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Stochastic Analysis and Optimization of Structures

Wei, Xiaofan
http://rave.ohiolink.edu/etdc/view?acc_num=akron1163789451

Abstract Details

2006, Doctor of Philosophy, University of Akron, Mechanical Engineering.
In structural engineering problems, uncertainty is inherent in the load, strength and material property. The resulting stochastic problem can be solved numerically using the computationally intensive Monte Carlo technique. The stochastic finite element method is an alternative approach. This method is based on the perturbation technique. Uncertainties are considered as random variables with a relatively modest fluctuation about the mean. The present study develops the perturbation formulation as the primary stochastic analysis tool. The formulation is analytically elegant and numerically inexpensive. The stochastic analyzer is integrated next into the design optimization testbed CometBoards of NASA Glenn Research Center. The design tool in the stochastic domain was also extended to obtain a robust formulation that can minimize the variation of the objective function. The stochastic analysis utilizes both force and displacement formulations. The force formulation in the literature is referred to as the integrated force method (IFM). Its dual or the dual integrated force method (IFMD) became the stiffness formulation. The first- and second-order perturbation techniques were applied to the governing formulae of force and displacement methods to obtain closed form expressions for the mean and standard deviation of response parameters consisting of internal force, displacement and member stress. Stochastic sensitivity analysis was formulated for selected response variables. The analytical methods also included Neumann expansion with Monte Carlo simulation as well as a variational energy formulation and simplification and reduction on stochastic calculations. Formulas of the stochastic analysis were programmed in Maple V software as well as in the FORTRAN language. Solutions were obtained for a set of examples, which were verified via Monte Carlo simulations. The IFM/IFMD perturbation methods yield response very efficiently for modest fluctuation in random variables. The difference between the first- and second-order perturbations methods was small. The stochastic sensitivity analysis also exhibited a similar trend. The mean value and standard deviation of response are in a good agreement with Monte Carlo simulation obtained for both IFM/IFMD and the regular stiffness method. Optimum designs were generated for the same set of examples for mechanical, thermal and initial deformation loads. The deterministic and stochastic solutions as well as robust designs were compared. The stochastic design solution matched the deterministic results for a fifty percent probability of success (p = 0.5); for other success level the mean value of the objective function increased or decreased with increasing or decreasing the probability of success. The standard deviation of the objective function followed a pattern that was similar to its mean value. The difference between the first- and second-order perturbations was small for both the mean value and standard deviation of objective function or weight of the structure. In summary, this study investigated the probabilistic analytical methods and stochastic optimization for structures. A set of illustrative examples were solved for stochastic analysis, sensitivity analysis and optimization. Structural response and design are influenced by the primitive random variables.
Dr. Michelle Hoo Fatt (Advisor)
Dr. Surya Patnaik (Advisor)
Dr. Graham Kelley (Other)
Dr. Craig Menzemer (Other)
Dr. Dmitry Golavaty (Other)
246 p.
stochastic analysis; structural optimization; sensitivity analysis; integrated force method; perturbation method; Monte Carlo simulation

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Citations

  • Wei, X. (2006). Stochastic Analysis and Optimization of Structures [Doctoral dissertation, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1163789451

    APA Style (7th edition)

  • Wei, Xiaofan. Stochastic Analysis and Optimization of Structures. 2006. University of Akron, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron1163789451.

    MLA Style (8th edition)

  • Wei, Xiaofan. "Stochastic Analysis and Optimization of Structures." Doctoral dissertation, University of Akron, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=akron1163789451

    Chicago Manual of Style (17th edition)

akron1163789451
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© 2006, all rights reserved.
This open access ETD is published by University of Akron and OhioLINK.