International Journal for Numerical Methods in Engineering最新文献

{"title":"A novel 3D mixed finite element for flexoelectricity in piezoelectric materials","authors":"Prince Henry Serrao,&nbsp;Sergey Kozinov","doi":"10.1002/nme.7500","DOIUrl":"10.1002/nme.7500","url":null,"abstract":"<p>Flexoelectricity is the intrinsic length-scale dependent higher-order electromechanical response of all centro- and non-centro-symmetric dielectrics, including piezoelectrics. Direct flexoelectricity is defined as the appearance of an electric field due to induced strain gradients. The numerical modeling of flexoelectricity is largely carried out using mixed FE, which has its historical foundations in strain gradient theories. However, existing finite elements are either limited to 2D or have inherited numerical instabilities due to the known saddle-point structuring. The current work presents a numerically robust three-dimensional mixed FE for higher-order electromechanical applications without the use of stabilization or penalty parameters. After its verification, the new finite element is applied to the new problem of truncated semicone torsion, taking into account flexoelectricity in piezoelectric solids, and the original findings are reported. Current research reveals the complex interaction between first-order (piezoelectricity) and higher-order (flexoelectricity) electromechanical coupling.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7500","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141165704","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 strain-gradient mixed elements using shared degrees of freedom for the discretised fields","authors":"Stefanos-Aldo Papanicolopulos","doi":"10.1002/nme.7536","DOIUrl":"10.1002/nme.7536","url":null,"abstract":"<p>A displacement-only finite-element formulation of strain-gradient models requires elements with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {C}^1 $$</annotation>\u0000 </semantics></math> continuous interpolation. Mixed formulations have been proposed to allow the use of more common <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {C}^0 $$</annotation>\u0000 </semantics></math> element shape functions. These mixed formulations are based on the interpolation of two different fields, displacement and some kind of displacement gradient, with the relation between the two fields enforced using either Lagrange multipliers or penalty methods. All elements proposed in the literature for such formulations use a distinct set of degrees of freedom to discretise each field. In this work, we introduce for the first time shared degrees of freedom, that lead to a mixed formulation with a significantly better numerical performance. We describe how this novel mixed formulation can be derived, present individual elements implementing this, and discuss the significance of the results.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7536","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141104019","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":"An analysis of high order FEM and IGA for explicit dynamics: Mass lumping and immersed boundaries","authors":"Lars Radtke,&nbsp;Michele Torre,&nbsp;Thomas J.R. Hughes,&nbsp;Alexander Düster,&nbsp;Giancarlo Sangalli,&nbsp;Alessandro Reali","doi":"10.1002/nme.7499","DOIUrl":"10.1002/nme.7499","url":null,"abstract":"<div>\u0000 \u0000 <p>We investigate the behavior of different shape functions for the discretization of hyperbolic problems. In particular, we consider classical Lagrange polynomials and B-splines. The studies focus on the performance of the these functions as a spatial discretization approach combined with an explicit time marching scheme. In this regard, a major concern is the maximum eigenvalue that imposes restrictions on the critical time step size and suitable lumping techniques that yield a diagonal mass matrix. The accuracy of the discretization methods is assessed in an asymptotic manner in terms of the convergence of eigenvalues and eigenvectors. Further, the global accuracy is investigated in terms of the full spectrum. The results show that B-spline discretization with a consistent mass matrix are more accurate than those based on Lagrange shape functions, which holds true in the boundary-fitted as well as in the immersed setting. On the other hand, Lagrange shape functions are more robust with respect to standard lumping techniques, which cannot be directly applied for B-splines without loss of accuracy. In general, we observe that none of the standard lumping schemes yields optimal results for B-splines, even in the boundary-fitted setting. For the immersed setting, also Lagrange shape functions show a drop in accuracy which depends on the position of the boundary that cuts the element. Several remedies are considered in order to overcome these issues, including interpolatory B-spline bases as well as eigenvalue stabilization methods. While accuracy and stability can be improved using these remedies, we conclude from our study that it is still an open question, how to design a discretization method that achieves large critical time step sizes in combination with a diagonal mass matrix and high accuracy in the immersed setting. We note that these considerations primarily relate to linear structural dynamics applications, such as for example, structural acoustics. In nonlinear problems, such as automotive crash dynamics, other considerations predominate. An example of a one-dimensional elastic-plastic bar impacting a rigid wall is illustrative.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141124072","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":"Finite element modeling of viscoelastic liquid crystal elastomers","authors":"Ali El Hajj Chehade,&nbsp;Beijun Shen,&nbsp;Chris M. Yakacki,&nbsp;Thao D. Nguyen,&nbsp;Sanjay Govindjee","doi":"10.1002/nme.7510","DOIUrl":"10.1002/nme.7510","url":null,"abstract":"<p>Liquid crystal elastomers (LCEs) are elastomeric networks with anisotropic monomers that reorient in response to applied loads, and in particular, thermomechanical loads. LCE complex microstructures translate into complex behaviors, such as soft elasticity, rate-dependency, and hysteresis. In this work, we develop a three-dimensional finite element implementation for monodomain LCEs, with the material modeled as a finite deformation viscoelastic network with a viscous director. The formulation is designed so that the director field can be modeled as an internal variable. Unique to this class of materials is that their deformation response function depends on the full deformation gradient and not just the right-stretch tensor. This results in the material tangent losing its ‘usual’ symmetry properties. Accordingly, this makes the use of a first Piola–Kirchhoff finite element formulation advantageous. We utilize this framework to examine a number of nuances associated with the simulation and design of LCE based systems. In particular, we investigate in some detail the importance of a careful characterization of an LCE's initial director field. Via simulations of separate tension and compression experiments, we highlight the possibility of incorrect predictions when even small perturbations to initial conditions occur. The simulations are also used to illustrate the goodness of the model in replicating simple and complex experimental results, including the first-of-their-kind buckling-like column compression and thick-walled balloon inflation simulations.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7510","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141123471","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":"Simultaneous analysis of continuously embedded Reissner–Mindlin shells in 3D bulk domains","authors":"Michael Wolfgang Kaiser,&nbsp;Thomas-Peter Fries","doi":"10.1002/nme.7495","DOIUrl":"10.1002/nme.7495","url":null,"abstract":"<p>A mechanical model and numerical method for the <i>simultaneous</i> analysis of Reissner–Mindlin shells with geometries implied by a continuous set of level sets (isosurfaces) over some three-dimensional bulk domain is presented. A three-dimensional mesh in the bulk domain is used in a tailored FEM formulation where the elements are by no means conforming to the level sets representing the shape of the individual shells. However, the shell geometries are bounded by the intersection curves of the level sets with the boundary of the bulk domain so that the boundaries are meshed conformingly. This results in a method which was coined Bulk Trace FEM before. The simultaneously considered, continuously embedded shells may be useful in the structural design process or for the continuous reinforcement of bulk domains. Numerical results confirm higher-order convergence rates.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7495","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141062873","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":"An extended isogeometric collocation method for fracture analysis","authors":"Farshid Fathi,&nbsp;Jeremy E. Oakley,&nbsp;René de Borst","doi":"10.1002/nme.7507","DOIUrl":"10.1002/nme.7507","url":null,"abstract":"<p>A collocation method is developed for discrete fracture models in the context of the partition-of-unity method. Spline technologies used in isogeometric analysis (IGA) are exploited to provide a smooth inter-element transition of gradients, thus allowing to get rid of extra flux terms at element boundaries which are generated by Lagrange polynomials. Bézier extraction is utilised to formulate IGA commensurate with a standard finite element data-structure. The efficacy of the proposed approach is examined through different numerical examples and is compared with other discrete methods for fracture analysis. The proposed approach is competitive in terms of accuracy with the least computational cost, rendering it a suitable candidate for superseding available collocation approaches for fracture simulation. Moreover, the approach naturally assesses the possibility of physics informed neural networks for fracture simulation, to which collocation is central.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7507","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140974970","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 solution to the ill-conditioning of gradient-enhanced covariance matrices for Gaussian processes","authors":"André L. Marchildon,&nbsp;David W. Zingg","doi":"10.1002/nme.7498","DOIUrl":"10.1002/nme.7498","url":null,"abstract":"<p>Gaussian processes provide probabilistic surrogates for various applications including classification, uncertainty quantification, and optimization. Using a gradient-enhanced covariance matrix can be beneficial since it provides a more accurate surrogate relative to its gradient-free counterpart. An acute problem for Gaussian processes, particularly those that use gradients, is the ill-conditioning of their covariance matrices. Several methods have been developed to address this problem for gradient-enhanced Gaussian processes but they have various drawbacks such as limiting the data that can be used, imposing a minimum distance between evaluation points in the parameter space, or constraining the hyperparameters. In this paper a diagonal preconditioner is applied to the covariance matrix along with a modest nugget to ensure that the condition number of the covariance matrix is bounded, while avoiding the drawbacks listed above. The method can be applied with any twice-differentiable kernel and when there are noisy function and gradient evaluations. Optimization results for a gradient-enhanced Bayesian optimizer with the Gaussian kernel are compared with the use of the preconditioning method, a baseline method that constrains the hyperparameters, and a rescaling method that increases the distance between evaluation points. The Bayesian optimizer with the preconditioning method converges the optimality, that is, the <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>$$ {ell}_2 $$</annotation>\u0000 </semantics></math> norm of the gradient, an additional 5 to 9 orders of magnitude relative to when the baseline method is used and it does so in fewer iterations than with the rescaling method. The preconditioning method is available in the open source Python library GpGradPy, which can be found at https://github.com/marchildon/gpgradpy/tree/paper_precon.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140926471","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":"Multiscale enhanced non-uniform transformation field analysis","authors":"A. Mishra,&nbsp;P. Carrara,&nbsp;S. Marfia,&nbsp;E. Sacco,&nbsp;L. De Lorenzis","doi":"10.1002/nme.7501","DOIUrl":"10.1002/nme.7501","url":null,"abstract":"<p>Enhanced transformation field analysis (E-TFA), recently proposed for reduced-order modeling, is here formulated for and applied to multiscale analysis. The approach is able to reproduce a highly complex nonlinear macroscale behavior, resulting from a microstructure with cohesive interfaces embedded in an elasto-plastic bulk. E-TFA features a consistent tangent matrix in its solution procedure, which enables a straightforward definition of the upscaled tangent stiffness tensor. Numerical tests show that, compared to FE<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mo> </mo>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {}^2 $$</annotation>\u0000 </semantics></math>, the proposed approach yields accurate solutions at a lower computational cost.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7501","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140939001","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":"Identification of dominant subspaces for model reduction of structured parametric systems","authors":"Peter Benner,&nbsp;Pawan Goyal,&nbsp;Igor Pontes Duff","doi":"10.1002/nme.7496","DOIUrl":"10.1002/nme.7496","url":null,"abstract":"<p>In this paper, we discuss a novel model reduction framework for linear structured dynamical systems. The transfer functions of these systems are assumed to have a special structure, for example, coming from second-order linear systems or time-delay systems, and they may also have parameter dependencies. Firstly, we investigate the connection between classic interpolation-based model reduction methods with the reachability and observability subspaces of linear structured parametric systems. We show that if enough interpolation points are taken, the projection matrices of interpolation-based model reduction encode these subspaces. Consequently, we are able to identify the dominant reachable and observable subspaces of the underlying system. Based on this, we propose a new model reduction algorithm combining these features and leading to reduced-order systems. Furthermore, we discuss computational aspects of the approach and its applicability to a large-scale setting. We illustrate the efficiency of the proposed approach with several numerical large-scale benchmark examples.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7496","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140926614","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":"Real-time topology optimization via learnable mappings","authors":"Gabriel Garayalde,&nbsp;Matteo Torzoni,&nbsp;Matteo Bruggi,&nbsp;Alberto Corigliano","doi":"10.1002/nme.7502","DOIUrl":"10.1002/nme.7502","url":null,"abstract":"<p>In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering contexts. This work proposes a multi-stage machine learning strategy that aims to predict an optimal topology and the related stress fields of interest, either in 2D or 3D, without resorting to any iterative analysis and design process. The overall topology optimization is treated as regression task in a low-dimensional latent space, that encodes the variability of the target designs. First, a fully-connected model is employed to surrogate the functional link between the parametric input space characterizing the design problem and the latent space representation of the corresponding optimal topology. The decoder branch of an autoencoder is then exploited to reconstruct the desired optimal topology from its latent representation. The deep learning models are trained on a dataset generated through a standard method of topology optimization implementing the solid isotropic material with penalization, for varying boundary and loading conditions. The underlying hypothesis behind the proposed strategy is that optimal topologies share enough common patterns to be compressed into small latent space representations without significant information loss. Results relevant to a 2D Messerschmitt-Bölkow-Blohm beam and a 3D bridge case demonstrate the capabilities of the proposed framework to provide accurate optimal topology predictions in a fraction of a second.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140926610","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}