Thermoelastic Analysis Of Lattice Sandwich Structures Based On Novel Implementation Of Asymptotic Homogenization Method

Lattice materials are widely used in aerospace structures due to their high specific stiffness,specific strength,and great potential in multi-functional applications.Because of its large number of mesoscopic components,the lattice structure has a huge workload for numerical modeling and response analysis.It is generally homogenized into a homogeneous structure having an equivalent property,and then structural analysis is performed.This paper analyzes and calculates the equivalent mechanical and thermal properties of three-dimensional periodic lattice core structure and two-dimensional periodic lattice sandwich structure based on the numerical implementation of asymptotic homogenization method(NIAH).For the three-dimensional periodic lattice core structure,the tensile stiffness,bending stiffness and torsional stiffness are calculated by the representative volume element(RVE)method and NIAH method respectively,and the calculation format of local stress downscale analysis of meso-members based on NIAH method is established.The macroscopic displacement response and mesoscopic stress response prediction of the periodic lattice core structure under bending conditions are realized by the format.At the same time,the calculation format of the macroscopic structure frequency analysis is established,and the frequency response prediction of the periodic lattice core layer structure is realized.For the three-dimensional periodic lattice core structure,the equivalent thermal conductivity and equivalent thermal expansion coefficient are calculated by the thermal resistance model method and NIAH method respectively,and the accuracy of the thermal resistance model and the NIAH equivalent heat conduction model are compared.The results show that the former is only suitable for the lattice core of simple configuration,while the latter is more applicable,and can be applied to the calculation of the equivalent properties of complex lattice unit cells,such as lattice structure in the form of gradient.At the same time,the adjustment of the thermal expansion coefficient of the octet truss lattice is realized by adjusting the position of the beam structure,and the influence of the adjustable thermal expansion coefficient on the structural stiffness efficiency is compared.For such weaker unit cells,it is necessary to consider both the shear stiffness and the periodicity requirements in order to obtain more accurate results.For the two-dimensional periodic lattice sandwich structure,the tensile stiffness,the coupling stiffness,the bending stiffness and the shear stiffness are calculated,and the macroscopic displacement response and frequency response analysis of the hourglass gradient lattice sandwich plate are carried out.For the two-dimensional periodic thin-walled composite structural member,the finite element format of its thermal conductivity is derived.The program implementation of finite element is completed and the program is verified by uniform isotropic plate structure.