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• A geometrically exact model (GEMP) is developed for mosaic multi-stable composites. • Besides GEMP, a common model based on classical laminated‐plate theory is used. • Mosaic bi-stable and tri-stable composite laminates with large rotations are studied. • Lagrange multiplier is used to apply linear and non-linear continuity conditions. • Effect of dimensions of mosaic multi-stable laminates on static behavior are studied. Multi-stable composite laminates are composite materials that exhibit multi-stable states, making them highly suitable for use in morphing structures. These materials are capable of maintaining each stable state without expending any energy. As a result, they are used extensively in numerous applications and garnered the interest of scholars and aerospace organizations. In the context of practical applications, such as morphing structures, it is insufficient for designers to rely solely on common bi-stable composite laminates that exhibit large deformations and medium rotations to achieve their desired objectives. Consequently, based on the objectives of the design, there are two potential resolutions to address this limitation. A designer may utilize mosaic multi-stable composite laminates to achieve a morphing structure that exhibits high flexibility, significant deformation, and substantial rotation. The utilization of a series connection between a bi-stable composite laminate and a symmetric composite laminate results in the formation of a mosaic bi-stable composite laminate with variable stiffness. Furthermore, the amalgamation of two asymmetric composite laminates with inverted orientations engenders a mosaic tri-stable composite laminate. The present research examines the static characteristics of mosaic bi-stable and tri-stable composite laminates. It also seeks to analyze the factors affecting the behavior of these types of laminates. A geometrically exact model was formulated for this objective. Apart from the geometrically exact model, a widely used and uncomplicated model relying on the conventional Classical Laminated-Plate Theory (CLPT) and Von-Karman nonlinear strains was employed. The proposed models were validated through finite element simulations. The system's static equations were derived using the virtual work principle and the Rayleigh-Ritz method. The present study examines and explores quasi-static snap-through behavior between stable states through the application of concentrated forces. The findings indicate a high level of concurrence between the outcomes derived from the geometrically exact model and the finite element analyses, particularly in composite laminates exhibiting significant deformations and rotations. [ABSTRACT FROM AUTHOR]

• A geometrically exact model is rendered to study the behavior of bi-stable laminate. • A model based on classical laminated-plate theory with Von-Karman strains is used. • Bi-stable laminates with very large displacements and large rotations are studied. • The effect of lateral length of square laminates on the statics behavior is studied. • The aspect ratio effect of rectangular laminates on the statics response is studied. The present study aimed to analyze the stable states and the snap-through forces of square and rectangular bi-stable composite laminates with [0 3 /90 3 stacking sequence and large to very large displacements and medium to large rotations. Also, the effect of lateral length and aspect ratio of these laminates on their stable states and snap-through forces were analyzed. For this purpose, a realistic geometric exact model of plate (GEMP) was developed based on continuum mechanics. In addition, the analysis was also performed with a commonly used model based on classical laminated‐plate theory (CLPT) with Von-Karman strains. FEM simulations were used to validate the results of these theoretical models. The static equations of the system were derived using the principle of virtual work and Rayleigh-Ritz method. Good consistency was observed between the results of the proposed GEMP and the FEM models, especially for laminates with very large displacements and large rotations. [ABSTRACT FROM AUTHOR]