Numerical simulation of the thermomechanical buckling analysis of bidirectional porous functionally graded plate using collocation meshfree method

This paper presents some new and valuable numerical results for the thermo-mechanical buckling analysis of bidirectional porous functionally graded plates with uniform and non-uniform temperature rise. The strong form formulation is implemented for thermo-mechanical buckling in the framework of higher-order shear deformation theory. The material property with four schemes of porosity distribution of bidirectional porous functionally graded plate is taken by a modified power law. The governing differential equations are accomplished utilizing the principle of virtual works. The multi-quadric radial basis function is implemented for discretizing the governing differential equations. The multi-quadric radial basis function Euclidean norm is modified to analyze the square as well as rectangular plates without changing the shape parameters. Convergence and validation studies are performed to show the accuracy, effectiveness, and consistency of the present meshfree collocation method. The influence of different porosity distributions, span to thickness ratios, aspect ratios, grading index, temperature raise, boundary conditions, and porosity index on thermomechanical buckling load is evaluated. Some novel results for the bidirectional porous functionally graded plate are also enumerated that can be utilized as benchmark results for future reference.

Finite Element Vibration Analysis of a Functionally Graded Plate

Functionally Graded (FG) materials are recent types of engineering materials Fdeveloped as a solution for applications where a couple of relevant properties of different materials are desired in a single continuous composite structure. In these materials, properties are patterned in a way to insure a gradient and continuous property transition direction-wise. This study is a contribution in the literature among other studies but provides an additional understanding of FG Plate structures vibrational behavior in terms of natural frequencies and modal shapes. For this end, an FG plate is modelized and analyzed using AnsysAPDL. Two boundary conditions (all sides clamped “CCCC” and two parallel sides clamped with two others free “CCFF”) for the same plate element and two power law indices “n” are considered. Results are compared with those in the literature and conclusions are drawn accordingly.

Exact solution by dynamic stiffness method for the natural vibration of porous functionally graded plate considering neutral surface

This paper presents the formulation of dynamic stiffness matrix for the natural vibration analysis of porous power-law functionally graded Levy-type plate. In the process of formulating the dynamic stiffness matrix, Kirchhoff-Love plate theory in tandem with the notion of neutral surface has been taken on board. The developed dynamic stiffness matrix, a transcendental function of frequency, has been solved through the Wittrick–Williams algorithm. Hamilton’s principle is used to obtain the equation of motion and associated natural boundary conditions of porous power-law functionally graded plate. The variation across the thickness of the functionally graded plate’s material properties follows the power-law function. During the fabrication process, the microvoids and pores develop in functionally graded material plates. Three types of porosity distributions are considered in this article: even, uneven, and logarithmic. The eigenvalues computed by the dynamic stiffness matrix using Wittrick–Williams algorithm for isotropic, power-law functionally graded, and porous power-law functionally graded plate are juxtaposed with previously referred results, and good agreement is found. The significance of various parameters of plate vis-à-vis aspect ratio ( L/b), boundary conditions, volume fraction index ( p), porosity parameter ( e), and porosity distribution on the eigenvalues of the porous power-law functionally graded plate is examined. The effect of material density ratio and Young’s modulus ratio on the natural vibration of porous power-law functionally graded plate is also explained in this article. The results also prove that the method provided in the present work is highly accurate and computationally efficient and could be confidently used as a reference for further study of porous functionally graded material plate.