Bistable polar-orthotropic shallow shells

Area of Science:

• Mechanics of Materials
• Structural Engineering
• Computational Mechanics

Background:

• Bistability in shells is crucial for developing advanced morphing structures.
• Stress singularities arise in polar-orthotropic shells when circumferential stiffness is less than radial stiffness (β < 1).
• Understanding factors influencing bistability is key to designing stable and adaptable structures.

Purpose of the Study:

• To investigate stabilizing and destabilizing factors affecting bistability in polar-orthotropic shells.
• To enhance the design of morphing structures through a better understanding of shell bistability.
• To analyze the impact of orthotropic ratio, in-plane support conditions, and geometric modifications on bistability.

Main Methods:

• Employed a higher-order, geometrically nonlinear analytical model using a Ritz approach.
• Carefully selected trial functions to handle stress singularities inherent in the material law.
• Analyzed the interaction between orthotropic ratio (β) and in-plane support conditions.

Main Results:

• Bistability is highly dependent on the orthotropic ratio (β) and in-plane support conditions.
• Hoop stiffness is stabilizing only by preventing radial expansion; its effect is redundant with in-plane supports.
• Fixed-pinned shells are more prone to stable inversions than roller-supported shells, especially with high radial stiffness.
• Cutting a central hole promotes bistability in roller-supported shells but has minimal effect on fixed-pinned ones.

Conclusions:

• The study provides closed-form approximations for the bistable threshold using single-curvature-term approaches.
• A strong coupling exists between the orthotropic ratio and support conditions for stiffer radial stiffness.
• Central holes offer a viable strategy to mitigate stress singularities and induce bistability in specific shell designs.