Nonlinear Numerical Modelling and Analysis of Porous Functionally Graded Curved Structures under Thermomechanical Loading

Abstract

The geometrical nonlinear behaviour of porous functionally graded (FG) curved/flat panels under thermomechanical loading is modelled mathematically and presented in this research. Three grading patterns, i.e. power-law (GT-I), sigmoid (GT-II) and exponential (GT-III) types of gradings, are adopted in this research to compute the porous multidirectional graded panel using Voigt’s micromechanical model approach. Additionally, porosity has been introduced in the current model by considering the even (PRT-I) and uneven (PRT-II) distribution patterns through the panel thickness. The practical applications of graded structure in high-performance engineering structures under elevated environmental conditions, the temperature-independent (TID) and temperature-dependent (TD) properties of the individual constituent of FG have been adopted to outline the final responses. Further, the temperature field variations, namely, the uniform (TD-I), linear (TD-II) and nonlinear (TD-III) types, are introduced to imitate the operational conditions as observed in the real-time structure. The structural model is derived mathematically by employing a HSDT to count the state space deformations. Moreover, due to the large deformation under the loading and environmental conditions, the present mathematical model adopted the Green-Lagrange type of nonlinear strain to count the large deformations. The graded structural system equations are derived suitably using either Hamilton’s principle or variational technique to compute the desired linear/nonlinear eigenvalue/particular solutions. The nonlinear structural responses are computed using the selective numerical integration (Gauss-Quadrature) scheme in conjunction with Picard’s direct iterative technique, Newmark’s constant acceleration steps (time-dependent responses) and isoparametric finite element steps. The graded panel model is discretized using a nine-noded quadrilateral Lagrangian element with nine-nodal degrees of freedom (DOF). A generalized computational algorithm in MATLAB is prepared using the currently developed mathematical model. Initially, the consistency of the numerical solution due to the change in elemental densities has been checked by presenting an adequate number of convergence tests. In addition, to improve the confidence in the prepared computational algorithm of the multidirectional porous graded structure, a few comparisons are undertaken by comparing with those of available solutions (grading in one or more directions). Further, a few linearly graded polymeric composite reinforced with natural fibre has been prepared to conduct the experimentations, including their elastic constants. Lastly, a series of parametric analyses have been conducted to examine the influence of varieties of design-associated parameters (type and magnitude of applied mechanical load, power-exponent, amplitude ratio, temperature and its distribution, geometrical shapes, curvature ratio, end-support conditions, thickness and aspect ratio) on the nonlinear responses (flexural, vibration and time-dependent deflection) of the FG curved/flat panel. Based on the parametric study, a few final recommendations are provided towards the end of this research for references in future research based on graded structural applicability.