Nonlinear Behavior of Functionally Graded Plates Containing Crack under Compression

Following the efforts of material scientists to obtain materials with very high thermal resistance, functionally graded materials (FGMs) were first introduced in 1984 by Koizumi [1] in Japan, which can be used in aircrafts, space vehicles and other engineering structures. These materials are made of a mixture of two different materials, usually one metal and another ceramic, so that the properties of the resulting composition change uniformly and gradually varying the volume fraction of constituent. The benefits of FGMs have helped to increase their popularity in engineering programs and have attract the attention of researchers to get a better understanding of their mechanical behaviors. Functionally graded plates (FGPs) can withstand under compressive mechanical loads more than the buckling load and for this reason many researchers have investigated the behavior of these structures after the buckling. In this situation, some failures such as cracks may occur in these plates. Understanding the nonlinear and post-buckling behaviors of these structures that contain crack are very important in the design procedure. However, a number of research papers have been published on the nonlinear analysis of FGPs such as work done by Alinia and Ghannadpour [2]. They have investigated the effect of nonlinearity on FGPs under lateral pressure loading. Tung and Duc [3] have studied the stability of a simply supported rectangular functionally graded plate under the influence of the volume fraction index, plate geometry, in-plane boundary conditions and imperfection on post-buckling behavior of the plate under mechanical and thermal loading. In recent years, a considerable bulk of research have focused on the investigation of the effect of material non-homogeneity on various failure mechanisms such as crack. Chen and Lin [4] have solved the elastic analysis FGPs that contain an edge-cracked under longitudinal tension loading with finite element method. Nasirmanesh and Mohammadi [5] have worked on the vibrational behavior of cracked FGM shells with XFEM formulation. In this study, nonlinear behavior of edge and internally cracked functionally graded plates have been investigated. The nonlinear formulation is based on the First-order Shear Deformation plate Theory (FSDT), in which geometric non-linearity is presented in the way of the Von-Karman assumptions for the strain-displacement equations. Legendre polynomials for the primary variable approximations are used in the Ritz method. The crack is modeled by dividing the entire domain of the laminates into several sub-plates and therefore, a plate decomposition technique is applied. In this study, penalty technique is used to enforce interface continuity between the sub-plates. Three types of out-of-plane essential boundary conditions such as clamp, simply support and free conditions have been investigated in this research. The laminated plates can be subjected to biaxial compressive loads and then a sensitivity analysis is done with respect to the crack direction along the parallel and orthogonal to the load axis. The integrals of potential energy are numerically computed by Gauss-Lobatto quadrature formulas to get adequate accuracy. Then, the obtained non-linear system of equations is solved by the Newton\u2013Raphson method. After that, the results are presented for influence of crack length, various locations of crack, crack direction, variation of volume fraction and boundary conditions. References [1] M. Koizumi, The concept of FGM, Ceramic Transactions Functionally Gradient Materials, 1993. 34: p.3-10. [2] M.M. Alinia, S.A.M.Ghannadpour, Nonlinear analysis of pressure loaded FGM plates, Composites Structures, 2009. 88: p.354-359. [3] H.V. Tung, N.D. Duc, Nonlinear analysis of stability for functionally graded plates under mechanical and thermal loads, Composites Structures, 2010. 92: p.1184-1191. [4] Y.Z. Chen, X.Y. Lin, Elastic analysis for a finite cracked plate of functionally graded materials, Multidiscipline Modeling in Materials and Structures, 2007.3: p.361-382. [5] A. Nasirmanesh, S. Mohammadi, An extended finite element framework for vibration analysis of cracked FGM shells, Composites Structures, 2017.180: p.298-315

Functionally graded multi-morphology lattice structures as an optimized sandwich core via digital light processing additive manufacturing

This investigation aims to present a high-strength sandwich core with functionally graded multi-morphology lattice inner structures through vat photo-polymerization additive manufacturing (AM). The five better strut-based designs based on [1], are considered here. All printed specimens have been fabricated from photopolymer resin to ensure manufacturability in a digital light processing (DLP) 3D printer. Firstly, the resin and structural characteristics have been examined. Simultaneously, the lattice core is divided into three regions based on the von Mises stress distribution and tensile and compression responses in finite element analysis (FEA). Based on the mechanical responses of the beam-based structures, these topologies have been applied in each region in an optimal fixed relative density distribution, considering different steps and types. This proposed technique is numerically investigated and experimentally validated using a three-point bending test. As a result, the optimized core demonstrated a 96% increase in maximum fracture force and a 174% increase in stiffness compared to the homogeneous body. Additionally, it exhibited a different deformation mode than the single morphology under similar conditions. These significant findings indicate that this approach provides a new perspective on a high-strength design involving more than three morphologies, and it is faster than computational topology optimization processes