The Extended Layer-by-layer Method For The Dynamic Fracture Of Functionally Graded Materials

Functionally Gradient Materials(FGM)is a kind of non-uniform material,characterized by continuous change of material properties,ability to adapt to complex environment and material design ability in thickness direction.It is currently widely applied in aerospace,electromechanical,acoustic-optic,petrochemical,nuclear energy and biomedicine.The typical damage pattern of FGM is a complex three-dimensional crack with interlaminar and transverse cracks.In this paper,based on the Extended Layerwise Method(XLWM),the dynamic fracture problem of FGM)plate and shell structures under typical damage mode is studied,which mainly includes the following three aspects:Firstly,the XLWM is applied to analyze the static fracture problems of FGM with damage.By using the displacement assumption in the direction of thickness and the in-plane displacement assumption mode,the displacement fields of multi-layer layered and transverse cracks of FGM plate is constructed,and the static governing equation of FGM plate is established.In the numerical examples,the distribution law of displacement and stress in thickness direction is studied,and the proposed results are compared with that of the existing methods in literature and the 3D models developed in the commercial software,in order to verify the proposed method.Then,the central difference method and the Newmark method are introduced into the XLWM to analyze the free vibration and transient response of the plate and shell structure of functionally graded materials with damage.The influence of gradient index,crack length,number of layers and position of layers on the natural frequency and central deflection is studied.The proposed results are compared with those of literature and the 3D models developed in the commercial software results to verify the proposed method.Finally,the Discrete Damage Zone Model(DDZM)was introduced into the XLWM to solve the embedding problem of materials on both sides of the damaged functionally gradient materials under pressure.The governing equations of damaged FGM plates are derived.The static and dynamic contact problems of damaged FGM plates under pressure are studied by numerical examples.