Study On Isogeometric Shape Sensitivity Analysis Of Shells

The sensitivity is a key issue in shape optimization of shells. The optimization domain isusually described by grid nodes in traditional shape optimization of shells, it is difficult toestablish explicit association between the grid and the optimization parameter. Therefore, theanalytical solution of the shape sensitivity is difficult to obtain. The sensitivity is usuallycalculated with semi-analytical method which has many defects: the calculation accuracy isdepended on differential step and the computational efficiency is low. These defects lead tolow efficiency of the optimization, and even cause optimization failure duo to inaccuratesensitivity. The NURBS-based isogeometric analysis use the same basis to describe CADmodel and analysis model, and the NURBS basis and its derivates have analytical expressions,so the analytical expressions of sensitivity which can avoid the defects efficiently can becomputed in isogeometric analysis.In this thesis, the analytical expression of sensitivity used in shape optimization of shellsis derived, and based on isogeometric analysis, the shape optimization of shells is fulfilledwith the sensitivity. Firstly, Isogeometric analysis is used in the finite analysis of the shells.Including: describing the shell displacement field with NURBS basis; constructing elementstiffness matrix with Jacobian matrix and displacement matrix; and assembling stiffnessmatrix to construct the total stiffness matrix. Finally, based on Reissner-Mindlin theory, anisogeometric analysis for3D shell is fulfilled on Matlab. The validity of isogeometric analysisfor3D shell is verified with a numerical example of a typical3D shell.Based on the isogeometric analysis of shells, the sensitivity is evaluated analytically. Inorder to obtain the sensitivity, the analytical computational formulae of the strain-displacement matrix, the Jacobin matrix and the stiffness matrix with respect to the positionsof the control points are calculated. Effectiveness of the presented analytical methods ofsensitivity is demonstrated with comparisons to the semi-sensitivity method. Finally, a shell isoptimized with this method.