Shape optimization of 4D printed structures for stiffness maximization

This study utilizes acrylonitrile butadiene styrene (ABS) and polycarbonate/acrylonitrile butadiene styrene (PC-ABS), materials with glass transition temperatures of 105°C and 120°C. During the 3D printing process where thick filaments are extruded through thin nozzles, filaments experience highly oriented tensile residual stress along the structural length. Heating the printed filaments to their glass transition temperature relieves this internal stress, leading to a reduction in structural length. By printing the top layers of a structure in the longitudinal direction and the bottom layers in the lateral direction, the difference in shrinkage causes the structure to bend upwards. This mechanism is adopted as the main shape morphing principle to achieve complex structural designs. However, 4D printed structures can experience instability during the shape morphing process, limiting their use in various engineering fields. To address this, the present study aims to maximize the structural stiffness through shape optimization. Finite element method (FEM) simulations were performed to observe changes in structural geometry when applied with heat and evaluate the structural stiffness. As a result, the optimized design increased structural stiffness by up to 24.13% while maintaining the structural volume. Experimental verification was done by conducting compression tests. This study successfully designed and fabricated a shape-morphing structure that significantly improves structural stiffness, while preserving both the functional integrity and geometric complexity of the original design.