Isogeometric Shape Design Sensitivity Analysis using Transformed Basis Functions for Kronecker Delta Property

In the thesis, two main topics are investigated. Firstly shape sensitivities by NURBS design parameters in the isogeometric optimization such as control points, weights and knots modification are derived and numerically verified. Secondly, the mixed transformation method for isogeometric sensitivity analysis is investigated to impose a kronecker delta property at a desired position. Isogeometric shape optimization method turns out to be effective from easy design parameterization and accurate in sensitivities due to higher order geometric information. NURBS design parameters originated from CAD information are essential parts to define the shape of the model in the isogeometric optimization. To evaluate the effect of NURBS design parameters, shape sensitivities analysis by NURBS design parameters in the isogeometric optimization process such as control points, weights and knots modification are derived and numerically verified. The results imply that a sufficiently refined mesh results in a satisfactory level of shape sensitivities. The rate of sensitivity convergence is different in three NURBS design parameters. The best convergence is observed in change in control points, but in the case of knot changes, only refined mesh gave satisfactory sensitivities. Sensitivity analysis for various loading conditions, including a fixed traction, a design dependent loading and the deformation dependent case is also derived and exactness is assessed. Due to non-interpolatory property of the NURBS basis functions, the treatment of essential boundary condition in the isogeometric analysis is not straightforward as in the finite element analysis. Applying a transformation method to the essential boundary conditions, an isogeometric design sensitivity analysis (DSA) method is developed. Numerical costs for the transformed isogeometric analysis and DSA is comparable or less than the original isogeometric analysis and DSA since the Kronecker delta property of transformed basis functions enables to reduce the size of the system matrix even though an additional transformation is required. The construction cost for the transformed basis functions is not so costly due to the NURBS property that the supports of boundary control points locate only on the boundary. Through numerical examples of essential boundary conditions, the effectiveness of the proposed DSA method is demonstrated and the accuracy and computing costs are investigated.Docto