A Higher-Order Variable Cross-Section Viscoelastic Beam Element Via ANCF for Kinematic and Dynamic Analyses of Two-Link Flexible Manipulators

A new viscoelastic beam element with variable cross-sections is developed based on the absolute nodal coordinate formulation, in which the higher-order slope coordinates are used to describe the variable geometric boundaries and circumvent possible shear-locking problem. The mass and stiffness matrices of the new element are derived by considering the variable geometrical boundary in the integration functions. The modified Kelvin–Voigt viscoelastic constitutive model for large deformation problems is introduced into the stiffness matrix. The dynamic model of a typical two-link manipulator with variable cross-section links is established where the constraint equations of revolute joints are considered with Lagrange multipliers. The kinematic trajectories of the manipulator with various materials and geometrical parameters are numerically studied. It is shown that the new element could circumvent shear-locking problem and yield improved accuracy and convergence compared with the conventional beam elements for solving large deformation problems. Also, the viscosity of the structural material helps to reduce the deformation of the links and improve the kinematic precision of the manipulator, hence the trajectory of the flexible manipulator could be controlled by changing the geometrical shape of the cross-section of links under the constraint of same mass.