International Journal for Numerical Methods in Engineering最新文献

{"title":"An Evidence Theory Based Decision Method for the Variable Sensitivity of Multi-Output Systems","authors":"Yudong Fang,&nbsp;Jun Lu,&nbsp;Weijian Han","doi":"10.1002/nme.70125","DOIUrl":"https://doi.org/10.1002/nme.70125","url":null,"abstract":"<div>\u0000 \u0000 <p>Sensitivity analysis is commonly used to identify key parameters of a system and gain insight into the effect of variables on system outputs. For systems with multiple outputs, traditional sensitivity analysis methods are typically carried out for each system response individually. However, obtaining the importance of variables from the system-level view still needs objective decision support. To address this issue, this study proposes a multi-output system sensitivity decision-making method based on evidence theory. The proposed method first conducts surrogate model-based Sobol sensitivity analysis for each output of the system. Subsequently, the global sensitivity information for each output is used as evidence to construct a basic probability assignment, according to a rule defined for determining basic probability assignment. Finally, a synthesis rule is applied to calculate comprehensive sensitivity information. The effectiveness of the proposed method is demonstrated through validation with three numerical examples and one engineering case. This method provides more objective and rational decision support for sensitivity analysis of multi-output systems, offering significant potential benefits in parametric studies of complex systems.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 17","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145011959","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 Level Set Topology Optimization Theory Based on Hamilton's Principle","authors":"Jan Oellerich,&nbsp;Takayuki Yamada","doi":"10.1002/nme.70120","DOIUrl":"https://doi.org/10.1002/nme.70120","url":null,"abstract":"<p>In this article, we propose a unified variational framework for deriving the evolution equation of the level set function in topology optimization, departing from conventional Hamilton–Jacobi-based formulations. The key idea is the introduction of an auxiliary domain, geometrically identical to the physical design domain, occupied by fictitious matter which is dynamically excited by the conditions prevailing in the design domain. By assigning kinetic and potential energy to this matter and interpreting the level set function as the generalized coordinate to describe its deformation, the governing equation of motion is determined via Hamilton's principle, yielding a modified wave equation. Appropriate combinations of model parameters enable the recovery of classical physical behaviors, including the standard and biharmonic wave equations. The evolution problem is formulated in weak form using variational methods and implemented in the software environment FreeFEM++. The influence of the numerical parameters is analyzed on the example of minimum mean compliance. The results demonstrate that topological complexity and strut design can be effectively controlled by the respective parameters. Notably, the proposed formulation inherently supports the nucleation of new holes and maintains a well-defined level set function without requiring explicit re-initialization procedures, both of which emerge naturally from the physically motivated variational framework. The inclusion of a damping term further enhances numerical stability. To showcase the versatility and robustness of our method, we also apply it to compliant mechanism design and a bi-objective optimization problem involving self-weight and compliance minimization under local stress constraints.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 17","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70120","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144998763","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 Novel Quadratic Exponential B-Spline Based Explicit Time Integration Approach With Energy Corrector Technique for Transient Heat Conduction Analysis","authors":"Weibin Wen,&nbsp;Yongyu Hong,&nbsp;Kexuan Kang,&nbsp;Xin Ye,&nbsp;Pan Wang,&nbsp;Jun Liang","doi":"10.1002/nme.70117","DOIUrl":"https://doi.org/10.1002/nme.70117","url":null,"abstract":"<div>\u0000 \u0000 <p>This research proposes a novel single-step explicit time integration approach, which is formulated with a quadratic exponential B-spline interpolation function. To obtain enhanced solution accuracy, especially for problems with discontinuous load, the “energy corrector” technique is developed. Through theoretical analysis, four cases of algorithm parameters for the new approach are determined, which achieve high-order accuracy and desirable stability. Numerical simulation demonstrates that the new approach can provide highly precise solutions for transient heat conduction problems, especially for those with discontinuous loads. Furthermore, the new approach possesses a far larger critical stable time step than the traditional approaches, which in return improves computational efficiency greatly.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 17","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144998627","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":"Regularization in Structural Model Updating in the Presence of Noisy Data","authors":"Maria Girardi,&nbsp;Cristina Padovani,&nbsp;Daniele Pellegrini,&nbsp;Leonardo Robol","doi":"10.1002/nme.70113","DOIUrl":"https://doi.org/10.1002/nme.70113","url":null,"abstract":"<p>This article addresses the presence of noise when solving the inverse problem of determining the material properties of an elastic engineering structure from measured vibration data. After identifying the frequencies, material properties are determined by solving an optimization problem. However, if the experimental frequencies are affected by noise (as often happens in practice), this can lead to inaccuracy due to the ill-conditioning of the problem. A regularization strategy based on Tikhonov regularization is discussed, and an automatic regularization parameter choice is introduced to deal with cases where the noise level is not known beforehand. The algorithm is tested on three examples, including artificial models where the exact solution is known and a case study from the Matilde donjon in Livorno, with experimental data measured by seismic stations during ambient vibration tests. The proposed method consistently performs well across all tests, validating the reliability of the approach.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 17","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70113","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144935146","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 Cluster Mean Approach for Topology Optimization of Natural Frequencies and Bandgaps With Simple/Multiple Eigenfrequencies","authors":"Shiyao Sun,&nbsp;Kapil Khandelwal","doi":"10.1002/nme.70092","DOIUrl":"https://doi.org/10.1002/nme.70092","url":null,"abstract":"<p>This study presents a novel approach utilizing cluster means to address the non-differentiability issue arising from multiple eigenvalues in eigenfrequency and bandgap optimization. This study builds upon the method proposed by Zhang et al., extending it to eigenfrequency topology optimization using bound formulations. By constructing symmetric functions of repeated eigenvalues—including cluster mean, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 <annotation>$$ p $$</annotation>\u0000 </semantics></math>-norm and Kreisselmeier–Steinhauser (KS) functions—the study confirms their differentiability when all repeated eigenvalues are included, that is, clusters are complete. Numerical sensitivity analyses indicate that, under some symmetry conditions, multiple eigenvalues may also be differentiable with respect to the symmetric design variables. Notably, regardless of enforced symmetry, the cluster mean approach guarantees the differentiability of multiple eigenvalues, offering a reliable solution strategy in eigenfrequency optimization. Optimization schemes are proposed to maximize eigenfrequencies and bandgaps by integrating cluster means with the bound formulations. The efficacy of the proposed method is demonstrated through numerical examples of 2D and 3D solids and plate structures. All optimization results demonstrate smooth convergence under simple/multiple eigenvalues.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 17","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70092","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144990692","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":"Efficient XFEM/GFEM Approach for the Analysis of Thick Plates Utilizing Global Enrichments","authors":"Athanasios Zisimos,&nbsp;Ameer Marzok,&nbsp;Haim Waisman","doi":"10.1002/nme.70101","DOIUrl":"https://doi.org/10.1002/nme.70101","url":null,"abstract":"<div>\u0000 \u0000 <p>Plates are common flat structural elements that support loads through their flexural bending rigidity. Because plate thickness is much smaller than their surface dimensions, plate theories have emerged to simplify full three-dimensional behavior. Since analytical solutions for plate elements are not always available, especially for general loads and boundary conditions, numerical methods, such as the finite element method (FEM), are often employed to solve these problems. Due to its general polynomial approximation of the solution field, FEM often requires a large number of degrees of freedom to achieve convergence, increasing the computational burden. In this study, we propose a new approach for the analysis of plates utilizing the eXtended finite element method (XFEM) within the Mindlin-Reissner thick plate theory. As opposed to the traditional XFEM, where the enrichment functions are applied locally, mainly targeting strong and weak discontinuities in the domain, in the proposed approach, the entire domain is globally enriched with functions inspired by analytical solutions available for simple cases of plates. The objective of the current formulation is to reduce the computational burden by reducing the number of degrees of freedom in the problem compared to the standard FE configuration. The deformation of rectangular plates is studied for different boundary and loading conditions. The enrichment functions added to the FE shape functions are based on the series expansion resulting from the analytical solution of a simply supported plate under uniform pressure. However, those functions may not necessarily match the actual problem studied. To this end, higher series terms are employed to improve the accuracy and response of the plates. A convergence study is conducted to investigate the efficiency and robustness of the proposed method. The results show an improved convergence rate of the XFEM compared to the standard FEM approach.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 17","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144990693","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":"Parameter Identification for a Reduced Transport Model in Fusion Plasma","authors":"Louis Lamérand,&nbsp;Didier Auroux,&nbsp;Francesca Rapetti","doi":"10.1002/nme.70115","DOIUrl":"https://doi.org/10.1002/nme.70115","url":null,"abstract":"<div>\u0000 \u0000 <p>Two-dimensional transport codes for the simulation of tokamak plasmas are simplified versions of full 3D fluid models, where plasma turbulence is averaged out. One of the main challenges in such reduced models is to accurately reconstruct transverse transport fluxes that arise from the averaging of stresses due to fluctuations. These transverse fluxes are typically approximated by ad-hoc diffusion coefficients (turbulent eddy viscosity), manually adjusted to align numerical solutions with experimental observations. They can vary significantly depending on the type of tokamak, the experimental conditions, and even the location within the device, severely limiting the predictive capability of these codes for new configurations. To address this issue, we recently proposed an innovative approach to fusion plasma simulations by introducing two additional transport equations for turbulence-related variables (specifically, the turbulent kinetic energy <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>κ</mi>\u0000 </mrow>\u0000 <annotation>$$ kappa $$</annotation>\u0000 </semantics></math> and its dissipation rate <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ε</mi>\u0000 </mrow>\u0000 <annotation>$$ varepsilon $$</annotation>\u0000 </semantics></math>) into the mean-flow system to estimate the turbulent eddy viscosity. This approach also introduces new free parameters, but they are primarily governed by the underlying transport physics and thus exhibit considerably less variation across devices and plasma regions. In this article, we continue an ongoing study of data assimilation techniques to determine the free parameters of the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>κ</mi>\u0000 <mo>−</mo>\u0000 <mi>ε</mi>\u0000 </mrow>\u0000 <annotation>$$ kappa -varepsilon $$</annotation>\u0000 </semantics></math> model for transverse turbulent plasma transport. Based on digital twin experiments within the framework of equations averaged over the magnetic surfaces of the tokamak, we provide an in-depth study of optimization strategies to improve the performance of the calibration algorithm in a complex configuration with considerable scale variation of the parameters.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 17","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934844","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 Stabilized Finite Element Framework for Incompressible Hyperelastic Materials at Finite Strains: Analysis, Implementation, and Applications","authors":"Ujwal Warbhe","doi":"10.1002/nme.70121","DOIUrl":"https://doi.org/10.1002/nme.70121","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;This paper presents a stabilized finite element method (FEM) for incompressible hyperelastic materials at finite strains, addressing the computational and implementational challenges of traditional inf-sup-stable mixed FEMs. By augmenting the weak formulation with Galerkin/Least-Squares (GLS) stabilization terms, the method enables equal-order Lagrange elements (&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℙ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℙ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {mathbb{P}}_k/{mathbb{P}}_k $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;), eliminating the need for complex element pairings like Taylor–Hood (&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℙ&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;/msub&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℙ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {mathbb{P}}_2/{mathbb{P}}_1 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;). The stabilization parameter is defined as &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;τ&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;.&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;h&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;mrow&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ tau =0.1kern0.3em frac{h^2}{mu } $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; where &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;/mrow&gt;\u0000 &lt;annotation&gt;$$ h $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; denotes the finite-element mesh siz","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 17","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934845","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":"Fourth- and Higher-Order Finite Element Methods for the Incompressible Navier–Stokes Equations With Dirichlet Boundary Conditions","authors":"Yang Li,&nbsp;Heyu Wang,&nbsp;Qinghai Zhang","doi":"10.1002/nme.70102","DOIUrl":"https://doi.org/10.1002/nme.70102","url":null,"abstract":"<div>\u0000 \u0000 <p>Inspired by the unconstrained pressure Poisson equation (PPE) formulation [Liu, Liu, &amp; Pego, Comm. Pure Appl. Math. 60 (2007): 1443–1487], we previously proposed the generic projection and unconstrained PPE (GePUP) formulation [Zhang, J. Sci. Comput. 67 (2016): 1134–1180] for numerically solving the incompressible Navier–Stokes equations (INSE) with no-slip boundary conditions. In GePUP, the main evolutionary variable does not have to be solenoidal, with its divergence controlled by a heat equation. This work presents GePUP–FEM, high-order finite-element solvers for the INSE under the framework of the method-of-lines. Continuous Lagrange finite elements of equal order are utilized for the velocity and pressure finite element spaces to discretize the weak form of GePUP in space, while high-order implicit–explicit Runge–Kutta methods are then employed to treat the stiff diffusion term implicitly and the other terms explicitly. Due to the implicit treatment of the diffusion term, the time step size is only restricted by convection. The solver is efficient in that advancing the solution at each time step only involves solving a sequence of linear systems either on the velocity or on the pressure, with geometric multigrid methods. Furthermore, the solver is enhanced with adaptive mesh refinement (AMR) so that the multiple length scales and time scales in flows at moderate or high Reynolds numbers can be efficiently resolved. Numerical tests with various Reynolds numbers are performed for the single-vortex test, the lid-driven cavity, and the flow past a cylinder/sphere, demonstrating the high-order accuracy of GePUP–FEM both in time and in space and its capability of accurately and efficiently resolving the right physics. Moreover, GePUP–FEM offers the flexibility in choosing velocity and pressure finite element spaces and is free of the standard inf-sup condition.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 17","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934931","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 New Contact Algorithm for the Total-Lagrangian Material Point Method","authors":"Quang Hieu Bui,&nbsp;Vinh Phu Nguyen,&nbsp;Alban de Vaucorbeil","doi":"10.1002/nme.70105","DOIUrl":"https://doi.org/10.1002/nme.70105","url":null,"abstract":"<p>The Total Lagrangian Material Point Method (TLMPM) is a relatively new variant of the now popular MPM, a method to solve partial differential equations appearing in solid and fluid mechanics problems. In TLMPM, each solid has its own grid, and all calculations are carried out in a configuration of reference, often the original configuration. Because of this, TLMPM is free of numerical fracture, cell crossing instability and is efficient. An unfortunate result of having individual grids is that TLMPM does not have a built-in contact algorithm. Recently, a contact algorithm based on particle-to-particle contact was published for TLMPM. However, it scales quadratically with the number of particles and is therefore slow for a large number of particles. This paper introduces a new contact algorithm for TLMPM using a flexible contact grid. The advantages of this algorithm are: (1) all the advantages of TLMPM are kept, such as the absence of numerical fracture and good convergence rates; (2) the core principle of using a background grid in the material point method for contacts is preserved; (3) different basis functions can be used for each grid, and (4) boundary conditions can be enforced with more flexibility. The performance of the new algorithm is demonstrated through several two and three-dimensional numerical examples exhibiting large elastic and plastic deformation.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 17","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70105","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934927","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}