A fast and accurate dynamic relaxation approach for form-finding and analysis of bending-active structures

Abstract

Active bending is an increasingly popular construction technique that uses elastically bent structural members to form complex curved shapes. The design and analysis of bending-active structures requires an accurate simulation of the bending process, which is often complicated by the occurrence of large displacements. In this article, we propose to combine a previously developed implicit dynamic relaxation method with co-rotational beam elements to obtain a fast and accurate method for form-finding and analysis of bending-active structures. This approach is applied to four test cases. Implicit dynamic relaxation is compared to the classic Newton–Raphson method and conventional dynamic relaxation. The results show that the proposed implicit dynamic relaxation approach can be stabilized intuitively by changing the time step and damping ratio, making it more stable than the classic Newton–Raphson method. Moreover, the proposed approach converges fast compared to the conventional dynamic relaxation: the total computation time is considerably lower, even though the computation time per iteration is higher. Finally, a high accuracy is achieved due to the use of co-rotational beam elements. The combination of high accuracy and low computation time makes this approach well-suited for both form-finding and analysis of bending-active structures.