Buckling Analysis of Functionally Graded Timoshenko Beams

Abstract

A finite element model based on the Timoshenko theory is developed to compute the critical buckling loading of functionally graded beams. The Trefftz criteria is used for the stability analysis considering both fundamental and incremental states. A finite element formulation is derived from the principle of virtual work. The Lagrange interpolation functions are used to approximate the field variables. Numerical results are validated with several benchmark problems found in literature.