Isogeometric configuration design optimization of built-up structures in generalized curvilinear coordinates

Abstract

In the thesis, an isogeometric configuration design optimization method for built-up and shell structures based on generalized curvilinear coordinate (GCC) is developed.We derive the isogeometric configuration sensitivity of the Mindlin plates by using the material derivative and adjoint approaches. This is utilized in the configuration design optimization that includes a variation of design components in its shape and orientation. Due to the non-interpolatory property of the Non-Uniform Rational B-Spline(NURBS) basis functions, a mismatch of patches in the built-up structures could occur during the isogeometric design optimization, which can be easily resolved using transformed basis functions. Also, isogeometric configuration sensitivity of shell structures is derived with separating shape and orientation effect. For the shell structures, the design is generally affected by the coupled effect of shape and orientation variations. But, at each material point, exact rotational transformation can be calculated using GCC system and isogeometric approach. An orientation variation is identified as rotational transformation of body-fixed local curvilinear coordinate system. Configuration design sensitivity of shell structure is verified by comparing finite difference sensitivity. And, configuration design optimization is performed for built-up and shell structures The built-up structure is made by combining various elements such as plate, beam and shell. When optimizing the built-up structure, configuration design sensitivity is necessary because shape and orientation variations simultaneously happen. Moreover, in theisogeometric analysis (IGA), the control points play the role of design variables so that no more design parameterization is necessary. Hence, the IGA-based one is suitable for the configuration optimization of the built-up structures By the IGA, the NURBS basis function in computer aided design (CAD) system is directly utilized in the response analysis, which enables the seamless incorporation of higher continuity and exact geometry such as curvature and normal vector into the computational framework. IGA provides a more accurate sensitivity of complex geometries including higher order geometric effects such as normal and curvature information. The impact of exact curvature in the bending problem of Mindlin plates on the configuration design sensitivity is demonstrated through numerical examples. The obtained design sensitivity is further utilized in the configuration design optimization of built-up structures. Configuration design sensitivity analysis (DSA) for shell structure based on GCC system is formulated using direct differentiation method (DDM). In the design sensitivity of the curved structure such as curved beam and shell, it is difficult to separate shape and orientation contributions. They affect design variation at the same time. We divide shape and orientation effects through exact transformation between two local curvilinear coordinate in the original design and perturbed design. It can be possible to calculate accurate sensitivity although amount of design perturbation is large.