Post-Buckling Analysis of FG-TPMS Shells with Geometric Imperfection and Porosity under Axial Compression

Imperfections can significantly reduce the load-carrying capacity of structures, especially in thin shells. Such imperfections can stem from inaccurate fabrication and erection and they should be taken into account in the analysis and design. For the first time, post-buckling behavior of functionally graded triply periodic minimal surface (FG-TPMS) shells under axial compression is investigated in this paper. The proposed formulation considers both geometric imperfection and porosity which can be considered as material imperfection. The two types of porosity in this study are the even and uneven porosity distributions. The nonlinear responses of FG-TPMS shells with six density distribution patterns along the thickness are investigated. The mechanical properties of the FG-TPMS materials were calculated using a fitting technique. The present formulation is based on isogeometric analysis (IGA) and first-order shear deformation shell theory (FSDT). Non-uniform rational B-Spline (NURBS) basis functions are utilized to model exact geometries and to approximate displacements. The non-linearity of shells is formulated based on the von Karman assumption and the total Lagrangian approach. A modified Riks method is employed to solve the discrete nonlinear equation system iteratively. The high reliability of the present formulation is confirmed by solving several problems. Effects of the density distribution pattern, geometrical imperfection, curvature, porosity volume fraction, and porosity distribution on post-buckling strength of FG-TPMS panel are thoroughly studied. Moreover, numerous new load-deflection paths of FG-TPMS shells subjected to compression and considering both geometric imperfection and porosity are proposed.