Topology Optimization Of Stiffeners In Plate And Shell Structures

Plate and shell structures are widely used in engineering fields. They can not only cover large design space, but also have strong flexibility in shape. Therefore, they are quite popular with engineers. However, in the meanwhile, plate and shell structures always have large deformation, so it is very critical to control the deformation when designing such kind of structures. To address this problem, people normally attach some stiffeners to increase the stiffness of plate and shell structures. But, it is not an easy thing for designers to determine the optimal layout of the stiffeners. So, in this paper, we profoundly explore the optimal layout of stiffeners in plate and shell structures by using the topology optimization technique.(1) We introduce the main topology optimization methods for continua, including homogenization method, variable density method, bubble method, level set method and so on. We analyze the strength and weakness of these methods, and at last choose the variable density method considering its simplicity. We also introduce some papers about optimal design of stiffeners in plate and shell structures, and find that some methods are not perfect, and even can not be implemented in practice.(2) We explore the variable density method systematically. To begin with, we analyze the difference between two material interpolation schemes, SIMP scheme and RAMP scheme, in variable density method, and build the mathematical model of topology optimization for continua. Continuously, we solve this mathematical model by using the optimality criteria method, and derive some useful theoretical equations. In addition, we research the numerical instability phenomenon in topology optimization of continuum structures, put forward some methods to overcome these problems and especially explore the sensitivity filtering method.(3) We develop a program over topology optimization for variable density method based on the ANSYS program. We use some classical examples to test the accuracy and stability of this program, which indicate that this program can be a useful tool to deal with the problem of topology optimization of stiffeners in plate and shell structures.(4) We study the optimal layout of stiffeners in plate and shell structures by means of the program we developed independently. We discuss the optimal layout of stiffeners in different plate and shell structures, and acquire some reasonable results, which can be a valuable reference for designers.