Efficient Inelasticity-Separated Finite-Element Method for Material Nonlinearity Analysis
Publication: Journal of Engineering Mechanics
Volume 144, Issue 4
Abstract
Material nonlinearity analyses are widely used to determine the safety of structural components or engineering structures. Although advanced computer hardware technology has considerably improved the computational performance of such analyses, large and complex emerging structures and expensive computational process still attract the attention of researchers toward finding more efficient and accurate numerical solution methods. This paper combines an inelasticity-separated (IS) concept with the finite-element method (FEM) to establish a novel and efficient framework (IS-FEM) for structures with material nonlinear behavior that only occurs within certain small local domains. The IS concept presented in this paper begins by decomposing the strain on a nonlinear material into its linear-elastic and inelastic components and runs through the whole framework. Based on the principle of virtual work, a novel governing equation for structures with an IS form is derived by treating the decomposed inelastic strain as additional degrees of freedom. Moreover, the changing stiffness matrix in the classical FEM is expressed as the sum of the invariant global linear elastic stiffness matrix and another changing inelastic stiffness matrix with a small rank, and it represents the material nonlinearity of local domains so that the efficient solution method can be applied to perform nonlinear analyses via the mathematical Sherman–-Morrison–Woodbury (SMW) formula. Because the unchanging global stiffness matrix is used throughout the whole nonlinear analysis and the computational effort only focuses on a small dimension matrix that represents the local inelastic behavior, the efficiency of the proposed IS-FEM is improved greatly. The proposed method is validated against the results of classical FEM via three separate numerical examples and its value and potential for use in any material nonlinearity analyses are also demonstrated.
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Acknowledgments
Funding for the authors was provided by the National Natural Science Foundation of China (Grant No. 51422802). The opinions, findings, and conclusions expressed in this paper are those of the authors and do not necessarily reflect the views of those acknowledged here.
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Published In
Journal of Engineering Mechanics
Volume 144 • Issue 4 • April 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: Feb 27, 2017
Accepted: Sep 27, 2017
Published online: Jan 19, 2018
Published in print: Apr 1, 2018
Discussion open until: Jun 19, 2018
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