Mechanical Properties And Optimal Design Of Hierarchical Corrugated Structure With The Second Order Core

Hierarchical cellular structure is a kind of reasonable "lightweight" structure, which can exhibit significant higher ratioes of strength to weight and stiffness to weight, and low relative density. It has been widely used in the aerospace, marine, civil and vehicle engineering and other fields. Although many researches were focused on the the hierarchical cellular structure, there is still a gap between the theoretical research and the practical applications because the hierarchical cellular structure has abundant failure modes, complex boundaries and geometrical parameters with different magnitude orders. The current researches on mechanical properties, failure mechanism, simplified models and design of the hierarchy are not enough. Therefore, the theories of elastic plates and Hoff s sandwich plates are used to analyze the mechanical property and failure modes of the second-order hierarchical corrugated truss structure in this dissertation. And it is also used to analyze the bending behavior of a sandwich beam with a second-order hierarchical corrugated truss core. Moreover, based on the deformation compatibility condition, the equivalent orthotropic elastic constants of the sandwich plate with a second-order hierarchical corrugated core were studied. Finally, to satisfy the different performance requirements of the second-order hierarchical corrugated truss structure, several optimization models were constructed.The main works of this dissertation are given as follows:(1) The theories of elastic plates and Hoff s sandwich plates are used to analyze the failure modes of the second order hierarchical corrugated truss structure. A plate model for the prediction of failure mode and bearing capacity is supplied. Besides the six competing failure modes obtained in the literature using the elementary elastic beam theory, another five competing failure modes have been identified herein, including the buckling plate and infinitely wide plate buckling of the small struts, sandwich plate buckling, infinitely wide sandwich plate buckling and surface wrinkling of the large struts. Expressions for the nominal stress of these modes under the compressive load are derived and used to construct failure mechanism maps for second order trusses, which is effective for selecting the geometries of second order trusses. It is found that there is a threshold value between the shear buckling of the large struts and the plastic yielding of the small struts. The failure modes have been classified and summarized with regard to the geometric parameters. By comparing the results of the finite element method (FEM), it shows that the plate model has higher accuracy than the beam model.(2) The bending behavior of sandwich beam with the second hierarchical corrugated core is analyzed. The plate model was used in the failure mode analyses. Compared with the classical sandwich beam with continuous medium core, the sandwich beam with porous discontinuous core has more failure modes. From the perspective of elastic-plastic buckling and yielding, the classical failure modes of core are subdivided into six competing modes. The expressions of the ultimate bearing capacity for the sandwich beam are derived and used to construct failure mechanism maps. And the influence of different geometry parameters on the failure mechanism has been discussed. Moreover, a correction factor, related to the structure form of core, is proposed to consider the contribution of the shear deformation core on sandwich beam deflection. And the accuracy of the modified formula is significantly improved. By comparing the results of the FEM, the influence of the geometric parameters on the accuracy of the proposed formula is studied, and the theoretical formula is verified. In addition, it is found that the bearing components of the sandwich beam under transverse loading are the surface plates and the surface sheets of the large struts.(3) The equivalent orthotropic elastic constants of the sandwich plate with a second order hierarchical corrugated core are studied by two-stage equivalent procedures. First, based on the "sandwich" equivalent and deformation compatibility conditions, the large struts is equivalent to an orthotropic solid. Through coordinate transformation, the constitutive relation of the equivalent orthotropic material in the new coordinate system is obtained. Then, the second-order hierarchical corrugated structure is viewed as a sandwich plate with a triangular truss-core, which is made of an orthotropic solid obtained by the first stage equivalent procedure, and is also equivalent to an orthotropic plate. The equivalent orthotropic elastic constants of structure with the second-order hierarchical corrugated core are obtained by the equivalent deformation. By comparing the results of the FEM, the error distribution of the equivalent formula is discussed, and the equivalent formulas are modified. In addition, the equivalent elastic constants are applicable to the deflection calculation of the sandwich beam in three-points bending. It is found that the results based on the equivalent elastic constants in this paper have a higher accuracy, compared with the results in the literature.[4] Cosidering the abundant failure modes and their different features of the second-order hierarchical corrugated structure, two kinds of optimization formulas are proposed:optimal desig of the structural weight and optimal design of the structural mechanical properties. The former contains two optimization models:optimal design of structural weight with the constraint of a given failure mode or a given failure sequence. And the latter contains four optimization models:maximising the strength subject to a given relative density, optimizing the equivalent elastic constants, minimizing the deflection of sandwich beam with a second-order hierarchical corrugated core and maximising the deformation energy subject to a given failure mode. Wherein, based on the relationship between load and deformation of the second-order hierarchical corrugated structure, the formula of the deformation energy is derived. And a differential equation is constructed to describe the bending deformation of the sandwich struts under the combined loads of axial force, shear force and moment. The optimization examples show that the optimized performance indices are improved significantly, which can help the designers to achieve a desired rational design.