International Journal for Numerical Methods in Engineering最新文献

{"title":"Space-time stochastic Galerkin boundary elements for acoustic scattering problems","authors":"Heiko Gimperlein,&nbsp;Fabian Meyer,&nbsp;Ceyhun Özdemir","doi":"10.1002/nme.7497","DOIUrl":"10.1002/nme.7497","url":null,"abstract":"<p>Acoustic emission or scattering problems naturally involve uncertainties about the sound sources or boundary conditions. This article initiates the study of time domain boundary elements for such stochastic boundary problems for the acoustic wave equation. We present a space-time stochastic Galerkin boundary element method which is applied to sound-hard, sound-soft and absorbing scatterers. Uncertainties in both the sources and the boundary conditions are considered using a polynomial chaos expansion. The numerical experiments illustrate the performance and convergence of the proposed method in model problems and present an application to a problem from traffic noise.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"125 15","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7497","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140926616","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":"Axisymmetric virtual elements for problems of elasticity and plasticity","authors":"Louie L. Yaw","doi":"10.1002/nme.7493","DOIUrl":"10.1002/nme.7493","url":null,"abstract":"<p>The virtual element method (VEM) allows discretization of elasticity and plasticity problems with polygons in 2D and polyhedrals in 3D. The polygons (and polyhedrals) can have an arbitrary number of sides and can be concave or convex. These features, among others, are attractive for meshing complex geometries. However, to the author's knowledge axisymmetric virtual elements have not appeared before in the literature. Hence, in this work a novel first order consistent axisymmetric VEM is applied to problems of elasticity and plasticity. The VEM specific implementation details and adjustments needed to solve axisymmetric simulations are presented. Representative benchmark problems including pressure vessels and circular plates are illustrated. Examples also show that problems of near incompressibility are solved successfully. Consequently, this research demonstrates that the axisymmetric VEM formulation successfully solves certain classes of solid mechanics problems. The work concludes with a discussion of results for the current formulation and future research directions.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"125 15","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140942353","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 optimization of nonlinear differential game problems using orthogonal collocation with analytical sensitivities","authors":"Long Xiao,&nbsp;Miao Liu,&nbsp;Benyun Shi,&nbsp;Ping Liu,&nbsp;Xinggao Liu","doi":"10.1002/nme.7491","DOIUrl":"10.1002/nme.7491","url":null,"abstract":"<p>This article presents an effective computational method based on the orthogonal collocation on finite element for nonlinear pursuit-evasion differential game problems. The original problems are transformed into two dynamic optimization problems at first, so that the difficulty of obtaining the solution is reduced. To improve the convergence rate and the efficiency, the sensitivities describing the influence of control and interval parameters on state are derived through the discretized dynamic equations for the resulting nonlinear programming problem. The convergence speed is introduced to measure the performance in the upper level iteration. The main structure and the algorithm of the method are also given. Two demonstrative differential game problems with different scenarios from practice are studied. Compared with the approach without sensitivity information, the proposed method needs less function evaluations and saves at least 68.4% of the computational time. The research results show the effectiveness of proposed approach.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"125 15","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140926510","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":"Efficient global sensitivity analysis method for dynamic models in high dimensions","authors":"Luyi Li,&nbsp;Iason Papaioannou,&nbsp;Daniel Straub","doi":"10.1002/nme.7494","DOIUrl":"10.1002/nme.7494","url":null,"abstract":"<p>Dynamic models generating time-dependent model predictions are typically associated with high-dimensional input spaces and high-dimensional output spaces, in particular if time is discretized. It is computationally prohibitive to apply traditional global sensitivity analysis (SA) separately on each time output, as is common in the literature on multivariate SA. As an alternative, we propose a novel method for efficient global SA of dynamic models with high-dimensional inputs by combining a new polynomial chaos expansion (PCE)-driven partial least squares (PLS) algorithm with the analysis of variance. PLS is used to simultaneously reduce the dimensionality of the input and output variables spaces, by identifying the input and output latent variables that account for most of their joint variability. PCE is incorporated into the PLS algorithm to capture the non-linear behavior of the physical system. We derive the sensitivity indices associated with each output latent variable, based on which we propose generalized sensitivity indices that synthesize the influence of each input on the variance of entire output time series. All sensitivities can be computed analytically by post-processing the coefficients of the PLS-PCE representation. Hence, the computational cost of global SA for dynamic models essentially reduces to the cost for estimating these coefficients. We numerically compare the proposed method with existing methods by several dynamic models with high-dimensional inputs. The results show that the PLS-PCE method can obtain accurate sensitivity indices at low computational cost, even for models with strong interaction among the inputs.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"125 15","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140926602","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":"Stabilization-free virtual element method for 2D elastoplastic problems","authors":"Bing-Bing Xu,&nbsp;Yi-Fan Wang,&nbsp;Peter Wriggers","doi":"10.1002/nme.7490","DOIUrl":"10.1002/nme.7490","url":null,"abstract":"<p>In this paper, a novel first- and second-order stabilization-free virtual element method is proposed for two-dimensional elastoplastic problems. In contrast to traditional virtual element methods, the improved method does not require any stabilization, making the solution of nonlinear problems more reliable. The main idea is to modify the virtual element space to allow the computation of the higher-order <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {L}_2 $$</annotation>\u0000 </semantics></math> projection operator, ensuring that the strain and stress represent the element energy accurately. Considering the flexibility of the stabilization-free virtual element method, the elastoplastic mechanical problems can be solved by radial return methods known from the traditional finite element framework. <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>J</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {J}_2 $$</annotation>\u0000 </semantics></math> plasticity with hardening is considered for modeling the nonlinear response. Several numerical examples are provided to illustrate the capability and accuracy of the stabilization-free virtual element method.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"125 15","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7490","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140829023","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 first-order hyperbolic arbitrary Lagrangian Eulerian conservation formulation for non-linear solid dynamics","authors":"Thomas B. J. Di Giusto,&nbsp;Chun Hean Lee,&nbsp;Antonio J. Gil,&nbsp;Javier Bonet,&nbsp;Matteo Giacomini","doi":"10.1002/nme.7467","DOIUrl":"10.1002/nme.7467","url":null,"abstract":"<p>The paper introduces a computational framework using a novel Arbitrary Lagrangian Eulerian (ALE) formalism in the form of a system of first-order conservation laws. In addition to the usual material and spatial configurations, an additional referential (intrinsic) configuration is introduced in order to disassociate material particles from mesh positions. Using isothermal hyperelasticity as a starting point, mass, linear momentum and total energy conservation equations are written and solved with respect to the reference configuration. In addition, with the purpose of guaranteeing equal order of convergence of strains/stresses and velocities/displacements, the computation of the standard deformation gradient tensor (measured from material to spatial configuration) is obtained via its multiplicative decomposition into two auxiliary deformation gradient tensors, both computed via additional first-order conservation laws. Crucially, the new ALE conservative formulation will be shown to degenerate elegantly into alternative mixed systems of conservation laws such as Total Lagrangian, Eulerian and Updated Reference Lagrangian. Hyperbolicity of the system of conservation laws will be shown and the accurate wave speed bounds will be presented, the latter critical to ensure stability of explicit time integrators. For spatial discretisation, a vertex-based Finite Volume method is employed and suitably adapted. To guarantee stability from both the continuum and the semi-discretisation standpoints, an appropriate numerical interface flux (by means of the Rankine–Hugoniot jump conditions) is carefully designed and presented. Stability is demonstrated via the use of the time variation of the <i>Hamiltonian</i> of the system, seeking to ensure the positive production of numerical entropy. A range of three dimensional benchmark problems will be presented in order to demonstrate the robustness and reliability of the framework. Examples will be restricted to the case of isothermal reversible elasticity to demonstrate the potential of the new formulation.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"125 15","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7467","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140664617","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 response modelling of material systems using constrained Gaussian processes","authors":"Sumudu Herath,&nbsp;Souvik Chakraborty","doi":"10.1002/nme.7486","DOIUrl":"10.1002/nme.7486","url":null,"abstract":"<p>This article investigates the suitability of constrained Gaussian process regression in predicting nonlinear mechanical responses of material systems with notably reduced uncertainties. This study reinforces the conventional Gaussian processes with mechanics-informed prior knowledge observed in various kinematic responses. Stiffening and softening responses of material systems mostly demonstrate at least one of the boundedness, monotonicity and convexity conditions with respect to some kinematic variables. These relationships or impositions in turn are encoded into a constrained Gaussian process for prediction, uncertainty quantification and extrapolation. Using numerous examples and comparative studies, this article evidently proves that the use of constrained Gaussian processes is data-efficient, highly accurate, yields low uncertainties, recovers model overfitting and extrapolates very well compared to unconstrained or conventional Gaussian processes. Moreover, the usability of the proposed numerical method across various engineering modelling domains such as multiscale homogenisation, experimentation, structural optimisation, material constitutive modelling and structural idealisation is demonstrated.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"125 14","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140677539","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":"Plug-and-play adaptive surrogate modeling of parametric nonlinear dynamics in frequency domain","authors":"Phillip Huwiler,&nbsp;Davide Pradovera,&nbsp;Jürg Schiffmann","doi":"10.1002/nme.7487","DOIUrl":"10.1002/nme.7487","url":null,"abstract":"<p>We present an algorithm for constructing efficient surrogate frequency-domain models of (nonlinear) parametric dynamical systems in a <i>non-intrusive</i> way. To capture the dependence of the underlying system on frequency and parameters, our proposed approach combines rational approximation and smooth interpolation. In the approximation effort, locally adaptive sparse grids are applied to effectively explore the parameter domain even if the number of parameters is modest or high. Adaptivity is also employed to build rational approximations that efficiently capture the frequency dependence of the problem. These two features enable our method to build surrogate models that achieve a user-prescribed approximation accuracy, without wasting resources in “oversampling” the frequency and parameter domains. Thanks to its non-intrusiveness, our proposed method, as opposed to projection-based techniques for model order reduction, can be applied regardless of the complexity of the underlying physical model. Notably, our algorithm for adaptive sampling can be used even when prior knowledge of the problem structure is not available. To showcase the effectiveness of our approach, we apply it in the study of an aerodynamic bearing. Our method allows us to build surrogate models that adequately identify the bearing's behavior with respect to both design and operational parameters, while still achieving significant speedups.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"125 14","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7487","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140588553","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":"Reducing time and memory requirements in topology optimization of transient problems","authors":"M. J. B. Theulings,&nbsp;R. Maas,&nbsp;L. Noël,&nbsp;F. van Keulen,&nbsp;M. Langelaar","doi":"10.1002/nme.7461","DOIUrl":"10.1002/nme.7461","url":null,"abstract":"<p>In topology optimization of transient problems, memory requirements and computational costs often become prohibitively large due to the backward-in-time adjoint equations. Common approaches such as the Checkpointing (CP) and Local-in-Time (LT) algorithms reduce memory requirements by dividing the temporal domain into intervals and by computing sensitivities on one interval at a time. The CP algorithm reduces memory by recomputing state solutions instead of storing them. This leads to a significant increase in computational cost. The LT algorithm introduces approximations in the adjoint solution to reduce memory requirements and leads to a minimal increase in computational effort. However, we show that convergence can be hampered using the LT algorithm due to errors in approximate adjoints. To reduce memory and/or computational time, we present two novel algorithms. The hybrid Checkpointing/Local-in-Time (CP/LT) algorithm improves the convergence behavior of the LT algorithm at the cost of an increased computational time but remains more efficient than the CP algorithm. The Parallel-Local-in-Time (PLT) algorithm reduces the computational time through a temporal parallelization in which state and adjoint equations are solved simultaneously on multiple intervals. State and adjoint fields converge concurrently with the design. The effectiveness of each approach is illustrated with two-dimensional density-based topology optimization problems involving transient thermal or flow physics. Compared to the other discussed algorithms, we found a significant decrease in computational time for the PLT algorithm. Moreover, we show that under certain conditions, due to the use of approximations in the LT and PLT algorithms, they exhibit a bias toward designs with short characteristic times. Finally, based on the required memory reduction, computational cost, and convergence behavior of optimization problems, guidelines are provided for selecting the appropriate algorithms.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"125 14","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7461","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140588549","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":"Thermodynamically consistent numerical modeling of immiscible two-phase flow in poro-viscoelastic media","authors":"Jisheng Kou,&nbsp;Amgad Salama,&nbsp;Huangxin Chen,&nbsp;Shuyu Sun","doi":"10.1002/nme.7479","DOIUrl":"10.1002/nme.7479","url":null,"abstract":"<p>Numerical modeling of immiscible two-phase flow in deformable porous media has become increasingly significant due to its applications in oil reservoir engineering, geotechnical engineering and many others. The coupling between two-phase flow and geomechanics gives rise to a major challenge to the development of physically consistent mathematical models and effective numerical methods. In this article, based on the concept of free energies and guided by the second law of thermodynamics, we derive a thermodynamically consistent mathematical model for immiscible two-phase flow in poro-viscoelastic media. The model uses the fluid and solid free energies to characterize the fluid capillarity and solid skeleton elasticity, so that it rigorously follows an energy dissipation law. The thermodynamically consistent formulation of the pore fluid pressure is naturally derived for the solid mechanical equilibrium equation. Additionally, the model ensures the mass conservation law for both fluids and solids. For numerical approximation of the model, we propose an energy stable and mass conservative numerical method. The method herein inherits the energy dissipation law through appropriate energy approaches and subtle treatments for the coupling between two phase saturations, the effective pore pressure and porosity. Using the locally conservative cell-centered finite difference methods on staggered grids with the upwind strategies for saturations and porosity, we construct the fully discrete scheme, which has the ability to conserve the masses of both fluids and solids as well as preserve the energy dissipation law at the fully discrete level. In particular, the proposed method is an unbiased algorithm, that is, treating the wetting phase, the non-wetting phase and the solid phase in the same way. Numerical results are also given to validate and verify the features of the proposed model and numerical method.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"125 14","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140588804","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}