Thermo-Mechanical Beam Element for Analyzing Stresses in Functionally Graded Materials

Modeling at the structural scale most often requires the use of beam and shell elements. This simplification reduces modeling complexity and computation requirements but sacrifices the accuracy of through-the-thickness information. Several studies have reported various design approaches for analyzing functionally graded material structures. One of these studies proposed a two-node beam element for functionally graded materials (FGMs) based on first-order shear deformable (FOSD) theory.

The derivation of governing equations included spatial temperature variation.  However, only the constant temperature case was carried through in the element formulation. This research explored the effects of spatial temperature variation in the axial and through the thickness direction of this proposed element and present a new standard three-node beam finite element modified for the structure constructed of FGMs.

Also, the influence of the temperature dependency of the thermo-elastic material properties on the thermal stresses distribution was studied. In addition, variations in the layer thicknesses within multilayer beam models were studied to determine the effect on stresses and factor of safety. Finally, based on the specific factor of safety, which combines together the strength and mass of the beam, the best layer thicknesses for the beam models were established.

The key contributions of this research were

  1. a three-node beam element implemented as finite element code into the commercial computational tool MATLAB to analyze thermo-mechanical stresses in structures constructed of functionally graded materials,
  2. a strategy to simulate different load cases in structures constructed of functionally graded materials,
  3. an analysis of the influence of the FGM interlayer thickness on the factor of safety/specific gravity ratio in structures constructed of functionally graded materials under thermo-mechanical loads, and
  4. an analysis/comparison of the advantages/benefits of using structures constructed of functionally graded materials with respect to those constructed with homogeneous materials.