Multiferroic　composite　structures　are　widely　used　in　sensing,　driving　and　communication.　The　study　of　their　magnetoelectric　(ME)　behavior　under　various　excitations　is　crucial.　This　study　investigates　the　nonlinear　ME　influence　of　a　multilayer　composite　ring　structure　consisting　of　Terfenol-D　(TD)　magnetostrictive　and　lead　zirconate　titanate　(PZT)　piezoelectric　rings　utilizing　a　multiphysics　field　modeling　framework　based　on　the　fully　coupled　finite　element　method.　The　ME　coupling　coefficient　of　the　PZT/TD　concentric　composite　ring　is　predicted　using　the　linear　piezoelectric　constitutive　model　and　the　nonlinear　magnetostrictive　constitutive　model,　which　is　congruent　to　the　experimental　data.　The　effect　of　the　interface　area　of　a　trilayered　structure　on　the　coupling　performance　at　the　resonant　frequency　is　investigated,　considering　the　magnitude　and　frequency　of　the　magnetic　field　and　keeping　the　material　ratio　constant.　The　ME　coupling　coefficient　of　a　trilayered　structure　is　larger　than　that　of　a　bilayered　structure　with　the　same　material　ratio,　and　the　maximum　ME　coupling　coefficient　of　a　trilayered　structure　increases　nonlinearly　with　the　increase　in　the　interface　area.　At　the　resonant　frequency,　the　structure＇s　ME　coupling　performance　is　considerably　improved.　An　optimization　technique　based　on　structural　geometric　design　and　magnetic　field　control　is　presented　to　optimize　the　ME　coupling　coefficient.