| Inspired by natural biomaterials and the development of composite manufacture process and new design concepts,a series of multi-functional composites with light weight and various excellent properties and their new structures have gradually emerged,which show a very broad application prospects in aerospace and other high-tech industries.This kind of new composite structure usually shows the characteristics of thin-walled plate and shell structure on the macro scale,and has the distribution and micro structure characteristics of heterogeneous component materials on the micro scale.It is helpful to guide the design and application of new multi-functional composite structures by deeply understanding the influence of different scale materials and multi-level microstructures on macroscopic properties.Due to the large difference between the maximum and minimum eigenvalue sizes of hierarchical composite structure,s the conventional finite element method based on the fine model needs huge computational resources and computing time,and even is difficult to analyze directly.Especially,when it comes to geometric nonlinearity analysis,damage evolution and structural optimization design,a large number of iterations increase the computational complexity of conventional finite element method dramatically and even become infeasible.In order to solve the above problems,a multiscale finite element method is developed in this paper,which can accurately and efficiently solve the large-scale numerical problems of composites with hierarchical microstructure characteristics.Firstly,a multiscale finite element method for linear elastic analysis of composite laminated plates with complex microstructures is proposed.Based on the thin plate theory and the theoretical framework of Extended Multiscale Finite Element Method(EMsFEM),the macro and micro finite element formulas of composite laminates with directional and layered characteristics are derived.Based on the coupled displacement modes of deflection and rotation in Kichhoff s thin plate theory,the decoupled nonlinear displacement boundary conditions are established by taking the displacements of macro nodes as zero and interpolating for micro nodes.By introducing additional coupling terms of multiscale basis functions among tension,bending,shear and torsion,the multiscale basis functions reflecting the coupling effects of composite laminates are accurately constructed.Numerical examples show that the proposed multiscale finite element method has well applicability and computational accuracy.Compared with the traditional finite element method,the computing efficiency is significantly improved.It is suitable for multiscale analysis of thin composite laminated plates with aperiodic microstructural characteristics and significant coupling effects.Secondly,an incremental/iterative multiscale finite element method for geometrically nonlinear analysis of thin-walled composite structures is developed.Based on Von-Karman large deflection theory and Total-Lagrange scheme,the incremental strain-displacement relationship for geometrically nonlinear analysis of thin-walled composite structures is described,and the incremental microscopic finite element formulation is derived.An oversample technique considering the full coupling effects of degrees of freedom is proposed to construct oscillating decoupled displacement boundary conditions reflecting the deformation characteristics of thin-walled composite structures.Based on the incremental microscopic FE formulation and the oscillating decoupled displacement boundary conditions,the multiscale basis functions considering the effects of anisotropy,lamination characteristics and coupling effects of composites are numerically constructed.The equivalent tangent,secant stiffness matrices and load vectors of macroscopic elements are derived,and the incremental macroscopic FE formulation is established.Based on Newton-Raphson iteration method,an incremental/iterative multiscale finite element model is established to carry out macroscopic and downscaling incremental/iterative computation.Among them,the macroscopic computation results can be used to construct the downscaling boundary conditions,while the down scale computation results can be used to update the macroscopic equivalent stiffness matrices and unbalanced load vectors.An incremental decoupled displacement boundary condition is constructed.The microscopic disturbance displacement is obtained by down scale computation.The macroscopic equivalent stiffness matrices and unbalanced load vectors are modified.The macro and micro responses are obtained by iteration until the multiscale iteration converges.By two groups of representative examples,it is proved that the developed multiscale analysis method has good computational accuracy and convergence.The effects of different oversample techniques on the computational accuracy are compared.The results obtained by using the oversample technique considering full coupling effects of DOF are more accurate.At the same time,compared with the conventional finite element method,the computing storage space and time required by the multiscale method are reduced significantly.Furthermore,a multiscale finite element method for geometrically nonlinear problems of composite grid structures with arbitrary stiffeners is proposed by using the mixed plane shell elements of micro triangles and macro rectangles.This method not only guarantees the physical fidelity of microscale computation,but also improves the efficiency of geometrically nonlinear analysis of composite grid structures.Two kinds of multiscale modeling strategies are proposed for composite grid structures,and corresponding extended displacement boundary conditions are constructed.On this basis,the virtual degree of freedom and additional coupling terms are introduced to consider the local reinforcement effects of grid structures and the coupling effects of composites,and the corresponding multiscale basis functions are constructed numerically.The geometric nonlinearity of composite grid structures with different reinforcement density,height and configuration are analyzed by multiscale computation.The application scope of different modeling strategies is compared,and the causes of errors are analyzed.Compared with the results of homogenization method,the multiscale finite element method has higher computational accuracy and applicability.Compared with the traditional finite element method,the developed multiscale finite element method has higher computing efficiency.This method has great potential in multiscale damage analysis and ultimate bearing capacity prediction of composite grid structures.In addition,in order to analyze the influence of micro and meso characteristics of component materials on the macro mechanical behavior of composites,based on the developed multiscale analysis method of laminated composite plates,a hybrid multiscale finite element model is proposed based on the plate and shell elements,super parametric shell elements and three dimensional solid elements.Based on the relationship between the displacements of the master-slave degrees of freedom of the super parametric shell element,the multiscale basis function connecting the stiffness matrix of the macro shell element and the micro three dimensional solid element is constructed to realize the effective transmission of the element information between different scales.Three groups of composite thin plates with different microstructure characteristics are analyzed,including fiber-reinforced composite lamina,laminate and thin plate with winding characteristics.The results show that the proposed hybrid multiscale model has high computational accuracy and consumes less computing time and resources.Finally,based on the multiscale finite element method and the bybrid multiscale model,a multiscale hybrid iterative analysis method is proposed to obtain the initial structural response through fast increment/iteration on the macro scale,and modify the structural response by multiscale iterative computation.The developed method can accelerate the process of multiscale iteration analysis while ensuring the accuracy,and further reduce the storage space and computing resource requirements in the multiscale iteration computation process.It is suitable for multiscale computation of composite structures with large loads and strong nonlinearity,especially.The developed method is carried out for hierarchical composite structures with stiffeners and hybrid fibers.The effects of structural characteristics such as ratio of height of stiffeners and configuration of hybrid fibers at different levels on computational accuracy are discussed.The good applicability of the proposed is verified. |
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