Reliability-based Design Optimization of a Nonlinear Elastic Plastic Thin-Walled T-Section Beam
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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).
- Doctoral Dissertations