Sensitivity analysis using fixed basis function finite element technique in structural shape optimization
- Paper number
IAC-06-E2.1.04
- Author
Ms. Tahoura T. Soltani, University of Toronto Institute for Aerospace Studies, Canada
- Coauthor
Prof. J. H. Hansen, University of Toronto, Canada
- Year
2006
- Abstract
As we continue climbing the steps of human evolution toward becoming more efficient, intelligent beings we naturally tend to take our creations with us along this path. On the other hand, the depletion of our energy resources and the destruction of our environment caused by our – sometimes irresponsible- appetite for new technologies, have also had an incredible impact on our design processes and the speed at which the new optimization techniques have been emerging.
The advanced and complex shapes of modern cars, planes and spacecrafts are the result of applying optimization - more specifically Structural Shape Optimization - techniques to preliminary designs. Due to the popularity of gradient based algorithms for shape optimization, sensitivity calculation techniques have naturally become a topic of much research. Methods such as Finite Element analysis (FEA) are also used throughout the design and optimization process to evaluate and analyze the state of the system at each stage. The most commonly used method to determine shape sensitivity, known as the Material Derivative approach, involves explicit or approximate differentiation of finite element matrices. The inaccessibility of these matrices and the reported inaccuracies associated with the results obtained by this method were the motivations for developing a more convenient and accurate technique for finding the gradients. One such new technique is “ Fixed Basis Function” Finite Element analysis. Using this method, in the sensitivity analysis, the variations in the domain of the structure can be assumed to be virtual in a sense that the finite element nodes will not change or move with the varying domain. Instead, the boundary conditions on the adjacent nodes will accommodate the change in the shape. As a result when employing this method the accuracy of the problem solution is dictated by the mesh being used and only modest calculations are involved on top of the reference problem to find the sensitivity matrices.
Computer implementation of the Fixed Basis Function technique, in one and two-dimensions, along with methods like Complex Step and the familiar Finite Difference method, helps to recognize the deficiencies of the conventional Material Derivative approach in sensitivity analysis and provides numerical proof for the validity and convenience of the new proposed technique.
- Abstract document
- Manuscript document
IAC-06-E2.1.04.pdf (🔒 authorized access only).
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