Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"Uniform multiple laminates interpolation model and design method for double–double laminates based on multi-material topology optimization","authors":"Pingchu Fang ,&nbsp;Tong Gao ,&nbsp;Yongbin Huang ,&nbsp;Longlong Song ,&nbsp;Hongquan Liu ,&nbsp;Pierre Duysinx ,&nbsp;Weihong Zhang","doi":"10.1016/j.cma.2024.117492","DOIUrl":"10.1016/j.cma.2024.117492","url":null,"abstract":"<div><div>Double–Double (DD) laminates, incorporating a repetition of sub-plies featuring two groups of balanced angles, offer broad design flexibility together with the ease of design and manufacturing. In this work, a novel optimization design method is proposed for DD composite laminates based on multi-material topology optimization. First, the uniform multiple laminates interpolation (UMLI) model is proposed to describe the certainty of the stacking direction in multi-layer composite structures, inspired by the interpolation model in multi-material topology optimization. Specifically, the stiffness matrices of all alternative angle combinations of laminates are interpolated to form virtual laminates. The UMLI model eliminates the need for adding interlayer constraints during the optimization process. Then, the optimization problem is defined to minimize the compliance of the composite structures and is solved using the gradient-based optimization algorithm. Finally, the proposed method is applied to the design of the composite stiffened panel, the composite Unmanned Aerial Vehicle (UAV) wing, and the rear fuselage. The results demonstrate that the UMLI model and proposed optimization method have considerable potential in the angle optimization design of multi-layer structures.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117492"},"PeriodicalIF":6.9,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 geometrically exact thin-walled rod model with warping and stress-resultant-based plasticity obtained with a two-level computational approach","authors":"Marcos Pires Kassab ,&nbsp;Eduardo de Morais Barreto Campello ,&nbsp;Adnan Ibrahimbegovic","doi":"10.1016/j.cma.2024.117497","DOIUrl":"10.1016/j.cma.2024.117497","url":null,"abstract":"<div><div>In this work, we propose an two-level computational approach to enrich a seven degree-of-freedom kinematically exact rod model for thin-walled members, allowing for a simple elastoplastic-hardening constitutive equation. The novelty lies in upper-level description, where the effects of coupled elastoplastic-local geometrical instabilities are characterized in terms of cross-sectional stress resultants and generalized rod strains in a fully 3D context. Torsion-warping degrees of freedom and arbitrary (plastic) failure mode capabilities are present, allowing for the modeling of complex structural behavior in thin-walled members. The lower level is based on a kinematically exact shell or 3D-solid model with usual von Mises plasticity and linear isotropic hardening. At such level, simulations are performed in a pre-process stage, with the resulting equivalent stress-resultant-based hardening plastic parameters directly transferred to the upper-level as input data. No iterative procedure further binding the upper/lower level representations is required. This rather phenomenological approach of incorporating local effects may satisfactorily replicate the overall behavior of thin-walled members consisted of ductile materials, such as, but not only, steel or aluminum beam/column profiles. Numerical solution of the upper-level is carried in the framework of operator split, whereby, the local variables are solved in an element-wise fashion through numerical condensation, thus not adding any extra DOFs to the upper-level. The model is implemented in an in-house finite element program for the analysis of flexible thin structures and is validated against reference solutions.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117497"},"PeriodicalIF":6.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552279","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Surrogate construction via weight parameterization of residual neural networks","authors":"Oscar H. Diaz-Ibarra ,&nbsp;Khachik Sargsyan ,&nbsp;Habib N. Najm","doi":"10.1016/j.cma.2024.117468","DOIUrl":"10.1016/j.cma.2024.117468","url":null,"abstract":"<div><div>Surrogate model development is a critical step for uncertainty quantification or other sample-intensive tasks for complex computational models. In this work we develop a multi-output surrogate form using a class of neural networks (NNs) that employ shortcut connections, namely Residual NNs (ResNets). ResNets are known to regularize the surrogate learning problem and improve the efficiency and accuracy of the resulting surrogate. Inspired by the continuous, Neural ODE analogy, we augment ResNets with weight parameterization strategy with respect to ResNet depth. Weight-parameterized ResNets regularize the NN surrogate learning problem and allow better generalization with a drastically reduced number of learnable parameters. We demonstrate that weight-parameterized ResNets are more accurate and efficient than conventional feed-forward multi-layer perceptron networks. We also compare various options for parameterization of the weights as functions of ResNet depth. We demonstrate the results on both synthetic examples and a large scale earth system model of interest.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117468"},"PeriodicalIF":6.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142550561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements","authors":"Khemraj Shukla ,&nbsp;Zongren Zou ,&nbsp;Chi Hin Chan ,&nbsp;Additi Pandey ,&nbsp;Zhicheng Wang ,&nbsp;George Em Karniadakis","doi":"10.1016/j.cma.2024.117498","DOIUrl":"10.1016/j.cma.2024.117498","url":null,"abstract":"<div><div>Multiphysics problems that are characterized by complex interactions among fluid dynamics, heat transfer, structural mechanics, and electromagnetics, are inherently challenging due to their coupled nature. While experimental data on certain state variables may be available, integrating these data with numerical solvers remains a significant challenge. Physics-informed neural networks (PINNs) have shown promising results in various engineering disciplines, particularly in handling noisy data and solving inverse problems in partial differential equations (PDEs). However, their effectiveness in forecasting nonlinear phenomena in multiphysics regimes, particularly involving turbulence, is yet to be fully established. This study introduces NeuroSEM, a hybrid framework integrating PINNs with the high-fidelity Spectral Element Method (SEM) solver, Nektar++. NeuroSEM leverages the strengths of both PINNs and SEM, providing robust solutions for multiphysics problems. PINNs are trained to assimilate data and model physical phenomena in specific subdomains, which are then integrated into the Nektar++ solver. We demonstrate the efficiency and accuracy of NeuroSEM for thermal convection in cavity flow and flow past a cylinder. The framework effectively handles data assimilation by addressing those subdomains and state variables where the data is available. We applied NeuroSEM to the Rayleigh–Bénard convection system, including cases with missing thermal boundary conditions and noisy datasets. Finally, we applied the proposed NeuroSEM framework to real particle image velocimetry (PIV) data to capture flow patterns characterized by horseshoe vortical structures. Our results indicate that NeuroSEM accurately models the physical phenomena and assimilates the data within the specified subdomains. The framework’s plug-and-play nature facilitates its extension to other multiphysics or multiscale problems. Furthermore, NeuroSEM is optimized for efficient execution on emerging integrated GPU–CPU architectures. This hybrid approach enhances the accuracy and efficiency of simulations, making it a powerful tool for tackling complex engineering challenges in various scientific domains.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117498"},"PeriodicalIF":6.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 dual experimental/computational data-driven approach for random field modeling based strength estimation analysis of composite structures","authors":"S. Sakata ,&nbsp;G. Stefanou ,&nbsp;Y. Arai ,&nbsp;K. Shirahama ,&nbsp;P. Gavallas ,&nbsp;S. Iwama ,&nbsp;R. Takashima ,&nbsp;S. Ono","doi":"10.1016/j.cma.2024.117476","DOIUrl":"10.1016/j.cma.2024.117476","url":null,"abstract":"<div><div>This paper proposes a dual experimental/computational data-driven analysis framework for apparent strength estimation of composite structures consisting of randomly arranged unidirectional fiber-reinforced plastics. In the proposed framework, multiscale stochastic analysis is performed with random field modeling of local apparent quantities such as apparent elastic modulus or strength. Significant improvements are needed in terms of computational accuracy, uncertainty quantification, random field modeling, and computational efficiency for the quantitative strength estimation by numerical analysis. For this problem, a novel computational framework assisted by the dual data-driven approach is established in this research. In the proposed approach, the accuracy of the strength estimation analysis for deterministic conditions is improved by an experimental data-driven approach based on the in-situ microscopic full-field displacement measurement. A computational data-driven approach based on random field modeling assisted by machine learning is employed for non-deterministic conditions. In this paper, the outline of the proposed dual data-driven multiscale stochastic analysis framework is introduced first. Subsequently, the details of the proposed experimental data-driven approach for determining the microscopic fracture criteria are presented, and the computational data-driven approach for improving the effectiveness and efficiency of the random field modeling-based probabilistic analysis is described. The presented approach is applied to the strength estimation of a randomly arranged unidirectional fiber-reinforced composite plate under transverse tensile loading, and its validity and effectiveness are discussed with comparisons between the experimental and numerical results obtained assuming several computational conditions.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117476"},"PeriodicalIF":6.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142551532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Uncertainty quantification for noisy inputs–outputs in physics-informed neural networks and neural operators","authors":"Zongren Zou ,&nbsp;Xuhui Meng ,&nbsp;George Em Karniadakis","doi":"10.1016/j.cma.2024.117479","DOIUrl":"10.1016/j.cma.2024.117479","url":null,"abstract":"<div><div>Uncertainty quantification (UQ) in scientific machine learning (SciML) becomes increasingly critical as neural networks (NNs) are being widely adopted in addressing complex problems across various scientific disciplines. Representative SciML models are physics-informed neural networks (PINNs) and neural operators (NOs). While UQ in SciML has been increasingly investigated in recent years, very few works have focused on addressing the uncertainty caused by the noisy inputs, such as spatial–temporal coordinates in PINNs and input functions in NOs. The presence of noise in the inputs of the models can pose significantly more challenges compared to noise in the outputs of the models, primarily due to the inherent nonlinearity of most SciML algorithms. As a result, UQ for noisy inputs becomes a crucial factor for reliable and trustworthy deployment of these models in applications involving physical knowledge. To this end, we introduce a Bayesian approach to quantify uncertainty arising from noisy inputs–outputs in PINNs and NOs. We show that this approach can be seamlessly integrated into PINNs and NOs, when they are employed to encode the physical information. PINNs incorporate physics by including physics-informed terms via automatic differentiation, either in the loss function or the likelihood, and often take as input the spatial–temporal coordinate. Therefore, the present method equips PINNs with the capability to address problems where the observed coordinate is subject to noise. On the other hand, pretrained NOs are also commonly employed as equation-free surrogates in solving differential equations and Bayesian inverse problems, in which they take functions as inputs. The proposed approach enables them to handle noisy measurements for both input and output functions with UQ. We present a series of numerical examples to demonstrate the consequences of ignoring the noise in the inputs and the effectiveness of our approach in addressing noisy inputs–outputs with UQ when PINNs and pretrained NOs are employed for physics-informed learning.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117479"},"PeriodicalIF":6.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142550565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 discrete sine–cosine based method for the elasticity of heterogeneous materials with arbitrary boundary conditions","authors":"Joseph Paux ,&nbsp;Léo Morin ,&nbsp;Lionel Gélébart ,&nbsp;Abdoul Magid Amadou Sanoko","doi":"10.1016/j.cma.2024.117488","DOIUrl":"10.1016/j.cma.2024.117488","url":null,"abstract":"<div><div>The aim of this article is to extend Moulinec and Suquet (1998)’s FFT-based method for heterogeneous elasticity to non-periodic Dirichlet/Neumann boundary conditions. The method is based on a decomposition of the displacement into a known term verifying the boundary conditions and a fluctuation term, with no contribution on the boundary, and described by appropriate sine–cosine series. A modified auxiliary problem involving a polarization tensor is solved within a Galerkin-based method, using an approximation space spanned by sine–cosine series. The elementary integrals emerging from the weak formulation of the equilibrium are approximated by discrete sine–cosine transforms, which makes the method relying on the numerical complexity of Fourier transforms. The method is finally assessed in several problems including kinematic uniform, static uniform and arbitrary Dirichlet/Neumann boundary conditions.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117488"},"PeriodicalIF":6.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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":"Towards high-order consistency and convergence of conservative SPH approximations","authors":"Bo Zhang,&nbsp;Nikolaus Adams,&nbsp;Xiangyu Hu","doi":"10.1016/j.cma.2024.117484","DOIUrl":"10.1016/j.cma.2024.117484","url":null,"abstract":"<div><div>Smoothed particle hydrodynamics (SPH) offers distinct advantages for modeling many engineering problems, yet achieving high-order consistency in its conservative formulation remains to be addressed. While zero- and higher-order consistencies can be obtained using particle-pair differences and kernel gradient correction (KGC) approaches, respectively, for SPH gradient approximations, their applicability for discretizing conservation laws in practical simulations is limited due to their lack of discrete conservation. Although the standard anti-symmetric SPH approximation is able to achieve conservation and zero-order consistency through particle relaxation, its straightforward extensions with the KGC fail to satisfy zero- or higher-order consistency. In this paper, we propose the reverse KGC (RKGC) formulation, which is conservative and able to satisfy up to first-order consistency when particles are relaxed based on the KGC matrix. Extensive numerical tests show that the new formulation considerably improves the accuracy of the Lagrangian SPH method. In particular, it is able to resolve the long-standing high-dissipation issue for simulating free-surface flows. Furthermore, with fully relaxed particles, it enhances the accuracy of the Eulerian SPH method even when the ratio between the smoothing length and the particle spacing is considerably reduced. The reverse KGC formulation holds the potential for extension to even higher-order consistencies with a pending challenge in addressing the corresponding particle relaxation problem.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117484"},"PeriodicalIF":6.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142550560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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":"Comparison of guaranteed lower eigenvalue bounds with three skeletal schemes","authors":"Carsten Carstensen ,&nbsp;Benedikt Gräßle ,&nbsp;Emilie Pirch","doi":"10.1016/j.cma.2024.117477","DOIUrl":"10.1016/j.cma.2024.117477","url":null,"abstract":"<div><div>Specially tailored skeletal schemes enable cell and face variables linked with a stabilisation and a fine-tuned parameter can provide guaranteed lower eigenvalue bounds for the Laplacian. This paper briefly presents a unified derivation of skeletal higher-order methods from Carstensen, Zhai, and Zhang (2020), Carstensen, Ern, and Puttkammer (2021), and Carstensen, Gräßle, and Tran (2024). It suggests a paradigm shift from conditional to unconditional lower eigenvalue bounds. Adaptive mesh-refining leads to optimal convergence rates in computational benchmark examples and underlines the superiority of higher-order methods.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117477"},"PeriodicalIF":6.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552277","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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":"System stabilization with policy optimization on unstable latent manifolds","authors":"Steffen W.R. Werner ,&nbsp;Benjamin Peherstorfer","doi":"10.1016/j.cma.2024.117483","DOIUrl":"10.1016/j.cma.2024.117483","url":null,"abstract":"<div><div>Stability is a basic requirement when studying the behavior of dynamical systems. However, stabilizing dynamical systems via reinforcement learning is challenging because only little data can be collected over short time horizons before instabilities are triggered and data become meaningless. This work introduces a reinforcement learning approach that is formulated over latent manifolds of unstable dynamics so that stabilizing policies can be trained from few data samples. The unstable manifolds are minimal in the sense that they contain the lowest dimensional dynamics that are necessary for learning policies that guarantee stabilization. This is in stark contrast to generic latent manifolds that aim to approximate all—stable and unstable—system dynamics and thus are higher dimensional and often require higher amounts of data. Experiments demonstrate that the proposed approach stabilizes even complex physical systems from few data samples for which other methods that operate either directly in the system state space or on generic latent manifolds fail.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117483"},"PeriodicalIF":6.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}