Multi-performance Optimization Of Structures And Its Application In Aerospace Structural Design

This dissertation investigates the design optimization of structures under the requirements on the multiple behaviors such as stiffness, frequency, thermal expansion and stability. The stability problems of common skin/stringer stiffened structures are studied for the practical application in aerospace structures. The explicit nonlinear dynamic algorithms are developed to predicte the load carrying capability of post-buckling of this kind of structure under static loading with reasonable engineering accuracy. The optimum design of skin/stringer stiffened structures is realized based on the previous analysis. Furthermore, the effects of mistuning on vibration characteristics of systems with cyclic symmetry (one of parts of mechanics engineering) are studied.The main works of this dissertation are as follows:1. When the SIMP (Solid Isotropic Material with Penalization) approach is employed for the topological design of continuum structures with fundamental frequency objective/constraints, local vibration modes may emerge in the area with relatively low value of design variables. An elaborate investigation is implemented on the causal reason for the local vibration mode. From studies on the continuity of fundamental frequency constraint at the design point where topology changes, the guideline for construction of the smooth interpolation function between the stiffness and the volumetric densities is presented. A novel polynomial interpolation function satisfying this guideline is proposed in order to alleviate the problems of local vibration modes in frequency design. Numerical experiments validate the proposed interpolation functions.2. The problem of topology optimization of structures with high stiffness and low thermal directional expansion subjected to thermal loading is investigated. A new bi-objective structural topology optimization formulation is proposed for the design of structure composed of three materials (two solid materials and one "void material") with differing Young's modulus and thermal expansion coefficients. Three-Phase topology optimization technique is adopted to optimize the structures, and different penalty factors are applied for different phases of materials in order to effectively penalize the intermediate values of design variables. The volume preserving Heaviside filter is adopted to obtain distinct black and white (0/1) solutions and suppress the checkerboard patterns. 3. The optimization problem of structures under thermal loading for maximizing fundamental frequency and critical thermal buckling temperature is considered. The sizing optimization of cross sections of beam and topology optimization of thin plate with the constraint on the amount of material to be used are studied respectively. In the topology optimization of plate for maximizing critical thermal buckling loading, the constraint on the minimum stiffness is introduced aiming at having sufficient mechanical load carrying capability when the critical thermal buckling temperature is increased. In the design for maximizing the fundamental frequency, the optimum designs are different for the problems with thermal loading and without thermal loading. It is found the optimum frequency is increased more significantly for the design with thermal loading. With increasing thermal loading, the optimum solution of frequency design is approaching to the solution of design for maximizing the critical thermal buckling temperature. The numerical experiments present that the critical thermal buckling temperature is significantly increased by design optimization. The designs for maximizing the critical thermal buckling temperature are verified by using nonlinear buckling analysis of ANSYS.4. The post-buckling analysis of ring and stringer stiffened cylinder structures under axial pressure is considered. An explicit algorithm for nonlinear analysis is proposed in this paper to solve the loading carrying capacity of postbuckling of structures with static loads approximately by comparison of the classical different algorithms of stabilization problem considering computational efficiency and precision. The post-buckling behavior of ring and stringer stiffened cylinder structures under axial pressure is analyzed with the algorithm and commercial software LS-DYNA. By tracking the deformati on and stress in the process of buckling of the whole structure, several suggestions are proposed to adjust the positions of the rings in order to increase the post-buckling limits. Based on these principles, the structures are optimized for increasing the limit of load carrying without significant increasing the weight of structure.5. The effects of mistuning on vibration characteristics of coupled pendulum system are studied. Using the mode decomposition method, the motion equations of the system in a dimensionless form are derived. As an example, the modes of vibration and the forced vibration responses excited by engine order excitation for a 5-DOF(degrees of freedom) and a 7-DOF coupled pendulum system are analyzed. Based on the simulation results, the relations between the phenomena of vibration mode localization and frequency response localization and peak split in mistuning system are discussed. The research of this dissertation was partially supported by the National Natural Science Foundation of China (Grant No.90816025,10902018), Analysis and optimization of strength and stiffness of launch vehicle structure (China academy of launch vehicle technology), and the Hi-Tech Research and Program of China (Grant No.2007AA04Z405). This support is gratefully acknowledged by the author.