The　chaotic　dynamic　snap-through　and　complex　nonlinear　vibrations　are　investigated　in　a　rectangular　asymmetric　cross-ply　bistable　composite　laminated　cantilever　shell,　in　cases　of　1　:　2　inter-well　internal　resonance　and　primary　resonance.　The　transverse　foundation　excitation　is　applied　to　the　fixed　end　of　the　structure,　and　the　other　end　is　in　a　free　state.　The　first-order　approximate　multiple　scales　method　is　employed　to　perform　the　perturbation　analysis　on　the　dimensionless　two-degree-of-freedom　ordinary　differential　motion　control　equation.　The　four-dimensional　averaged　equations　are　derived　in　both　polar　and　rectangular　coordinate　forms.　Deriving　from　the　obtained　frequency-amplitude　and　force-amplitude　response　curves,　a　detailed　analysis　is　conducted　to　examine　the　impacts　of　excitation　amplitude,　damping　coefficient,　and　tuning　parameter　on　the　nonlinear　internal　resonance　characteristics　of　the　system.　The　nonlinear　softening　characteristic　is　exhibited　in　the　upper　stable-state,　while　the　lower　stable-state　demonstrates　the　softening　and　linearity　characteristics.　Numerical　simulation　is　carried　out　using　the　fourth-order　Runge-Kutta　method,　and　a　series　of　nonlinear　response　curves　are　plotted.　Increasing　the　excitation　amplitude　further　elucidates　the　global　bifurcation　and　chaotic　dynamic　snap-through　characteristics　of　the　bistable　cantilever　shell.