Journal ArticleDOI
Tracing post-limit-point paths with reduced basis technique
Ahmed K. Noor,Jeanne M. Peters +1 more
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TLDR
In this article, a reduced basis technique and a problem-adaptive computational algorithm are presented for predicting the post-limit-point paths of structures, where the structure is discretized by using displacement finite element models.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 1981-09-01. It has received 63 citations till now. The article focuses on the topics: Basis function & Nonlinear system.read more
Citations
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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.
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An arc‐length method including line searches and accelerations
TL;DR: In this paper, a line search method was proposed to improve the convergence of the arc-length solution for both geometrically nonlinear analysis of shallow shells and material nonlinear analyses of reinforced concrete beams and slabs.
ReportDOI
Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations
TL;DR: The text is focused on formulation, analysis, and computational procedures for reduced basis approximation and a posteriori error estimation for parametrized PDEs in the real-time and many-query contexts.
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A Reduced-Order Method for Simulation and Control of Fluid Flows
TL;DR: In this paper, the Lagrange approach is used to define reduced bases and the basis functions in this approach are obtained from the numerical solutions, and the feasibility of this method for flow control is demonstrated on boundary control problems in closed cavity and wall-bounded channel flows.
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POD and CVT-based reduced-order modeling of Navier-Stokes flows
TL;DR: Reviews of the POD (proper orthogonal decomposition) and CVT (centroidal Voronoi tessellation) approaches to reduced-order modeling are provided, including descriptions of POD andCVT reduced- order bases, their construction from snapshot sets, and their application to the low-cost simulation of the Navier–Stokes system.
References
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Journal ArticleDOI
An incremental approach to the solution of snapping and buckling problems
TL;DR: In this paper, an incremental approach to the solution of buckling and snapping problems is explored, where the authors use the length of the equilibrium path as a control parameter, together with the second order iteration method of Newton.
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A fast incremental/iterative solution procedure that handles "snap-through"
TL;DR: In this article, a modified version of the Newton-Raphson method is proposed to overcome limit points in the finite element method with a fixed load level and a constraint equation.
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Discrete approximations related to nonlinear theories of solids
TL;DR: In this paper, a generalized arc-length is introduced in the configuration-load space in order to facilitate the incremental computations near limit points, and the arc length is used as the loading parameter in some illustrative problems.
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Incremental displacement algorithms for nonlinear problems
Jean-Louis Batoz,G. Dhatt +1 more