The　failures　of　mechanical　structure　featuring　high　nonlinearity,　non-normal　and　non-independent　are　implicit　function　and　small-probability　events.　This　normally　results　in　low　computational　efficient　and　accuracy　for　gradient　algorithm　scenario,　which　can　hardly　calculate　models　for　large　complex　structure　and　flexible　systems.　To　deal　with　the　above　constraints,　an　efficient　and　accurate　reliability　numerical　method　named　adaptive　reliability　index　importance　sampling-based　extended　domain　PSO　(ARIIS-EDPSO)　is　proposed　to　combine　the　reliability　numerical　simulation　and　the　particle　swarm　optimization　(PSO)　algorithm.　The　reliability　index　and　limit　state　equation　in　ARIIS-EDPSO　are　regarded　as　the　objective　function　and　the　constraint　function.　The　Nataf　transformation　is　adopted　to　complete　the　conversion　process　from　an　original　variable　space　to　an　independent　standard　normal　space,　which　only　requires　the　marginal　probability　density　function　and　the　correlation　coefficient　among　the　random　variables.　To　verify　the　effectiveness　of　the　proposed　ARIIS-EDPSO,　experimental　studies　are　conducted　with　five　case　studies.　The　results　indicate　that　the　constraint　conflict　function　obtained　via　ARIIS-EDPSO　is　smaller　than　that　is　obtained　via　the　other　methods,　and　its　convergence　can　be　guaranteed.　Also,　the　accuracy　of　the　ARIIS-EDPSO　is　superior　to　the　other　methods　for　nonlinear　reliability　calculation.　Furthermore,　the　ARIIS-EDPSO　can　accurately　predict　the　failure　probability.　This　approach　exhibits　advantageous　global　search　ability,　high　efficiency　and　high　accuracy　in　solving　constrained　reliability　engineering　problems.　©　2020　Elsevier　Inc.