Variational Asymptotic Equivalent Model And Mechanical Properties Of FRP Concave-convex Plates

The periodic concave-convex plate is a new type of lightweight plate structure.Due to its unique structure,it has good bending resistance,sound insulation and heat insulation performance,strong plasticity and so on.At present,there are few researches on periodic concave-convex plate structure,which limits the application and popularization of concave-convex plate structure.In this paper,based on the variational asymptotic method,combined with the finite element software Abaqus,the static and dynamic characteristics of the bi-directional hemispherical FRP concave-convex plate structure are studied,which provides guidance for the study of the static and dynamic characteristics of the periodic FRP concave-convex plate structure.The main contents and research results are as follows:(1)Based on the variational asymptotic theory,the 2D-EPM(two-dimensional equivalent plate model)of the bi-directional hemispherical FRP concave-convex plate is established according to the energy equivalent principle by using the height of the bi-directional hemispherical concave-convex plate is much smaller than the macroscopic size of the structure.The equivalent stiffness,local displacement field,stress field and displacement field reconstruction relationship of the 2D-EPM of the bi-directional hemispherical FRP concave-convex plate are derived by the variational asymptotic homogenization theory.(2)The global displacement,global buckling,free vibration and local field reconstruction of the 2D-EPM and 3D-FEM(three-dimensional finite element model)are compared.The results show that the the 2D-EPM can accurately predict the global displacement,global buckling,free vibration and local field of the bi-directional hemispherical concave-convex plate,error within 5%.Compared with 3D-FEM,the2D-EPM can effectively reduce the number of elements and nodes,and greatly reduce the calculation amount and improve the calculation efficiency.(3)The equivalent stiffness of the hemispherical FRP concave-convex plate and the ordinary FRP laminates is compared.The FRP concave-convex plate structure can greatly improve the bending stiffness and tensile-bending coupling stiffness of the plate structure.The effective performance of five bi-directional FRP concave-convex plate structures with different convex shapes is compared,and the comparison shows that the bi-directional hemispherical FRP concave-convex plate structure has good structural stability.The influence of different structural parameters on the effective performance of bi-directional hemispherical FRP concave-convex plate is analyzed.The equivalent tensile stiffness and tensile-bending coupling stiffness of the structure increase with the decrease of diameter-to-length ratio(r/l),while the equivalent bending stiffness(except D₁₂)decreases nonlinearly,which makes the first six-order buckling critical loads and natural frequencies of the structure gradually decrease.The equivalent stiffness of the bi-directional hemispherical FRP concave-convex plate increases with the increase of the plate thickness t,and the change of the natural frequency increases approximately linearly,while the buckling critical load increases nonlinearly.The effect of plate thickness t on the effective performance of bi-directional hemispherical FRP concave-convex plate is greater than that of radius r and edge length t of unit cell.(4)Based on the variational asymptotic method,the micromechanics model of fiber-matrix was established.The effects of FRP fiber volume fraction and ply angle on the equivalent engineering constants and structural effective performance of bi-directional hemispherical FRP concave-convex plates were investigated.The results show that the equivalent engineering constant of material and the equivalent stiffness,buckling loads and natural frequencies of structure are positively correlated with the fiber volume fraction,and the influence of changing the fiber volume fraction is greater than that of changing the fiber ply mode.Among the five common ply mode,the antisymmetric paving has the largest buckling loads and natural frequencies.The change of?under specific ply[0/?/0/?/0]_s has little effect on the structural buckling loads and natural frequencies.