Multi-scale Analysis Of Mechanical Properties Of Periodic Composite Structures

With the continuous development of new material technology,periodic composite structures have been widely used in aerospace,automotive and other engineering fields.In terms of structural form,the periodic composite structure is composed of composite materials with a periodic arrangement,and usually has a porous structure;In terms of mechanical properties,the periodic composite structure has excellent mechanical properties such as high specific stiffness,high specific strength and excellent vibration damping properties.In order to meet the actual needs of the engineering field,the microstructure of the periodic composite structure needs continuous to be designed and optimized.So it is necessary to establish the mathematical relationship between the geometric parameters of the microstructure and the macroscopically equivalent mechanical properties,so as to accurately predict the equivalent mechanical properties of the periodic composite structure.In this paper,the mechanical properties of the composite periodic structure were studied.The relationship between the geometric parameters of the representative characteristic unit cells at the Microscopic scale and the equivalent mechanical properties of the macrostructure of the periodic composite structure is discussed.Firstly,based on the multi-scale asymptotic expansion theory,the multi-scale asymptotic homogenization analysis method for bidirectional fiber-reinforced composite material plate structures is proposed.The transversely isotropic carbon fibers and the isotropic resin matrix are selected to form the characteristic unit cell of the bidirectional fiber-reinforced composite plate structure.The multi-scale asymptotic homogenization analysis method is used to obtain the tensile,bending and tension bending coupling stiffness matrix,verifying the effectiveness of our algorithm through simulation analysis.Then,the effects of fiber shape and fiber distance on each stiffness component are discussed.It has great engineering significance for rational use of bidirectional fiber reinforced composite plates.Secondly,the multi-scale asymptotic homogenization analysis method of sine wave-shaped plate structure is studied.The representative volume element of the sine wave-shaped plate is selected.The multi-scale asymptotic homogenization analysis method is used to obtain the tensile and bending stiffness matrix.The calculation result shows that the sine wave-shaped plate structure can be equivalent to a homogeneous orthotropic plate.The influence of the parameters of the sine wave-shaped plate's wavelength,wave height and plate thickness on the stiffness components and the anisotropic parameters of the equivalent plate are discussed.Using the calculated equivalent stiffness parameters,a fast modal analysis of the corrugated plate is performed,and the influence of different geometric parameters of the structure on the vibration frequency of the corrugated plate is analyzed.It has great significance for using the equivalent model to quickly and accurately analyze the static and dynamic mechanics properties of the corrugated plate.Finally,according to the geometrical characteristics of composite honeycomb sandwich panel structure,the macroscopically equivalent mechanical properties were calculated using the double asymptotic homogenization analysis method.First,a three-dimensional periodical asymptotic homogenization analysis is performed on the microscopic scale of the composite material that constitutes the upper and lower panel ply structure,and the macroscopic equivalent elastic matrix of the composite material is obtained to acquire the engineering constant of the composite material.Then,according to the micro-geometrical characteristics of the composite honeycomb sandwich structure,and then applying the asymptotic homogenization analysis of the plate and shell structure to calculate the equivalent stiffness matrix of the structure.Further analysis was made on the effect of different layup methods of the top and bottom panels and the different fiber volume fractions of the composite materials that constitute of the up and down panels on the equivalent stiffness component.It has great engineering significance to reasonably analyze the equivalent mechanical properties of the composite concave honeycomb panel and optimize the structure of the upper and lower panels and the core layer.