Mechanical models in computational form finding of bending-active structures

Abstract

This article reviews the different aspects involved in computational form finding of bending-active structures based on the dynamic relaxation technique. Dynamic relaxation has been applied to form-finding problems of bending-active structures in a number of references. Due to the complex nature of large spatial deformations of flexible beams, the implementation of suitable mechanical beam models in the dynamic relaxation algorithm is a non-trivial task. Type of discretization and underlying beam theory have been identified as key aspects for numerical implementations. References can be classified into two groups depending on the selected discretization: finite-difference-like and finite-element-like. The first group includes 3- and 4-degree-of-freedom implementations based on increasingly complex beam models. The second gathers 6-degree-of-freedom discretizations based on co-rotational three-dimensional Kirchhoff–Love beam elements and geometrically exact Reissner–Simo beam elements. After reviewing and comparing implementation details, the advantages and drawbacks of each group have been discussed, and open aspects for future work have been pointed out.