Innovative Approaches to Torsion Analysis in Functionally Graded iso/orthotropic sections: A Differential Quadrature and pb2-Rayleigh Rit exploration.

This study focuses on the determination of torsional rigidity and maximum shear stresses in arbitrarily shaped isotropic and orthotropic composite sections with functional grading of material. A series of numericalexamples are solved to validate this approach, with a comprehensive parametricstudy also conducted. The paper presents the practical application of the DQM and pb-2 Rayleigh-Ritz methods for evaluating shear stress and torsionalrigidity in various section shapes including quadrilaterala sn triang;es wotj nptj straogjt amd cirved edges. as well as elliptical, circular and rounded poygonal shapes. The boundaryconditions are speciried as Drichlet. To facilitate the analysis, four - nodded (for sections with straight edges) or eight-nodded (for sections with curved edges) iso-parametric rectangular element, andthree-nodded (for sections with straight edges) or six-nodded (for sections with curved edges) for triangular elements are used to map the irregular physical domain into a square or trangular computational domain,as appropriate. A noteworthy advantage of this approach is that the governing equatin for torsion, which relies on the Prandtl stress function approach, reduces to a second-order differential equation (Poisson's equation). The transformation to this second-order equation is ficiently accomplished, resulting in reduced computational effort. Both within the computational domain andalong its boundary, the primary unknowns are the values of Prandtl's stress functional ( for Poisson' equation) or the warping displacement function (for Laplace's equation). This approach streamlines the analysis, making it a power tool for understanding the torsional behaviour of functionally graded isotropic and orthotropic and coposite sections with complex shapes.