Geometrically nonlinear elasto-plastic analysis of clustered tensegrity based on the co-rotational approach

• Geometrically nonlinear elasto-plastic analysis of clustered tensegrity is carried out.
• A large deformation of clustered cables is decomposed into a rigid body motion and a pure small deformation.
• A new tangent stiffness is derived based on the co-rotational approach.
• The proposed method is efficient and requires less iteration than the force density method.

An efficient finite element formulation is developed for geometrically nonlinear elasto-plastic analyses of classical and clustered tensegrities based on the co-rotational approach. Large deformation of a clustered cable is decomposed into a rigid body motion in the global coordinate system and a pure small deformation in the local coordinate system. The merit of the proposed method is that elasto-plastic behaviors of cables and bars can be described using engineering strain and stress is calculated directly by the small-deformation elasto-plastic theory, although geometrical nonlinearity must be taken into account. A tangent stiffness matrix, including an additional stiffness that describes the sliding effect of running pulleys is derived and nonlinear iteration is implemented by the Newton–Raphson scheme. Several numerical examples are employed to validate the proposed formulation. It can be found that the proposed formulation requires less iteration than the force density method.