Homogenization-based Method For Geometrically-nonlinear Analysis Of Composite Structures

Composite structures have important applications in aerospace and other advanced equipment due to their light weight,high specific stiffness and strength,excellent performance and high design freedom.Thin-walled composite structures are the main structure form in the application of aerospace structures.Thin-walled composite structures are prone to large deformation under load,and buckling is an important failure mode.Accurate characterization of geometrical nonlinear properties such as large deformation responses and buckling of composite structures is the key to accurately evaluate structural safety and obtain high quality design.Composite structures are highly heterogeneous,and the solution based on finite element method requires precise mesh,large computation scale and time-consuming.Furthermore,a series of iterations are needed to solve the geometrical nonlinear problems of composite materials,which leads to high complexity and difficulty in solving the finite element method.Therefore,it is of great significance to develop an efficient geometric nonlinear analysis method.This dissertation intends to develop efficient methods,based on the idea of homogenization method,for analysis of large geometric deformation responses and buckling of periodic composite structures.Based on the updated Lagrange iterative scheme,the problem solved by each iteration step is transformed into an elastic problem with equivalent properties and initial stresses,and an analytical method for the equivalent properties and initial stresses is established.In order to solve the buckling problem,the equivalent property prediction method of composite structure was established,which considered the influence of local non-uniform stress field of microstructure,and the two-scale method of buckling analysis of composite structure was established,which considered the influence of initial non-uniform stress distribution.Specific research contents and achievements include:(1)Geometric large deformation analysis of composite structures based on homogenization method.The core idea of the method is based on the Update-Lagrange method and the idea of homogenization method,and the linear elasticity problem of composite material with initial stress solved by each iteration step is transformed into the elastic response problem of equivalent medium with equivalent elastic properties and initial stress,thus greatly reducing the number of discrete mesh and the calculation workload.The calculation formula of the equivalent elastic properties considering the effect of initial stress and the governing equation of the equivalent problem are derived.The realization flow of the equivalent method is given,and a geometric large deformation analysis method of composite structures based on homogenization method is formed.(2)Finite element scheme of homogenization method for large deformation of composite structures and analysis of typical structural properties.Based on the process of homogenizing large deformation analysis method of composite materials,the finite element format of homogenizing large deformation analysis method of composite structures is constructed.The elastic large deformation properties of perforated composite plates and particle reinforced composite plates were analyzed by using the established analysis method.In order to verify the effectiveness of the proposed method,the response results of different sizes of perforated composites were discussed.The results show that the proposed method can accurately give the large-deformation response of composite materials.The accuracy of the method is improved when the number of microstructures(cell)in the composite structure is increased.The results of large deformation analysis of particle reinforced composite plates also have good calculation accuracy.In this paper,the equivalent elastic properties of hollow material and particle reinforced composites considering the effect of initial stress are given,and the influence of the modification of equivalent properties on the topology optimization results is explored.(3)Two-scale method for buckling analysis of composite structures based on homogenization method.Based on the idea of homogenization method for the geometrical large deformation analysis of composite structures,a two-scale analysis method for buckling analysis of composite structures is established.The core idea of this method is to transform the buckling analysis problem of composite structures into the buckling analysis problem of homogeneous structures with equivalent elastic properties and initial stresses.The equivalent elastic properties are determined by the prediction method based on the homogenization method,and the governing equation of the equivalent buckling problem is given considering the effect of the initial stress on the elastic stiffness.The buckling performance of perforated plate and particle reinforced composite plate was analyzed and compared with the traditional analysis method.The analysis results verified the effectiveness of the two-scale method.