International Journal for Numerical Methods in Engineering最新文献

{"title":"An Energy-Conserving Time Integration Scheme for Nonlinear Dynamics Analysis of Geometrically Exact 3D Euler–Bernoulli Beams","authors":"Sophy Chhang,&nbsp;Carlo Sansour,&nbsp;Pisey Keo,&nbsp;Mohammed Hjiaj,&nbsp;Jean-Marc Battini,&nbsp;M. V. Bento Santana","doi":"10.1002/nme.7611","DOIUrl":"https://doi.org/10.1002/nme.7611","url":null,"abstract":"<div>\u0000 \u0000 <p>In the nonlinear large deformation regime, the beam theory is usually based on the Timoshenko assumption which considers shear deformations. The formulation of a 3D Euler–Bernoulli beam has been significantly delayed and only recently it did attract the attention of few researchers. The main reason lies in the challenging complexities met once an attempt to develop such a theory is undertaken. The main obstacle in defining a three-dimensional Euler–Bernoulli beam theory lies in the fact that there is no natural way of defining a base system at the deformed configuration. In this article, we provide a novel methodology to do so leading to the development of a spatial rod formulation which incorporates the Euler–Bernoulli assumption. The first approach makes use of Gram–Schmidt orthogonalisation process coupled to a one-parametric rotation. The latter completes the description of the torsional cross sectional rotation and overcomes the nonuniqueness of the Gram–Schmidt procedure. In a second approach, the rotation tensor is defined based on first and second derivatives of the displacement vector of the centre line. It is followed by one parametric rotation. The proposed formulation is extended to the dynamical case and a stable, energy and momentum conserving time-stepping algorithm is presented as well. Specifically, the proof of conservation of angular momentum of the time stepping algorithm is highly demanding and is given here in full.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143118306","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":"Modelling the effect of point forces and moments in plate bending with hybrid-Trefftz stress elements","authors":"J. A. Teixeira de Freitas,&nbsp;C. Tiago,&nbsp;E. M. B. R. Pereira","doi":"10.1002/nme.7587","DOIUrl":"https://doi.org/10.1002/nme.7587","url":null,"abstract":"<p>The formulation of the hybrid-Trefftz stress element for plate bending is extended to the modelling of concentrated forces and moments, either as prescribed loads or as reactions at point supports. As the bending, torsion and shear fields are hypersingular, the flexibility matrix of the element involves the use of the finite part integration concept. In addition, it requires the confirmation of the positive-definiteness of the flexibility under gross shape distortion. The tests illustrate the modelling of applied concentrated forces and moments and also the combination of boundary layer and point reaction effects. The results obtained are validated using converged solutions obtained with a stress-based hybrid-mixed element (HMS) and a displacement-based mixed element (MITC).</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"125 24","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142707980","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":"Compliant Mechanism Synthesis Using Nonlinear Elastic Topology Optimization With Variable Boundary Conditions","authors":"Lee R. Alacoque,&nbsp;Anurag Bhattacharyya,&nbsp;Kai A. James","doi":"10.1002/nme.7613","DOIUrl":"https://doi.org/10.1002/nme.7613","url":null,"abstract":"<p>In topology optimization of compliant mechanisms, the specific placement of boundary conditions strongly affects the resulting material distribution and performance of the design. At the same time, the most effective locations of the loads and supports are often difficult to find manually. This substantially limits topology optimization's effectiveness for many mechanism design problems. We remove this limitation by developing a method which automatically determines optimal positioning of a prescribed input displacement and a set of supports simultaneously with an optimal material layout. Using nonlinear elastic physics, we synthesize a variety of compliant mechanisms with large output displacements, snap-through responses, and prescribed output paths, producing designs with significantly improved performance in every case tested. Compared to optimal designs generated using manually designed boundary conditions used in previous studies, the mechanisms presented in this paper see performance increases ranging from 47% to 380%. The results show that nonlinear mechanism responses may be particularly sensitive to boundary condition locations and that effective placements can be difficult to find without an automated method.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7613","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143120552","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":"Deformation Analysis of Cosserat Rods Using Piecewise Clothoid Approximation","authors":"Sreejath Sivaj,&nbsp;Subir Kumar Saha,&nbsp;Satinder Paul Singh","doi":"10.1002/nme.7608","DOIUrl":"https://doi.org/10.1002/nme.7608","url":null,"abstract":"<p>This paper presents an alternative to isogeometric analysis (IGA) for static analysis of planar curved slender beams. Geometrically exact Cosserat rod model is employed to establish the governing equations. In contrast to conventional IGA, which uses NURBS as the basis function, our method incorporates clothoid curves to represent the curved geometry. We use piecewise clothoid curves to approximate the initial curvature of the undeformed beam, facilitating a seamless integration into the Cosserat rod model. A straightforward solution of the governing equations is implemented using shooting method, verifying applicability across a range of problems. Interestingly, the parameters that define the clothoid segments also appear in the governing equations of the beam. This bridges the gap between the geometric design of the beams and their static simulations. In this way, we present the proposed formulation as an alternative to conventional IGA. The notable features of the method are easy implementation, good accuracy, and convergence. Moreover, the method predicts bending stress in the beam, capturing the nonlinearity of the deformation.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143120236","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":"Constraint Realization-Based Hamel Field Integrator for Geometrically Exact Planar Euler–Bernoulli Beam Dynamics","authors":"Benliang Wang,&nbsp;Donghua Shi,&nbsp;Zhonggui Yi","doi":"10.1002/nme.7603","DOIUrl":"https://doi.org/10.1002/nme.7603","url":null,"abstract":"<div>\u0000 \u0000 <p>In this article, we first introduce a Hamel field integrator designed for a geometrically exact Euler–Bernoulli beam with infinite-dimensional holonomic constraints, constructed using a Lagrange multiplier. This method addresses the complexities introduced by constraints, but the additional multiplier introduces a new degree of freedom and hence results in a system with mixed-type partial differential equations. To address this issue, we further propose a constraint realization method based on perturbation theory for infinite-dimensional mechanical systems within the framework of Hamel's formalism. This method circumvents the use of additional Lagrange multiplier, significantly reducing the computational complexity of modeling problems. Building on this, we construct a perturbed Hamel field integrator optimized for parallel computing and incorporate artificial viscosity to accelerate constraint convergence. While applicable to three dimensions, our method is demonstrated in a simplified context using planar Euler–Bernoulli beam examples to illustrate the effectiveness of the unified mathematical framework.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143119590","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":"Treatment of inelastic material models within a dynamic ALE formulation for structures subjected to moving loads","authors":"Atul Anantheswar,&nbsp;Ines Wollny,&nbsp;Michael Kaliske","doi":"10.1002/nme.7599","DOIUrl":"https://doi.org/10.1002/nme.7599","url":null,"abstract":"<p>This article showcases the development of a dynamic Arbitrary <span>Lagrangian Eulerian</span> (ALE) formulation to account for inelastic material models within a finite element framework. Such a formulation is commonly utilized in research domains like fluid mechanics, fluid-structure interaction, quasi static remeshing techniques, and quasi static load movement. The work at hand describes the application of the ALE formulation to efficiently analyse structures subjected to moving loads in the field of transient inelastic solid mechanics. In particular, structures such as pavements, gantry crane girders etc., which are subjected to moving loads, can be numerically simulated, and their transient response in the relevant region around the load can be obtained without relying on moving loads. The focus of this article is to facilitate the treatment of history variables stemming from inelastic material models. Of particular interest is the advection procedure required to transport the history variables through the mesh, as the material appears to flow through it. The mathematical framework necessary to treat this advection process is described in detail, considering a nonlinear viscoelastic material model on a neo-<span>Hookean</span> base at finite deformations. Then, four methods for numerically achieving the advection are implemented within a transient finite element ALE formulation. These methods are compared against each other, and additionally with the conventional <span>Lagrangian</span> method for validation. The results demonstrate satisfactory agreement with conventional simulation methods, while offering a significant improvement in terms of computation speed. With the work at hand, the dynamic response of inelastic materials subjected to moving loads can be numerically simulated in a computationally efficient manner.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7599","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143119270","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":"On some energy-based variational principles in non-dissipative magneto-mechanics using a vector potential approach","authors":"Philipp Gebhart,&nbsp;Thomas Wallmersperger","doi":"10.1002/nme.7593","DOIUrl":"https://doi.org/10.1002/nme.7593","url":null,"abstract":"<p>This contribution covers the variational-based modeling of non-dissipative magneto-mechanical systems using a vector potential approach and the thorough analysis and discussion of corresponding conforming finite element methods. Since the construction of divergence-free finite element spaces explicitly enforcing the Coulomb gauge poses some major challenges, we propose some primal and mixed variational principles that ensure well posedness of the problem and allow to seek the vector potential in unconstrained function spaces. The performance of these methods is assessed in two comparative benchmark studies. The focus of both studies lies on the accurate approximation of field quantities in systems with material discontinuities and re-entrant corners.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"125 24","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7593","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142707756","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":"Constitutive description of snow at finite strains by the modified cam-clay model and an implicit gradient damage formulation","authors":"Ahmad Moeineddin,&nbsp;Jakob Platen,&nbsp;Michael Kaliske","doi":"10.1002/nme.7595","DOIUrl":"https://doi.org/10.1002/nme.7595","url":null,"abstract":"<p>Snow, characterized as a unique granular and low-density material, exhibits intricate behavior influenced by the proximity to its melting point and its three-phase composition. This composition entails a structured ice skeleton surrounded by voids filled with air and spread with liquid water. Mechanically, snow experiences dynamic transformations, including bonding/degradation between its grains, significant inelastic deformations, and a distinct rate sensitivity. Given snow's varied structures and mechanical strengths in natural settings, a comprehensive constitutive model is necessary. Our study introduces a pioneering formulation grounded on the modified Cam-Clay model, extended to finite strains. This formulation is further enriched by an implicit gradient damage modeling, creating a synergistic blend that offers a detailed representation of snow behavior. The versatility of the framework is emphasized through the careful calibration of damage parameters. Such calibration allows the model to adeptly capture the effects of diverse strain rates, particularly at high magnitudes, highlighting its adaptability in replicating snow's unique mechanical responses across various conditions. Upon calibration against established experimental benchmarks, the model demonstrates a suitable alignment with observed behavior, underscoring its potential as a comprehensive tool for understanding and modeling snow behavior with precision and depth.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"125 24","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7595","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142707757","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":"Phase Field Coupled Finite Deformation Plasticity Formulation of Ductile Fracture With Nonlinear Kinematic Hardening and Modified Energy Release Function","authors":"Sumit Kumar,&nbsp;B. P. Patel","doi":"10.1002/nme.7607","DOIUrl":"https://doi.org/10.1002/nme.7607","url":null,"abstract":"<div>\u0000 \u0000 <p>A ductile damage theory is presented by coupling the covariant formulation of finite deformation plasticity with the phase field modeling of fracture, including kinematic hardening for the ductile response of the materials. A phase field coupled nonlinear kinematic hardening equation is proposed in the reference configuration having equivalent representation through the Lie derivative of the kinematic hardening tensor by push-forward operation in the spatial configuration, thus ensuring the satisfaction of frame invariance. To capture the correct physical response of the material by the phase field evolution equation, the fracture driving function, that is, the difference between the sum of elastic and plastic energies and threshold energy, after the damage initiation is modified by an energy release controlling function, which is an empirical relation of equivalent plastic strain. In defining the energy release controlling function, well-defined points with physical significance in the experimental load versus displacement curve are used. To simulate the response of the material in relatively large time steps, a modified staggered scheme is presented, evaluating the fracture driving and energy release controlling functions from the previous converged step and using the updated phase field variable in the weak form of the momentum balance equation. To quantify different material parameters from available experimental results in the literature, the developed phase field coupled elasto-plastic model uses a neural network optimization procedure consisting of neural network training together with optimization in MATLAB and finite element model evaluation in Abaqus user element subroutine UEL. Model capabilities are demonstrated by simulating the crack propagation in complex 3D geometries such as the second and third Sandia Fracture Challenges.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143117519","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":"Partial-differential-algebraic equations of nonlinear dynamics by physics-informed neural-network: (I) Operator splitting and framework assessment","authors":"Loc Vu-Quoc,&nbsp;Alexander Humer","doi":"10.1002/nme.7586","DOIUrl":"https://doi.org/10.1002/nme.7586","url":null,"abstract":"<p>Several forms for constructing novel physics-informed neural-networks (PINNs) for the solution of partial-differential-algebraic equations (PDAEs) based on derivative operator splitting are proposed, using the nonlinear Kirchhoff rod as a prototype for demonstration. The present work is a natural extension of our review paper (Vu-Quoc and Humer, <i>CMES-Comput Modeling Eng Sci</i>, 137(2):1069–1343, 2023) aiming at both experts and first-time learners of both deep learning and PINN frameworks, among which the open-source DeepXDE (DDE; <i>SIAM Rev</i>, 63(1):208–228, 2021) is likely the most well documented framework with many examples. Yet, we encountered some pathological problems (time shift, amplification, static solutions) and proposed novel methods to resolve them. Among these novel methods are the PDE forms, which evolve from the lower-level form with fewer unknown dependent variables (e.g., displacements, slope, finite extension) to higher-level form with more dependent variables (e.g., forces, moments, momenta), in addition to those from lower-level forms. Traditionally, the highest-level form, the balance-of-momenta form, is the starting point for (hand) deriving the lowest-level form through a tedious (and error prone) process of successive substitutions. The next step in a finite element method is to discretize the lowest-level form upon forming a weak form and linearization with appropriate interpolation functions, followed by their implementation in a code and testing. The time-consuming tedium in all of these steps could be bypassed by applying the proposed novel PINN directly to the highest-level form. We also developed a script based on JAX, the High Performance Array Computing library. For the axial motion of elastic bar, while our JAX script did not show the pathological problems of DDE-T (DDE with TensorFlow backend), it is slower than DDE-T. Moreover, that DDE-T itself being more efficient in higher-level form than in lower-level form makes working directly with higher-level form even more attractive in addition to the advantages mentioned further above. Since coming up with an appropriate learning-rate schedule for a good solution is more art than science, we systematically codified in detail our experience running optimization (network training) through a normalization/standardization of the network-training process so readers can reproduce our results.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"125 24","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7586","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142707688","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}