This dissertation addresses the ultimate strength analysis of nonlinear beam-columns under axial compression, the sensitivity of the ultimate strength, structural optimization and reliability analysis using ultimate strength analysis, and Reliability-Based Design Optimization (RBDO) of the nonlinear beam-columns. The ultimate strength analysis is based on nonlinear beam theory with material and geometric nonlinearities. Nonlinear constitutive law is developed for elastic-perfectly-plastic beam cross-section consisting of base plate and T-bar stiffener. The analysis method is validated using commercial nonlinear finite element analysis. A new direct solving method is developed, which combines the original governing equations with their derivatives with respect to deformation matric and solves for the ultimate strength directly. Structural optimization and reliability analysis use a gradient-based algorithm and need accurate sensitivities of the ultimate strength to design variables. Semi-analytic sensitivity of the ultimate strength is calculated from a linear set of analytical sensitivity equations which use the Jacobian matrix of the direct solving method. The derivatives of the structural residual equations in the sensitivity equation set are calculated using complex step method. The semi-analytic sensitivity is more robust and efficient as compared to finite difference sensitivity. The design variables are the cross-sectional geometric parameters. Random variables include material properties, geometric parameters, initial deflection and nondeterministic load. Failure probabilities calculated by ultimate strength reliability analysis are validated by Monte Carlo Simulation. Double-loop RBDO minimizes structural weight with reliability index constraint. The sensitivity of reliability index with respect to design variables is calculated from the gradient of limit state function at the solution of reliability analysis. By using the ultimate strength direct solving method, semi-analytic sensitivity and gradient-based optimization algorithm, the RBDO method is found to be robust and efficient for nonlinear beam-columns. The ultimate strength direct solving method, semi-analytic sensitivity, structural optimization, reliability analysis, and RBDO method can be applied to more complicated engineering structures including stiffened panels and aerospace/ocean structures. / Ph. D. / This dissertation presents a Reliability-Based Design Optimization (RBDO) procedure for nonlinear beam-columns. The beam-column cross-section has asymmetric I shape and the nonlinear material model allows plastic deformation. Structural optimization minimizes the structural weight while maintaining an ultimate strength level, i.e. the maximum load it can carry. In reality, the geometric parameters and material properties of the beam-column vary from the design value. These uncertain variations will affect the strength of the structure. Structural reliability analysis accounts for the uncertainties in structural design. Reliability index is a measurement of the structure’s probability of failure by considering these uncertainties. RBDO minimizes the structural weight while maintaining the reliability level of the beam-column. A novel numerical method is presented which solves an explicit set of equations to obtain the maximum strength of the beam-column directly. By using this method, the RBDO procedure is found to be efficient and robust.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/82958 |
| Date | 30 April 2018 |
| Creators | Li, Zhongwei |
| Contributors | Aerospace and Ocean Engineering, Patil, Mayuresh J., Kapania, Rakesh K., Wang, Kevin Guanyuan, Brown, Alan J. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Dissertation |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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