| Abstract: | The equilibrium problem of nonlinear, isotropic and hyperelastic square membranes, stretched by a double symmetric system
of dead loads, is investigated. Depending on the form of the stored energy function, the problem considered may admit asymmetric
solutions in addition to the expected symmetric solutions. For compressible materials, the mathematical condition allowing
the computation of these asymmetric solutions is given. Moreover, explicit expressions for evaluating critical loads and bifurcation
points are derived. Results and basic relations obtained for general isotropic materials are then specialized for a compressible
Mooney–Rivlin material and a broad numerical analysis is performed. The qualitatively more interesting branches of asymmetric
equilibrium are shown and the influence of the material parameters is discussed. Finally, using the energy criterion, some
stability considerations are made. |
