Analysis and Optimization of Laminated Composite Shell Structures

The objective of the present work is to develop finite element based optimization techniques for laminated composite shell structures. The platform of implementation is the finite element based analysis and design tool MUST (MUltidisciplinary Synthesis Tool) and a number of features have been added and updated. This includes an updated implementation of finite elements for shell analysis, tools for investigation of nonlinear effects in multilayered topology optimization and a novel framework called Discrete Material Optimization (DMO) for solving the material layout and orientation problem. A necessary tool for optimization is robust finite elements and consequently, the finite element library in MUST is extended with a new three-node element and an updated four-node element. These are designated MITC3 and MITC4, respectively, since they use Mixed Interpolation of Tensorial Components to avoid problems with shear locking. The SHELLn family of standard isoparametric shell finite elements in MUST has also been updated for improved performance. All elements have laminate and geometrically nonlinear capabilities and tests show that the performance and computational efficiency are very good. Geometrically nonlinear effects are investigated to determine if these should be taken into account when designing for maximum stiffness of laminated composite structures using structural optimization. Facilities for nonlinear topology optimization of multilayered shell structures is implemented using a Newton-Raphson scheme for the analysis, the adjoint variable method for sensitivity analysis and the MMA optimizer for solving the optimization problem. The SIMP method is used for layer-wise stiffness scaling to allow material to be added/removed in specific layers. Several examples illustrate the effect of the nonlinearities on the optimal topologies and, depending on the problem, the increase in performance is significant. Existing methods for solving for optimal material orientation and maximum stiffness inherently suffer from problems with local optima, which inspired the development of Discrete Material Optimization (DMO), which is a novel approach for simultaneous solution for material distribution and orientation. The DMO method uses an element level parametrization in a weighted sum formulation that allows the optimizer to choose a single material from a set of pre-defined materials by pushing the weights to 0 and 1. The success of the method is therefore dependent on the optimizers ability to push the weights to 0 and 1 and several weighting schemes are implemented. Numerical examples indicate that the method is indeed able to solve the combined material distribution and orientation problem. Furthermore, an industry related design problem of a wind turbine blade main spar is solved and the obtained results are very encouraging. The DMO method thus shows promising potential for application to problems of industrial relevance and no problems with local optima could be identified in the tested examples.