  Shell structures with a high stiffness-to-weight ratio are desirable in
various engineering applications. In such scenarios, topology optimization
serves as a popular and effective tool for shell structures design. Among the
topology optimization methods, solid isotropic material with penalization
method(SIMP) is often chosen due to its simplicity and convenience. However,
SIMP method is typically integrated with conventional finite element
analysis(FEA) which has limitations in computational accuracy. Achieving high
accuracy with FEA needs a substantial number of elements, leading to
computational burdens. In addition, the discrete representation of the material
distribution may result in rough boundaries and checkerboard structures. To
overcome these challenges, this paper proposes an isogeometric analysis(IGA)
based SIMP method for optimizing the topology of shell structures based on
Reissner-Mindlin theory. We use NURBS to represent both the shell structure and
the material distribution function with the same basis functions, allowing for
higher accuracy and smoother boundaries. The optimization model takes
compliance as the objective function with a volume fraction constraint and the
coefficients of the density function as design variables. The Method of Moving
Asymptotes is employed to solve the optimization problem, resulting in an
optimized shell structure defined by the material distribution function. To
obtain fairing boundaries in the optimized shell structure, further process is
conducted by fitting the boundaries with fair B-spline curves automatically.
Furthermore, the IGA-SIMP framework is applied to generate porous shell
structures by imposing different local volume fraction constraints. Numerical
examples are provided to demonstrate the feasibility and efficiency of the
IGA-SIMP method, showing that it outperforms the FEA-SIMP method and produces
smoother boundaries.
