Geometrically nonlinear analysis of 3D fluid actuated cellular structures using extended multiscale finite element method

Abstract

An efficient three-dimensional (3D) multiscale method has been introduced to simulate the geometrically nonlinear behaviors of the plant inspired smart cellular structures. In this method, the scale gap between the geometrical information of motor cells in the small-scale and mechanical behaviors of the cellular structures at the macroscale is bridged through a multiscale framework named multiscale finite element method. The heterogeneous information of the microstructure is then equivalent to the macroscopic coarse elements through the multiscale base functions about the displacements for the solid matrix as well as the fluid pressure. Combined with the “element-independent” corotational algorithm, both the tangent stiffness matrix of the coarse grid elements and their nodal forces can be directly deduced, which will be utilized to decompose the geometrically nonlinear motions of equivalent coarse grid elements at the macroscale level. Consequently, the initial geometrically nonlinear behaviors of the 3D fluidic cellular structures could be simulated by the iteration procedures on the coarse-grid meshes, which will greatly reduce the computation time and memory cost. At the same time, the mechanical responses of the motor cells in the microscale could be easily computed from the obtained macroscopic solutions by the downscaling technique of the multiscale method. To verify the proposed nonlinear multiscale method, some numerical examples are presented. The results demonstrated that the developed nonlinear multiscale formulation for the 3D problems could provide high precision solutions as well as acceptable numerical efficiencies.