Abstract
This is the first attempt to utilize the refined zigzag theory (RZT) to study the bending and buckling behavior of a functional graded (metal/ceramic) thick beam. RZT, which has been exploited for the analysis of multilayered composite and sandwich beams does not employ shear correction factor. Furthermore, the number of kinematics variables of the RZT is not dependent to the number of layers in comparison with the layerwise theory. With regarding to the numerical solution, RZT, also requires C0 continuity interpolation, which leads to the development of this theory in finite element method. It is assumed that the mechanical properties of the beam varies through the thickness. According to the volume fraction of metal and ceramic, it is discretized across the thickness; consequently, the functionally graded beam (FGB) is modeled as a multi-layered one. The beam subjected to uniformly transverse and axial loadings. The equilibrium equations are established using the principle of virtual work. Using the shape functions of the first and second order forms, the non-isoparametric finite element consisting of three nodes and nine degrees of freedom are extracted. To confirm the excellent accuracy of the present approach, some numerical examples are provided and compared with those available in the literature that reveals that RZT is a trusty and validated theory to analyze the FG thick beams.
Highlights
Since multilayer composite structures are included of different mechanical properties through the thickness, depended to material consistent of each layer; there is a discontinuity in normal and transverse shear stresses at the interface between the layers
The idea of establishing the gradual variations in composition of new composites, from heat-resistant ceramics and metals with high machinery ability is formed [1,2]. This demands for new engineering materials has led to the production and development of new kinds of composite materials so called the functional grading material (FGM), which the mechanical and thermal properties change smoothly and continuously
The finite element approach of buckling and bending of FG Timoshenko were considered by exploiting of refined zigzag theory (RZT)
Summary
Since multilayer composite structures are included of different mechanical properties through the thickness, depended to material consistent of each layer; there is a discontinuity in normal and transverse shear stresses at the interface between the layers. The idea of establishing the gradual variations in composition of new composites, from heat-resistant ceramics and metals with high machinery ability is formed [1,2] This demands for new engineering materials has led to the production and development of new kinds of composite materials so called the functional grading material (FGM), which the mechanical and thermal properties change smoothly and continuously. Kahya and Turan [13] suggested an element based on the first-order shear deformation theory to analyze the vibration and critical buckling load of a multi-layered FG sandwich beam. Good accuracy and the convenient application of the RTZ, beside the benefit of avoiding of shear correction factor, as well as the independency of the degree of freedom of elements from the number of layers, evaluated this theory appropriate for analyzing of multi-Layer composite and sandwich structures using the finite element method.
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