Title page for ETD etd-05262004-131642

Type of Document Dissertation
Author Ba-abbad, Mazen
Author's Email Address mbaabbad@vt.edu
URN etd-05262004-131642
Title Reliability-based Design Optimization of a Nonlinear Elastic Plastic Thin-Walled T-Section Beam
Degree PhD
Department Aerospace and Ocean Engineering
Advisory Committee
Advisor Name Title
Kapania, Rakesh K. Committee Chair
Allen, Michael J. Committee Member
Johnson, Eric R. Committee Member
Thangjitham, Surot Committee Member
West, Robert L. Jr. Committee Member
  • Nonlinear
  • Reliability-Based Optimization
  • Finite Element
Date of Defense 2004-03-23
Availability unrestricted
A two part study is performed to investigate the application of reliability-based design

optimization (RBDO) approach to design elastic-plastic stiffener beams with Tsection.

The objectives of this study are to evaluate the benefits of reliability-based

optimization over deterministic optimization, and to illustrate through a practical

design example some of the difficulties that a design engineer may encounter while

performing reliability-based optimization. Other objectives are to search for a

computationally economic RBDO method and to utilize that method to perform

RBDO to design an elastic-plastic T-stiffener under combined loads and with

flexural-torsional buckling and local buckling failure modes. First, a nonlinear

elastic-plastic T-beam was modeled using a simple 6 degree-of-freedom non-linear

beam element. To address the problems of RBDO, such as the high non-linearity and

derivative discontinuity of the reliability function, and to illustrate a situation where

RBDO fails to produce a significant improvement over the deterministic

optimization, a graphical method was developed. The method started by obtaining a

deterministic optimum design that has the lowest possible weight for a prescribed

safety factor (SF), and based on that design, the method obtains an improved

optimum design that has either a higher reliability or a lower weight or cost for the

same level of reliability as the deterministic design. Three failure modes were

considered for an elastic-plastic beam of T cross-section under combined axial and

bending loads. The failure modes are based on the total plastic failure in a beam

section, buckling, and maximum allowable deflection. The results of the first part

show that it is possible to get improved optimum designs (more reliable or lighter

weight) using reliability-based optimization as compared to the design given by

deterministic optimization. Also, the results show that the reliability function can be

highly non-linear with respect to the design variables and with discontinuous

derivatives. Subsequently, a more elaborate 14-degrees-of-freedom beam element

was developed and used to model the global failure modes, which include the

flexural-torsional and the out-of-plane buckling modes, in addition to local buckling

modes. For this subsequent study, four failure modes were specified for an elasticplastic

beam of T-cross-section under combined axial, bending, torsional and shear

loads. These failure modes were based on the maximum allowable in-plane, out-ofplane

and axial rotational deflections, in addition, to the web-tripping local buckling.

Finally, the beam was optimized using the sequential optimization with reliabilitybased

factors of safety (SORFS) RBDO technique, which was computationally very

economic as compared to the widely used nested optimization loop techniques. At

the same time, the SOPSF was successful in obtaining superior designs than the

deterministic optimum designs (either up to12% weight savings for the same level of

safety, or up to six digits improvement in the reliability for the same weight for a

design with Safety Factor 2.50).

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