An efficient curved beam element for thermo-mechanical nonlinear analysis of functionally graded porous beams

Abstract

This research is aimed to develop an efficient and high-performance four-node iso-parametric beam element, which is composed of Functionally Graded Material (FGM). In addition, different patterns of material distribution will be considered through the height of element. On the other hand, beam’s imperfection, presented here with porosity, is taken into account by using the rule of mixture. In order to alleviate the shear locking, Mixed Interpolation of Tensorial Components (MITC) is utilized by using tying points. Strain interpolation at some tying points reduces the order of strain functions. Therefore, three Gauss points can be employed for numerical integration instead of four Gauss points. Furthermore, the geometrically nonlinear effects are incorporated by using Green-Lagrange strains. Since the material properties are considered to be thermal-independent, they remain constant during the analysis. Finally, some benchmark problems are solved to illustrate the correctness of formulation and accuracy of the proposed element. Several parameters, including porosity percentage, FGM patterns and corresponding power indices, are investigated in the other examples. It is observed that the proposed element is more accurate for linear and nonlinear analyses of the thin beam with large deformations and rotations, even by using fewer numbers of elements compared to other developed elements. On the other hand, both axial and transverse displacements decrease when the value of the exponent of sigmoid pattern increases. On the contrary, the exponent of power pattern has a different effect on the axial displacement.