Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"Uncertainty quantification for noisy inputs–outputs in physics-informed neural networks and neural operators","authors":"","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":null,"pages":null},"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":"","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":null,"pages":null},"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":"","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":null,"pages":null},"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":"","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":null,"pages":null},"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":"","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":null,"pages":null},"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}

{"title":"An efficient numerical algorithm to solve hydrodynamic lubrication problems with cavitation","authors":"","doi":"10.1016/j.cma.2024.117470","DOIUrl":"10.1016/j.cma.2024.117470","url":null,"abstract":"<div><div>In this paper we present an efficient numerical algorithm to solve stationary problems of hydrodynamic lubrication with cavitation in bearings using the method of characteristics in a finite element framework. The problem is based on the Elrod–Adams mathematical model for the lubricant fluid behavior. To achieve realistic pressure solutions, cavitation must be considered. This leads to a non-linear system of equations including a multivalued operator. In order to solve this problem, we propose a modified Newton algorithm that presents a high convergence speed, allowing one to use small tolerances to solve the problem with high accuracy and efficiency using a low number of iterations, in comparison with alternative numerical algorithms in the literature to solve the same problem. Numerical results are presented and analyzed in the work.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142550564","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":"Second-order computational homogenization for bridging poromechanical scales under large deformations","authors":"","doi":"10.1016/j.cma.2024.117481","DOIUrl":"10.1016/j.cma.2024.117481","url":null,"abstract":"<div><div>We introduce a second-order computational homogenization procedure designed to address heterogeneous poromechanical media. Our approach relies on the method of multiscale virtual power, a variational multiscale method that extends the Hill–Mandel principle of macro-homogeneity. Constraints on displacement and pore pressure fields are managed using periodic and second-order minimally constrained fluctuating spaces. Numerical comparisons reveal that first-order models fail to accurately represent nonzero net fluid flow and volume changes at the micro-scale. In contrast, our second-order approach effectively captures nonuniform fluid flow across representative volume element boundaries, in agreement with results from direct numerical simulations. Our findings indicate that the classical first-order expansion of the pressure field is inadequate for poromechanical homogenization in cases involving micro-scale volume changes, such as swelling or contraction. The proposed second-order approach not only overcomes these limitations but also proves effective in cases where the principle of separation of scales is not strictly upheld.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142550566","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":"Direct serendipity finite elements on cuboidal hexahedra","authors":"","doi":"10.1016/j.cma.2024.117500","DOIUrl":"10.1016/j.cma.2024.117500","url":null,"abstract":"<div><div>We construct direct serendipity finite elements on general cuboidal hexahedra, which are <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-conforming and optimally approximate to any order. The new finite elements are <em>direct</em> in that the shape functions are directly defined on the physical element. Moreover, they are <em>serendipity</em> by possessing a minimal number of degrees of freedom satisfying the conformity requirement. Their shape function spaces consist of polynomials plus (generally nonpolynomial) supplemental functions, where the polynomials are included for the approximation property and supplements are added to achieve <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-conformity. The finite elements are fully constructive. The shape function spaces of higher order <span><math><mrow><mi>r</mi><mo>≥</mo><mn>3</mn></mrow></math></span> are developed first, and then the lower order spaces are constructed as subspaces of the third order space. Under a shape regularity assumption, and a mild restriction on the choice of supplemental functions, we develop the convergence properties of the new direct serendipity finite elements. Numerical results with different choices of supplements are compared on two mesh sequences, one regularly distorted and the other one randomly distorted. They all possess a convergence rate that aligns with the theory, while a slight difference lies in their performance.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142551904","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":"A new floating node-based element formulation for modelling pressure-driven fracture","authors":"","doi":"10.1016/j.cma.2024.117482","DOIUrl":"10.1016/j.cma.2024.117482","url":null,"abstract":"<div><div>When simulating pressure-driven fracture with the Finite Element Method (FEM), significant difficulties can arise upon representing newly formed complex damage surfaces and their concurrent crack face loading. Application of this loading can also be required when additional physics is involved as in the case of hydraulic fracture where fluid physics inside a damage need to be considered. This paper presents a new Finite Element based practical numerical framework which can model pressure-driven fractures as they form on-the-fly without remeshing. The exact location of physical discontinuities passing through the element domain can be represented in the numerical model. The numerical framework can be implemented as a user-defined element and can be integrated into any FE package. A new element (called <em>pressure</em> element) is formulated with the capability to apply pressure and associated forces onto the crack surfaces in an adaptive manner. This element is verified using relevant examples from literature. The framework can also be configured for multi-physics problems where crack face loading is dictated by an additional physics. The element formulation is then extended for multi-physics problems involving fluid–solid interaction. The formulation provides the capability for multi-physics coupling adaptively as the crack propagates. The element is used to successfully simulate a test case from literature using different solution procedures (iterative and simultaneous). This element is also used to model failure in different pressure vessel problems to demonstrate its potential use in structural applications. A new higher-scale <em>vessel</em> element is developed which can represent different size, partitioning and failure states of composite vessel systems at element level. Composite vessel failure involving high number of pressurized cracks and delaminations as well as their interaction is modelled, and burst pressures are predicted for different vessel systems. The proposed numerical framework can be used towards designing more damage-tolerant vessels critical for the sustainable propulsion technologies.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142550567","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":"An assemblable interlocking joint generation method for multi-material topology optimization using interfacial partial stress constraints and dimensional constraints","authors":"","doi":"10.1016/j.cma.2024.117475","DOIUrl":"10.1016/j.cma.2024.117475","url":null,"abstract":"<div><div>Multi-material topology optimization has become a promising method in structural design due to its excellent structural performance. However, existing research assumes that the multi-material structures are joined by welding, adhesive, or other methods that do not support reassembly and disassembly and are unsuitable for manufacturing, limiting the practical application of topology optimization. An interlocking joint is a type of connection between two parts where the shapes of the parts are designed to fit together precisely, the multi-material structure joined by interlocking joints can be easily reassembled repeatedly. To solve the joint problem of multi-material structure, this study proposes an assemblable interlocking joint generation method for multi-material topology optimization, the connection between material components is achieved through compression at the joint areas. To generate the interlocking joints, a novel interfacial partial stress constraint is proposed by converting a part of the interface bearing tensile stress into the interface bearing compressive stress. A novel filtering process is used to control the shape of the interlocking joints and the filtered tensile stresses are integrated by a P-norm function. To constrain the distribution area of material components and ensure structural manufacturability, dimensional constraints are applied. The sensitivity is based on the topological derivative and adjoint variable method. The proposed method was applied to several numerical examples including one manufactured prototype to demonstrate its effectiveness and contribution to the practical application of topology optimization.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142550563","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}