Reduced Basis Technique for Nonlinear Analysis of Structures

1980/04/01 by Ahmed K. Noor, Jeanne M. Peters · 17 citations
Mathematics · Engineering · #Numerical methods for differential equations #Vibration and Dynamic Analysis #Dynamics and Control of Mechanical Systems

paper · doi:10.2514/3.50778

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.

Citations

• Automatic choice of global shape functions in structural analysis

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