Edge Projected Planar Rectangular Element for Modeling Flexible Multibody Systems

A four-node planar rectangular element, suitable for modeling flexible multibody systems, is described. Linear interpolation is used for the element shape and normal stresses. The element normal stresses are projected to the element edges. The element shear strain is set to the average of the change of the element corners’ angles. The average shear strain is projected to torsional-springs at each of the element corners in order to model the element shear mode. The element is strategically designed to eliminate locking and spurious modes. Cartesian nodal coordinates are used as degrees-of-freedom. A total Lagrangian displacement formulation where the element deformations are measured relative to the unstressed element is employed. The equations of motion are integrated using an explicit temporal integration algorithm. Standard finite element and flexible multibody dynamics test problems are solved to demonstrate the accuracy and robustness of the element.