Topology Optimization For Plate And Shell Structure Under Static Loads

Plate and shell structure is rare yet important structural form in engineering due to the fact that it can assume transverse loads. However, the present design method for plate and shell structure largely relies on the former experiences, lacking rational guidance. Consequently, it is cannot tap the potentiality of structure thoroughly. In order to enable optimal design of the plate and shell structure in topological level, it is necessary to apply the topology optimization theory to the design of plate and shell structure. The dissertation is based on Independent Continuous and Mapping (ICM) method. The optimal topologies of the plate and shell structure under static loads are investigated:(1) Based on ICM method, an approximately explicit topological optimization model of plate and shell structure is established to minimize the weight with displacement and stress constraints under multiple loading cases. The model is solved by sequential quadratic programming algorithm which has higher efficiency. In order to adapt the convergence behavior of plate and shell's problem, the graphics filter formulation according to the normal number theory is employed to eliminate checkerboard patterns and mesh dependency. In order to stabilize the optimization process, the dynamic inversion strategy is introduced. Examples show that both the improvement can fulfill their job very well.(2) An explicit formulation of displacement constraint is obtained using Mohr's theorem and the problem of plate and shell's structural topology optimization with weight objective and displacement constraint is solved. The filter function in exponential type is adopted to establish topology optimization model. After the optimization algorithm converges in the continuous space, topology design variables are discretized into 0 and 1 by dynamic inversion. Numerical examples indicate that ICM method can obtain the optimal topologies of the plate and shell structure under different boundary conditions and different displacement constraint values, with less iteration.(3) Based on distortion energy theory, the local stress constraints are replaced by the global structural distortion strain energy constraints. The topology optimization of structural weight minimization with stress constraint is formulated and solved. The stress globalization strategy sharply reduces the number of constraints. Numerical examples demonstrate that ICM method can get the reasonable optimal topologies for the plate and shell structure under stress constraints, with advantages of fast convergence and wide adaptability.(4) ICM method is integrated with commercial finite element analysis software, forming relatively independent topology optimization software for the plate and shell structure. With the joint use of MSC.Patran/Nastran and Matlab, the software is enabled to solve large-scale engineering problems. A fully automated optimization process is also realized, improving the work efficiency. Moreover, the software has friendly user interface in order to facilitate the structural parameters'input and enhance the software's utility.