Generalized Mixed Finite Element Method For Stress Concentration Around A Circle Hole In Composite Structure

Composite materials have been widely used in modern aircraft structures.In order to meet the need of assembly,holes or openings are often made in composite plates.For this kind of structure,the biggest problem is the stress concentration at the hole edge.Due to the particularity of mechanical behavior of composite laminated plates and shells,there is no analytical formulas for calculating the stress concentration factor of hole in such structures.In the design of engineering structures,people can usually only solve problems with experiments and numerical methods like finite element method.The most common displacement finite element method is difficult to give more accurate results when the mesh is sparse.Therefore,It is of great engineering significance to study and explore more efficient and reliable numerical methods.The main research contents of this paper include:(1)Based on the analysis of the advantages and disadvantages of common displacement finite element method and classical hybrid finite element method,this paper firstly derives the compatible mixed element formula by the H-R variational principle.Then,based on the generalized H-R variational principle,a generalized mixed finite element formula and a noncompatible generalized mixed finite element formula are established.On the other hand,considering the computational efficiency,a noncompatible generalized mixed finite element substructure is proposed for analyzing stress values in high stress regions.(2)In order to verify the reliability and accuracy of the proposed method,the programs of compatible and noncompatible generalized mixed finite element method and noncompatible generalized mixed finite element substructure method are written on the basis of Mathematica FEM package.Firstly,the 2D 8-node element of the above three methods are used to analyze stress of high stress position of the isotropic material plate,which proves the correctness and reliability of the three finite element methods.The numerical results show that the accuracy of the noncompatible generalized mixed finite element substructure is basically the same as that of the noncompatible generalized mixed finite element.The above three finite element methods are extended to analyze the problem of the stress concentration factor of the single-layer anisotropic composite laminates with hole,which further proves the correctness of this method.(3)In order to analyze the stress concentration factor problem of the 3D composite laminates with hole,firstly,considering the problem of composite laminate which has accurate solution,and verify the correctness of various generalized mixed finite elements methods.Then,the influence of the ply angle of the composite laminate with hole on the stress concentration factor results is analyzed in detail.Compared with the related literature,the values of the noncompatible generalized mixed finite element method and the noncompatible generalized mixed finite element substructure are reliable.The research work in this paper provides an effective new finite element method for the analysis of stress concentration factors of composite laminates with hole.