Thermo-mechanical analysis of axially and transversally Function Graded Beam

A generalized non-conventional finite element model for beam structure have been conducted, based on Timoshenko beam theory, this model is capable of static and dynamic analysis for both axially and transversally Function Graded Beam (FGB), its shape function not only depend on length but also depend on the material properties and cross-section geometry. A new convergence model for analysis of axially FGB has been developed, overcoming the problem of number of elements to length dependency in axial gradation, proposed model based on numerical integration by defining a local constant value of property for each element. Model validation for both transversally and axially FGB was done, by comparing the obtained results with published ones. Thermal analysis had been conducted for FGB operating in high temperature environment, with studying the effect of temperature change on the constituent material properties in both cases and its effect on dynamic response and natural frequencies. Concluding high accuracy model, its accuracy could reach high order shear deformation theory (HOSDT) in some applications, new convergence model for analysis of axially FGB, great influence of shear correction factor in Timoshenko beam and finally a good comparison between thermo-mechanical loading in axial and transversal FGBs.