A reliability-based optimization approach for material and thickness composition of multidirectional functionally graded plates

A reliability-based design optimization (RBDO) methodology is first proposed to simultaneously optimize material and thickness distribution of multidirectional functionally graded (MFG) plates for compliance minimization under uncertainties of design variables and system parameters. The modified sequential optimization and reliability assessment (MSORA) method is integrated into the recently suggested adaptive hybrid evolutionary firefly algorithm (AHEFA) to release a novel RBDO approach which is the so-called MSORA-AHEFA. The MSORA is refined from its original for computational cost savings by eliminating the iterative process of finding most probable points (MPPs). An isogeometric multimesh design (IMD) approach is presented to form two separate non-uniform rational B-spline (NURBS) surfaces via the k-refinement strategy. In which, a coarser design NURBS one is employed to define design variables of the ceramic volume fraction and z-axis coordinate of the top side coincidentally assigned at each of control points. A finer analysis NURBS one constructed by the isogeometric analysis (IGA) and a generalized shear deformation theory (GSDT) is used for bending analyses of MFG plates with arbitrary thickness. Applying such two separately defined surfaces dramatically lessens the number of design variables and the computational cost in optimization problems, yet still manifesting optimal profiles properly. Meanwhile, mechanical behavior of the plate in analysis ones is precisely simulated as well. For the validation of the suggested MSORA-AHEFA, its results for the benchmark welded beam are compared with those of formerly published work. Several numerical examples regarding RBDO of MFG plates are then executed to attest the effectiveness of the current paradigm.