Nonlinear Transient Dynamic Behavior of Functionally Graded Beams

Abstract

The objective of the following investigation deals with the geometrically nonlinear transient dynamic analysis of functionally graded beams. The effect of thickness stretching, and shear strain is considered within the formulation of the improved beam theory, which requires five independent variables and fully utilizes the constitutive equations. The graded material properties are realized under two material phases and are distributed by power law. The dynamic formulation is based on the Hamilton principle, which comes from the principle of minimum energy and being able to use the Lagrange´s function. The model is implemented by means of the Finite Element method for its numerical resolution, for this the modified Newmark method is used, in which the NewtonRaphson method is applied to solve the system of nonlinear equations. High order interpolation functions are used to reduce the Poisson locking effect. Finally, the results are compared with benchmark problems and proposing new case studies.