| An approach for the determination of solution sensitivity to changes in problem domain, using a new method referred to as a 'fixed basis function' finite element shape sensitivity analysis, is further developed. This approach is developed from the finite element force displacement formulation; however, the finite element basis functions and grid are fixed during the sensitivity analysis. This new sensitivity analysis does not require explicit differentiation of stiffness matrices, force vectors or displacement vectors; the sensitivity to boundary shape change is determined exactly. An overview of the analysis is illustrated by a one-dimensional problem. Then the work is further developed and applied in some two-dimensional plate problems. A beam similar to the aircraft support beam used in Air Bus passenger carrier is redesigned and optimized; the new sensitivity analysis is used to calculate the design gradient during the optimization. The analysis is then applied in a more complicate plate optimization problem. Finally, the advantages and possible improvements for the approach are mentioned in the conclusion. |
