Abstract
Investigated in this paper are comprehensive static, dynamic and internal-resonance analyses on a wide range of hyperelastic shell structures, including cylindrical, spherical, doubly-curved, and hyperbolic hyperelastic shallow shells. Donnell's nonlinear shell theory and the Mooney-Rivlin strain energy density model are used to formulate the hyperelastic shell structure. Coupled equations of motion are obtained using Hamilton's principle with highly nonlinear terms due to the curvature in the structure, together with the material nonlinearity and large deformations. The coupled equations of motion are converted to a large set of equations using a two-dimensional Galerkin technique and are solved by employing the Newton-Raphson approach and dynamic equilibrium technique. The strength of the current methodology and model is first verified by comparing the static response of the structure with those obtained by using a finite element software. After verifying the model, a detailed analysis of the bending behaviour of the structure under a time-independent pressure is presented. Moreover, the free and forced vibration responses of the shell structure are presented for different cases, showing that the curvature terms play a significant role in changing the mechanical response of the hyperelastic shell. Furthermore, it is shown that for specific sets of curvatures, internal resonances are present which leads to a complicated, rich nonlinear responses. The nonlinear forced vibration response of the hyperelastic shell is also presented for different shell types and resonances.
Published Version
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