Failure Behavior And Optimization Of Hierarchical Corrugated Structure With Second-Order Core Based On Mindlin Plate Theory

As a type of new lightweight structure, hierarchical corrugated structures with second-order core have a broad application prospect in automobile, aerospace industry and bridge structures due to high strength-to-weight and stifness-to-weight ratios. However, multiple failure modes may occur at each level of hierarchical corrugated structures, which may be dangerous for engineering applications, and also this makes it possible to design distinctive structures with various properties to meet different requirements. Existing studies mainly focus on the mechanical characteristic, failure modes, performance design of hierarchical corrugated structures, however, with the increase of structure thickness, the error of existing methods becomes unacceptable. Therefore, the Mindlin plate theory is used to analyze the failure behavior of hierarchical corrugated structures with second-order core in this dissertation, and moderately thick plate model is then established through derivation. The main work of this dissertation includes the following three parts:(1) The analytical expressions of the nominal stress of six failure modes of the unit cell are derived based on the moderately thick plate model of second-order hierarchical corrugated structures under compressive or shear loads. Also, elastic beam model and thin plate model in the literature are expanded, and then the angles of the large struts and small struts can be arbitrary. The precision of the moderately thick plate model is compared with the results of six different unit structures by using the finite element methods (FEM). Structures with different thicknesses are investigated to validate the applicability of the moderately thick plate model. The results are also compared with the thin plate model and verified by using FEM as the benchmark.(2) Moderately thick plate model and thin plate model are used to analyze the failure behavior of the sandwich beam with second-order hierarchical corrugated core, respectively, where three load conditions are considered:three-point bending, uniform load and concentrated load, respectively. The failure modes can be classified into eight categories according to the failure regions and types, i.e. plastic yielding and elastic buckling of surface plate, plastic yielding, elastic buckling, wrinkling and shear buckling of large struts, plastic yielding and elastic buckling of small struts. The analytical expressions of corresponding limit load of the eight failure modes under three load conditions are further given.(3) Multi-objective optimizations of the unit cell in the second order hierarchical corrugated structures are performed based on the simplified moderately thick plate model and thin plate model with failure modes constraints. To be specific, the failure modes can be designed by comparing the nominal stress and the deflection of the structure (obtained by FEM). Two optimization formulations are established, one is controlling a special failure mode occurs first, while another one classifies the failure modes into two grades considering the loss degree, then controlling the failure mode occurs in a specific sequence. The NSGA-II algorithm is used to minimize both weight and deflection, on this basis, the performance index of several typical design points from the Pareto front of two models is discussed. Finally, the failure modes are verified by FEM, and the respective constraints are satisfied.