UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Reliability-based design optimization using DDM enabled finite elements Gavrilovic, Stevan


Rts is a risk-based structural optimization, multi-platform computer program that incorporates uncertainty into structural analysis with the utilization of random variable parameters. The major contribution to this thesis is that Rts now has the capability to perform reliability-based design optimization using Finite Element Method (FEM) analytical sensitivities. Analytical gradients are exact, more efficient, and convergence is achieved more rapidly in gradient- based optimization methods when compared to finite difference sensitivity methods. For this thesis, I have derived and implemented both nodal and material analytical gradients throughout the Rts framework starting at the finite element level up through to the optimization level. The Reliability-Based Design Optimization (RBDO) model stream includes an FEM model, a COST model, a RISK model with built-in First-Order Reliability Model (FORM), and the orchestrating RBDO model. A program wide Direct Differentiation Method (DDM) framework was additionally established that provides efficient analytical gradient calculations throughout the model stream. The FEM elements implemented consist of the Bilinear-Mindlin four node and nine node plate elements. An academic COST model was created to showcase the multi-model capabilities of Rts and the ability to calculate DDM dependencies of downstream models. Additionally, a RISK model was implemented that incorporated a built-in FORM model with gradient-history capabilities and in-model DDM dependency calculations; the RISK measure used is the mean cost. The RBDO model was also built upon to include DDM capabilities and downstream model integration. Finally, two reliability-based design optimization examples were implemented using both nodal and material sensitivities. The thickness and width of a timber cantilever beam was optimized with respect to mean cost taking into account deflection damage and construction cost.

Item Citations and Data


Attribution-NonCommercial-NoDerivs 2.5 Canada