Origami has inspired the engineering design of self-assemble and re-configurable devices. Under particular crease patterns, a 2D flatten object can be transformed into a complex 3D structure. This work intends to find out a systematic solution for topology optimization of origami structures. The origami mechanism is simulated using shell models where the in-plane membrane, out of plane bending, and shear deformation can be well captured. Moreover, the pattern of the folds is represented implicitly by the boundaries of the level set function. The topology of the folds is optimized by minimizing a new multiobjective function, aiming to balance the kinematic performance with the structural stiffness as well as the geometric requirements. Besides regular straight folds, our proposed model can mimic crease patterns with curved folds. With the folding curves implicitly represented, the curvature flow are utilized to control the complexity of the generated folds. The effectiveness of the proposed method is demonstrated through the computational generation and physical validation of a thin-shell origami gripper.

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