Research Papers

Nonlinear Finite Element Analysis of Frames Under Interval Material and Load Uncertainty

[+] Author and Article Information
Rafi L. Muhanna

School of Civil and Environmental Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: rafi.muhanna@gatech.edu

Robert L. Mullen

Department of Civil and Environmental Engineering,
University of South Carolina,
Columbia, SC 29208
e-mail: rlm@cec.sc.edu

M. V. Rama Rao

Department of Civil Engineering,
Vasavi College of Engineering,
Hyderabad 500 031, India
e-mail: mv.ramarao@staff.vce.ac.in

Manuscript received October 14, 2014; final manuscript received May 6, 2015; published online October 2, 2015. Assoc. Editor: Alba Sofi.

ASME J. Risk Uncertainty Part B 1(4), 041003 (Oct 02, 2015) (8 pages) Paper No: RISK-14-1071; doi: 10.1115/1.4030609 History: Received October 14, 2014; Accepted May 08, 2015; Online October 02, 2015

The present study focuses on the development of nonlinear interval finite elements (NIFEM) for beam and frame problems. Three constitutive models have been used in the present study, viz., bilinear, Ramberg–Osgood, and cubic models, to illustrate the development of NIFEM. An interval finite element method (IFEM) has been developed to handle load, material, and geometric uncertainties that are introduced in a form of interval numbers defined by their lower and upper bounds. However, the scope of the previous methods was limited to linear problems. The present work introduces an IFEM formulation for problems involving material nonlinearity under interval material parameters and loads. The algorithm is based on the previously developed high-accuracy interval solutions. An iterative method that generates successive approximations to the secant stiffness is introduced. Examples are presented to illustrate the behavior of the formulation. It is shown that bounding the response of nonlinear structures for a large number of load combinations under uncertain yield stress can be computed at a reasonable computational cost.

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Grahic Jump Location
Fig. 1

Three nonlinear models: bilinear, cubic, and Ramberg–Osgood

Grahic Jump Location
Fig. 3

Cantilever beam-deflection of free end at various levels of load uncertainty

Grahic Jump Location
Fig. 4

Four-bay one-story frame

Grahic Jump Location
Fig. 5

Four-bay three-story frame

Grahic Jump Location
Fig. 6

Four-bay three-story frame loading pattern




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