topology optimization is to consider the following additive manufacturing constraints: minimal length scale and overhang. The aim of this paper is to propose a new numerical method to control globally such additive manufacturing constraints. The idea relies on penalizing a regularized version of the perimeter: an isotropic version for global length and an anisotropic version for overhang. Besides, we show that the method may be used with density and level set approaches. Several numerical examples, including compliant mechanisms and material design, show that some bars have been removed, decreasing the complexity of the shape, and vertical tendency orientation of boundaries is generally obtained.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143117044","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":"A Stable Mixed Finite Element Method for the Simulation of Stokes Flow Using Divergence Balanced H(Div)-L2 Pair of Approximation Spaces","authors":"Carlos H. C. Puga,&nbsp;Giovane Avancini,&nbsp;Nathan Shauer,&nbsp;Pablo G. S. Carvalho,&nbsp;Philippe R. B. Devloo","doi":"10.1002/nme.7629","DOIUrl":"https://doi.org/10.1002/nme.7629","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;The Stokes equations are used to model the motion of fluid flows where inertial terms can be neglected. Traditional finite element approaches such as the Taylor–Hood element do not ensure local conservation pointwise of the mass. This can be achieved by employing a mixed formulation with the proper combination of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mtext&gt;div&lt;/mtext&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ Hleft(operatorname{div}right) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {L}^2 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; spaces. In this context, this article presents a new hybrid-hybrid formulation to solve the Stokes equations. By applying Lagrange multipliers, the continuity of the tangential velocity is enforced, which is not intrinsically guaranteed by &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mtext&gt;div&lt;/mtext&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ Hleft(operatorname{div}right) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; spaces. In addition, a variation of the traditional &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mtext&gt;div&lt;/mtext&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ Hleft(operatorname{div}right) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; space, called Hdiv-C, is used to approximate the fields. The Hdiv-C space is created using concepts of the exact De Rham sequence and is shown to yield a smaller global system of equations than traditional finite element &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mtext&gt;div&lt;/mtext&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ Hleft(operatorname{div}right) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; spaces. A two-dimensional manufactured solution problem and the three-dimensional Annular-Couette flow problem are used to verify the hybrid-hybrid formulation's convergence rates, which are compared to Taylor–Hood's results. Application examples based on lab-on-chip mixers are analyzed to demonstrate the robustness of the proposed method. The examples consist of three different serpentine channel geometries: two in two dimensions (a sinusoidal","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143116628","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":"Explicit Topology Optimization Based on the Joint-Driven Moving Morphable Components","authors":"Jiaqi Xu,&nbsp;Chuhui He,&nbsp;Chang Liu,&nbsp;Xu Guo","doi":"10.1002/nme.7650","DOIUrl":"https://doi.org/10.1002/nme.7650","url":null,"abstract":"<div>\u0000 \u0000 <p>The moving morphable component (MMC) topology optimization method has garnered increasing attention recently due to its ability to provide explicit geometric parameters of optimized structures and seamless integration with CAD systems. However, the classical MMC method may encounter instability during the iterative process due to the excessively free movement of components and geometric defects caused by the incomplete fusion of components. This article proposes a novel joint-driven MMC (JMMC) method to address these issues. The core idea involves introducing a set of joint components to control and constrain the movement and deformation of the ordinary components. These ordinary components are interconnected through the joint components, guiding their movement and deformation within the design domain to facilitate structural layout changes, and the sizes of both ordinary and joint components can also be simultaneously optimized to alter the structural topology. Compared to the classical MMC method, the JMMC method retains the advantages of fewer design variables, explicit geometric information of structural boundaries, and seamless CAD integration while effectively mitigating iterative instability and avoiding the “dirty geometry” issues caused by incomplete component fusion. Numerical examples demonstrate the effectiveness and robustness of the proposed method.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143112785","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}