Journal: International Journal for Numerical Methods in Engineering

Abbreviation

Int. J. Numer. Meth. Engng

Publisher

Wiley

Journal Volumes

ISSN

1097-0207
0029-5981

Description

Filters

Reset filters

Search Results

Publications 1 - 10 of 19
  • An augmented Lagrangian algorithm for contact mechanics based on linear regression
    Item type: Journal Article
    De Lorenzis, Laura; Zavarise, Giorgio (2012)
    International Journal for Numerical Methods in Engineering
  • Formulation for wave propagation in dissipative media and its application to absorbing layers in elastoplastic analysis using mathematical programming
    Item type: Journal Article
    Wang, Liang; Zhang, Xue; Tinti, Stefano (2023)
    International Journal for Numerical Methods in Engineering
    In this article, we propose a new solution scheme for modeling elastoplastic problems with stress wave propagation in dissipative media. The scheme is founded on a generalized Hellinger-Reissner (HR) variational principle. The principle renders the discretized boundary-value problem into an equivalent second-order cone programming (SOCP) problem that can be resolved in mathematical programming using the advanced optimization algorithm-the interior point method. In such a way, the developed method not only inherits admirable features of the SOCP-based finite element method in solving elastoplastic problems but also enables the enforcement of absorbing layers (i.e., Caughey absorbing layer), which is essential in modeling stress wave propagation problems, to absorb wave energy. The proposed scheme is validated via the comparison between analytical and numerical results for seismic wave propagation in dissipative media. Its application to elastoplastic dynamic problems with stress wave propagation is also illustrated to demonstrate its efficiency.
  • Step size adjustment and extrapolation for time-stepping schemes in non-smooth dynamics
    Item type: Journal Article
    Studer, C.; Leine, R. I.; Glocker, Ch. (2008)
    International Journal for Numerical Methods in Engineering
  • A modified node-to-segment algorithm passing the contact patch test
    Item type: Journal Article
    Zavarise, Giorgio; De Lorenzis, Laura (2009)
    International Journal for Numerical Methods in Engineering
  • A three‐dimensional hybrid finite element – spectral boundary integral method for modeling earthquakes in complex unbounded domains
    Item type: Journal Article
    Albertini, Gabriele; Elbanna, Ahmed E.; Kammer, David S. (2021)
    International Journal for Numerical Methods in Engineering
    We present a 3D hybrid method which combines the finite element method (FEM) and the spectral boundary integral method (SBIM) to model nonlinear problems in unbounded domains. The flexibility of FEM is used to model the complex, heterogeneous, and nonlinear part— such as the dynamic rupture along a fault with near fault plasticity—and the high accuracy and computational efficiency of SBIM is used to simulate the exterior half spaces perfectly truncating all incident waves. The exact truncation allows us to greatly reduce the domain of spatial discretization compared to a traditional FEM approach, leading to considerable savings in computational time and memory requirements. The coupling of FEM and SBIM is achieved by the exchange of traction and displacement boundary conditions at the computationally defined boundary. The method is suited to implementation on massively parallel computers. We validate the developed method by means of a benchmark problem. Three more complex examples with a low velocity fault zone, low velocity off-fault inclusion, and interaction of multiple faults, respectively, demonstrate the capability of the hybrid scheme in solving problems of very large sizes. Finally, we discuss potential applications of the hybrid method for problems in geophysics and engineering.
  • Integral equations and model reduction for fast computation of nonlinear periodic response
    Item type: Journal Article
    Buza, Gergely; Haller, George; Jain, Shobhit (2021)
    International Journal for Numerical Methods in Engineering
    We propose a reformulation for a recent integral equations approach to steady-state response computation for periodically forced nonlinear mechanical systems. This reformulation results in additional speed-up and better convergence. We show that the solutions of the reformulated equations are in one-to-one correspondence with those of the original integral equations and derive conditions under which a collocation-type approximation converges to the exact solution in the reformulated setting. Furthermore, we observe that model reduction using a selected set of vibration modes of the linearized system substantially enhances the computational performance. Finally, we discuss an open-source implementation of this approach and demonstrate the gains in computational performance using three examples that also include nonlinear finite-element models.
  • Accelerating structural dynamics simulations with localised phenomena through matrix compression and projection-based model order reduction
    Item type: Journal Article
    Agathos, Konstantinos; Vlachas, Konstantinos; Garland, Anthony; et al. (2024)
    International Journal for Numerical Methods in Engineering
    In this work, a novel approach is introduced for accelerating the solution of structural dynamics problems in the presence of localised phenomena, such as cracks. For this category of problems, conventional projection-based Model Order Reduction (MOR) methods are either limited with respect to the range of system configurations that can be represented or require frequent solutions of the Full Order Model (FOM) to update the low-dimensional spaces, in which solutions are represented. In the proposed approach, low-dimensional spaces, constructed for the healthy structure, are enriched with appropriately selected columns of the flexibility matrix of the system. It can be shown that these spaces contain the solution to the original problem for the static case, while their dimension is much smaller. In order to allow their online construction for arbitrary localised features, the full flexibility matrix of the system should be available. To this end, a hierarchical representation is used for the matrices involved, allowing to compute the flexibility matrix efficiently and with reduced memory requirements. The resulting method offers significant speedups, without sacrificing the flexibility and accuracy of the full order model. The performance and limitations of the approach are studied through a series of examples in structural dynamics.
  • A discretization-convergent level-set-discrete-element-method using a continuum-based contact formulation
    Item type: Journal Article
    Feldfogel, Shai; Karapiperis, Konstantinos; Andrade, Jose; et al. (2024)
    International Journal for Numerical Methods in Engineering
    The level-set-discrete-element-method (LS-DEM) was developed to overcome the shape limitation of traditional discrete element method. LS-DEM's shape generality relies on a node-based surface discretization of grain boundary, and it has been used to shed new light of a variety of granular mechanics applications with realistically shaped grains and structural assemblies made of unbonded building blocks. Due to the node-based discretization of grain boundary, the original LS-DEM is discretization-sensitive and it suffers from divergence of the response with discretization refinement, particularly for highly compressible problems. Previous studies have identified and addressed this issue in different ways, each with its own advantages and shortcomings. Here, we propose a methodologically-rigorous and computationally-efficient adapted formulation which solves LS-DEM's discretization-sensitivity issue. It adopts the classical contact description of continuum mechanics, wherein the contact interactions are traction-based. We demonstrate the convergence of the adapted LS-DEM in several highly compressible cases studies, show that it is key to correctly capturing the mechanical response, and compare it to alternative formulations.
  • Parametrized reduced order modeling for cracked solids
    Item type: Journal Article
    Agathos, Konstantinos; Bordas, Stéphane P.A.; Chatzi, Eleni (2020)
    International Journal for Numerical Methods in Engineering
    A parametrized reduced order modeling methodology for cracked two dimensional solids is presented, where the parameters correspond to geometric properties of the crack, such as location and size. The method follows the offline‐online paradigm, where in the offline, training phase, solutions are obtained for a set of parameter values, corresponding to specific crack configurations and a basis for a lower dimensional solution space is created. Then in the online phase, this basis is used to obtain solutions for configurations that do not lie in the training set. The use of the same basis for different crack geometries is rendered possible by defining a reference configuration and employing mesh morphing to map the reference to different target configurations. To enable the application to complex geometries, a mesh morphing technique is introduced, based on inverse distance weighting, which increases computational efficiency and allows for special treatment of boundaries. Applications in linear elastic fracture mechanics are considered, with the extended finite element method being used to represent discontinuous and asymptotic fields.
  • A numerical study of steady plane granular chute flows using the Jenkins-Savage model and its extension
    Item type: Journal Article
    Szidarovszky, Ferenc; Hutter, Kolumban; Yakowitz, Sydney (1987)
    International Journal for Numerical Methods in Engineering
    The granular flow model proposed by Jenkins and Savage and extended by us is used here to construct numerical solutions of steady chute flows thought to be typical of granular flow behaviour. We present the governing differential equations and discuss the boundary conditions for two flow cases: (i) a fully fluidized layer of granules moving steadily under rapid shear and (ii) a fluidized bottom-near bed covered by a rigid slab of gravel in steady motion under its own weight. The boundary value problem is transformed into a dimensionless form and the emerging system of non-linear ordinary differential equations is numerically integrated. Singularities at the free surface and (in one case) also at an unknown point inside the solution interval make the problem unusual. Since the non-dimensionalization is performed with the maximum particle concentration and the maximum velocity, which are both unknown, these two parameters also enter the formulation of the problem through algebraic equations. The two-point boundary value problem is solved with the aid of the shooting method by satisfying the boundary conditions at the end of the soluton interval and these normalizing conditions by means of a minimization procedure. We outline the numerical scheme and report selective numerical results. The computations are the first performed with the exact equations of the Jenkins–Savage model; they permit delineation of the conditions of applicability of the model and thus prove to be a useful tool for the granular flow modeller.
Publications 1 - 10 of 19