Journal ArticleDOI
Reduced Basis Technique for Nonlinear Analysis of Structures
Ahmed K. Noor,Jeanne M. Peters +1 more
TLDR
In this paper, a reduced basis technique and a computational algorithm are presented for predicting the nonlinear static response of structures, where a total Lagrangian formulation is used and the structure is discretized by using displacement finite element models.Abstract:
A reduced basis technique and a computational' algorithm are presented for predicting the nonlinear static response of structures. A total Lagrangian formulation is used and the structure is discretized by using displacement finite element models. The nodal displacement vector is expressed as a linear combination of a small number of basis vectors and a Rayleigh-Ritz technique is used to approximate the finite element equations by a reduced system of nonlinear equations. The Rayleigh-Ritz approximation functions (basis vectors) are chosen to be those commonly used in the static perturbation technique namely, a nonlinear solution and a number of its path derivatives. A procedure is outlined for automatically selecting the load (or displacement) step size and monitoring the solution accuracy. The high accuracy and effectiveness of the proposed approach is demonstrated by means of numerical examples.read more
Citations
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Journal ArticleDOI
Nonlinear Model Reduction via Discrete Empirical Interpolation
TL;DR: A dimension reduction method called discrete empirical interpolation is proposed and shown to dramatically reduce the computational complexity of the popular proper orthogonal decomposition (POD) method for constructing reduced-order models for time dependent and/or parametrized nonlinear partial differential equations (PDEs).
Journal ArticleDOI
An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations
TL;DR: Barrault et al. as discussed by the authors presented an efficient reduced-basis discretization procedure for partial differential equations with nonaffine parameter dependence, replacing non-affine coefficient functions with a collateral reducedbasis expansion, which then permits an affine offline-online computational decomposition.
Journal ArticleDOI
Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations
TL;DR: (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for linear functional outputs of affinely parametrized elliptic coercive partial differential equations are considered.
Journal ArticleDOI
Digital Twin: Values, Challenges and Enablers From a Modeling Perspective
TL;DR: This work reviews the recent status of methodologies and techniques related to the construction of digital twins mostly from a modeling perspective to provide a detailed coverage of the current challenges and enabling technologies along with recommendations and reflections for various stakeholders.
Journal ArticleDOI
Reliable Real-Time Solution of Parametrized Partial Differential Equations: Reduced-Basis Output Bound Methods
Christophe Prud'Homme,Dimitrios V. Rovas,Karen Veroy,Luc Machiels,Yvon Maday,Anthony T. Patera,Gabriel Turinici +6 more
TL;DR: The method is ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control.
References
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Journal ArticleDOI
Automatic choice of global shape functions in structural analysis
Journal ArticleDOI
Solution techniques for non-linear finite element problems
TL;DR: In this paper, a classification of mathematical commonly encountered in connection with solution of non-linear finite element problems is presented, and the principal methods for numerical solution of the nonlinear equations are surveyed and discussed.
Journal ArticleDOI
Buckling of Shallow Arches
TL;DR: In this article, the exact solution to the nonlinear problem of the buckling of a shallow, circular arch subjected to a uniform pressure or a concentrated load is given, and an explicit bifurcated equilibrium path is presented.
Journal ArticleDOI
An approximate analysis technique for design calculations
R. L. Fox,H. Miura +1 more