Study On Mechanical Properties Of Bi-periodic Trapezoidal Corrugated Plate Based On Variational Asymptotic Method

The bi-periodic trapezoidal corrugated plate is a new type of structure with light weight,high strength and good energy absorption characteristics,which shape changes periodically along two plane directions.At present,the research is mainly focused on the uni-periodic change corrugated plate,and there is little research on the relationship between its mechanical properties and structural parameters of the bi-periodic trapezoid plate,limiting the popularization and application of this structure.Based on the fact that the period of the corrugated shape is much smaller than the size of the whole plate structure,a numerical model of the represent element called unit cells established by using the variational asymptotic method to calculate the equivalent stiffness with the variational asymptotic method as the theoretical basis for analysis and calculation.Combined with the finite element discrete technology for calculation,it provides guidance for the performance research of bi-periodic trapezoidal corrugated plate structure.The main contents and conclusions of this paper are as follows:（1）The period of the bi-periodic trapezoidal corrugated plate is far less than the size of the whole structure.According to this feature,based on the variational asymptotic theory,the equivalent model of the bi-periodic trapezoidal corrugated plate is established from the perspective of energy concept.By extracting the structure genome of the bi-periodic corrugated plate structure,the stress characteristics of the trapezoidal structure genome are analyzed in depth,and combined with the periodic boundary conditions,the equivalent stiffness characteristics,the reconstruction of local stress field and displacement field are obtained.The results show that compared with the base plate,the tensile stiffness of the bi-periodic structure is greatly reduced and the bending stiffness is significantly increased.（2）Combining the variational asymptotic homogenization software Swift Comp and the general finite element software Abaqus,the accuracy of the homogenization model and the feasibility of Swift Comp mechanical analysis are verified by comparing the global displacement response,buckling analysis and local field reconstruction of the double period trapezoidal corrugated plate.The results show that the error of displacement and reconstruction field can be controlled within 1%,and the error of buckling eigenvalue is within 5%.It is analyzed that the relationship between the equivalent stiffness characteristics and the structural parameters of the unit cell of the bi-period trapezoidal structure.The results show that the equivalent stiffness and structural parameters of the bi-period trapezoidal corrugated plate show obvious non-linear change law.With the increase of spacing,A₁₁、D₁₂and D₃₃ increase,A₁₂and D₁₁ decreases,while A₃₃has little effect.With the increase of height,A₁₁ and A₃₃decrease,A₁₂ decreases and then increases,D₁₁ and D₃₃ increase,and the effect of height on D₁₂ changes with spacing.（3）According to the total energy functional of fiber-reinforced composite,the constitutive model of fiber-reinforced material is established,and the regularity between the equivalent stiffness characteristics and parameters of the bi-period trapezoid structure of fiber-reinforced composite is explored.The results show that through the combination of layers with different layup angles,and the optimization of the structural properties of the anisotropic composite can be realized by the combination of different layupply.