Multiscale Finite Element Method Based On Polyhedral Cells For Fluidic Cellular Structures

Smart materials are widely used in the design of deformable wings.The deformable wings can smoothly and continuously change the shape of the wings,such as the sweep of the wings.The change of the wingspan and the curvature,in response to changing flight conditions,radically improves the aircraft's cruise and sprint capabilities,as well as flight maneuverability.The biomimetic smart materials with the inspiration from the nastic motion of the higher plants are a promising alternative to design smart wing structures,which have extremely high energy density.They have advantages in adaptability,intelligent active control,and have broad application prospects.However,the heterogeneous characteristics of this type of smart structure bring great challenges in the numerical simulations and experimental tests for their mechanical behaviors.First,a three-dimensional extended multiscale finite element method for liquid porous structures is proposed to solve the problem of optimization design of 3D fluidic liquid cellular structures.In this method,the coupled mechanical behaviors of the 3D smart structures with fluidic cells are simulated by extended multiscale finite element method.Furthermore,the 3D structural topology algorithm is developed by combining the multiscale method and the standard topology optimization method to optimize the mechanical behaviors of the plant inspired cellular structures.Consequently,the self-actuated biomimetic compliant mechanisms or minimization of structural compliance about the cellular structures can be efficiently solved by the proposed two-scale methods.Furthermore,the we focus on the lightweight design problems about the fluidic cellular structure under the one or multiple constraints and loading conditions.Finally,Numerical examples of morphing wings are further analyzed to indicate the efficiency of the two-scale topology optimization method used to design the 3D plant inspired cellular structures.Second,a three-dimensional multiscale approach based on the theoretical framework of the multiscale finite element method is proposed to solve the behaviors of heterogeneous materials and structures containing irregular polyhedral inclusions with arbitrary numbers of vertices and faces.The heterogeneous structures are meshed with arbitrary polyhedral elements with coarse-scale sizes,according to the geometric information of irregular inclusions.The mechanical information about the polyhedral inclusions at the fine-scale are constructed through multiscale base functions for the macroscopic deformations of the structures.This work further concentrates on the applications of the proposed method to simulate the smart materials and structures that composed of polyhedral heterogeneous inclusions,such as bio-inspired smart materials with inspirations from nastic movements of plants.Numerical examples of heterogeneous structures such as bionic liquid porous cantilever beam structures and smart wing structures are analyzed by the proposed multiscale method,and the results are compared with those calculated by the standard finite element method.A good correlation between the two method is observed,providing the evidence that the proposed method can accurately predict the behaviors of the heterogeneous materials with polyhedral inclusions.