Abstract
Bidirectional functionally graded material (2D-FGM) plates have mechanical properties that vary continuously in both the thickness and one-edge directions; these plates are more and more widely used in design and engineering applications. When these structures are subjected to strong loads, they can be largely deformed; therefore, nonlinear calculations, in this case, are necessary. In this paper, nonlinear static bending and nonlinear free vibration behaviors of 2D-FGM plates are studied by using the finite element method based on the third-order shear deformation theory; the Newton-Raphson method is used to solve this problem. The accuracy of this approach is confirmed by comparing the results with respect to other papers. The effects of some numerical aspect ratios such as volume fraction index and thickness-to-length ratio on nonlinear static bending and free vibration of the plates are explored. This study shows that there is a big difference between the numerical results obtained from the nonlinear problem and those from the linear one.
Highlights
Graded materials are a new smart type of composites that were introduced for the first time by Japanese researchers in 1984
For 2D-functionally graded materials (FGMs) structures, their formulations are based on three material components to take advantage of all three materials, where the mechanical properties change in two directions, which are the thickness direction and the longitudinal direction
When P ∗ >5, the results between the linear problem are much different from those of the nonlinear problem. This demonstrates that nonlinear results are much different from linear results when the load applied to the structure has great intensity, so that nonlinear analysis is more useful than the linear one
Summary
Graded materials are a new smart type of composites that were introduced for the first time by Japanese researchers in 1984. The main difference between the new material and the classical composite layer is that the mechanical properties change continuously from one interface to the other. For 1D-FGM structures (usually called FGM structures), they are made up of two different materials (ceramic and metal), in which the material properties vary smoothly from one surface to the other one by the thickness direction. For 2D-FGM structures, their formulations are based on three material components to take advantage of all three materials, where the mechanical properties change in two directions, which are the thickness direction and the longitudinal direction. Considering the mechanical behaviors of these types of structures is really important. It is very helpful in designing, manufacturing, and using them in engineering practice
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