Reduced order modeling based on an element-wise stiffness evaluation procedure for photo-reponsive polymer structures

The photo-responsive polymers(PRPs) structure undergoes photo-deformation via a photo-isomerization. Most PRPs structure photo-deformation have large displacement and rotation. In order to design a PRPs structure suitable for a purpose, accurative analysis and repetitive calculation for photostrain patterning optimization are required. It is too inefficient to analyze this process as a 3D finite element method. In this paper, we adopt a shell finite element with co-rotational formulation, which can efficiently represent large displacement and rotation of PRPs structure. Also, we propose an equivalent reduced order model based on Element-wise stiffness evaluation procedure (E-STEP) and Proper Orthogonal Decomposition (POD) method for the co-rotational formulation to increase efficiency. In the co-rotational formulation, the internal force is calculated in the local frame. However, using the E-STEP method, we construct an equivalent model for internal force that can be calculated with global frame. Then, the equivalent reduced order model was constructed by applying the POD method to the equivalent model. Therefore, by using proposed model, the deformation of the PRPs structure can be efficiently analyzed. The.