Numerical investigation of the slope discontinuities in large deformation finite element formulations

Abstract

In many multibody system applications, the system components are made of structural elements that can have different orientations, leading to slope discontinuities. In this paper, a numerical investigation of a new procedure that can be used to model structures with slope discontinuities in the finite element absolute nodal coordinate formulation (ANCF) is presented. This procedure can be applied to model slope discontinuities in the case of commutative rotations of gradient deficient elements that are used for modeling thin beam and plate structures. An important special case to which the proposed procedure can be applied is the case of all planar gradient deficient ANCF finite elements. The use of the proposed method leads to a constant orthogonal element transformation that describes an arbitrary initial configuration. As a consequence, one obtains, in the case of large commutative rotations and large deformations, a constant mass matrix for structures which have complex geometry. The procedure used in this investigation to model slope discontinuities requires the use of the concept of the intermediate finite element coordinate system. For each finite element, a new set of gradient coordinates that define, at the discontinuity node, the element deformation with respect to the intermediate element coordinate system is introduced. These new gradient coordinates are assumed to be equal for the two finite elements at the point of intersection. That is, the change of the gradients of two elements at the intersection point from their respective intermediate initial reference configuration is assumed to be the same. This procedure leads to a set of linear algebraic equations that define the orthogonal transformation matrix for the finite element. Numerical examples are presented in order to demonstrate the use of the proposed procedure for modeling slope discontinuities.

Absolute Nodal Coordinate Formulation in a Pre-Stressed Large-Displacements Dynamical System

“…In this paper a planar gradient deficient [25] Euler-Bernoulli beam element is used [30][31][32], Fig. 1.…”

Weak form quadrature shell elements based on absolute nodal coordinate formulation

“…However, the use of gradient vectors instead of rotational angles as nodal variables poses a significant challenge to such applications. For slope discontinuity problems, Shabana et al [13][14][15] demonstrated that a constant linear transformation of slope variables can be performed using body coordinate system or intermediate coordinate system. The transformation which is valid for linear connectivity conditions in cases like spherical hinges and rigid joints does not introduce additional constraint equations during the process of element assembly.…”