Comparison of Deflection in Two-Directional Functionally Graded Tapered Beam

Abstract

Traditional engineering materials lack the necessary properties that are needed in aerospace as well as other modern industries. In order to address the aforementioned problem, a number of different materials are used in concert. With the help of functionally graded material, all the necessary characteristics can be achieved. A fast transition between two different materials can lead to debonding, thermal stresses, residual stresses, and stress concentrations; a gradual change in material properties might mitigate these problems. This work provides a comparison of the analytical solutions for the deflections in Two Dimensional Functionally Graded Taper Beam (2D-FGTB) under a uniformly distributed load, adapting Reddy’s higher-order shear deformation theory. All the material properties of the beam are graded along the thickness and length dimensions using the power-law formula. The thickness of the beam is assumed to change linearly along its length. Equations of motion are derived based on Hamilton's principle and Navier’s solutions. A parametric investigation is conducted to explore the effects of various material and geometrical parameters on the mechanics of 2D-FGTB. These parameters are found to be very significant in studying the static responses of 2D-FGTB.

Keywords

• comparison of deflection
• reddy’ s higher order shear deformation theory
• two-dimensional functionally graded taper beam
• hamilton' s principle
• static responses