Finite-strain three-dimensional solids with rotational degrees of freedom: non-linear statics and dynamics

Abstract

In this paper we seek refined yet efficient computational models of large overall motion in statics and dynamics. The efficiency is achieved by the proposed model of 8-node brick element with rotational degrees of freedom which allows to separate large displacements and large rotations. The independent rotation field leads to an intrinsic representation of the rotation tensor, ensuring a smooth interaction between 3D solids and beam elements. The element is based on a sound variational formulation and the incompatible mode method which allows to construct enhanced strain representation. Several numerical examples are presented to show an excellent performance of this element in the whole range of large overall motion in the statics and dynamics problems.

On the Use of Drilling Degrees of Freedom to Stabilise the Augmented Finite Element Method

“…Instead, it only employs vertex rotations to enhance the displacement field. This is in contrast to elements with drilling DOFs, which interpolate the rotation field and displacement field independently (as seen in [20,23]). Furthermore, it is important to note that the vertex rotations introduced in Allman's approach are not true rotations as defined in continuum mechanics, but they are closely related.…”

“…According to MacNeal and Harder, membrane finite elements with drilling degrees of freedom (DOFs) were proposed several times between 1960 and 1980, but these attempts were mostly unsuccessful [3]. The distinct approaches taken by Bergan and Felippa [18] and Allman [19], as well as the mathematical framework proposed by Hughes and Brezzi [20] paved the way for the successful formulations used today (see, for example, [21][22][23]). In this work, we will consider the approach proposed by Allman in 1984 to design membrane elements with in-plane rotational DOFs [19].…”

Practical Calculation of Flexible Members With the Use of Non-Linear Deformation Model as Exemplified by Typical Girder RGD 4.56-90

“…Obviously, the calculation of construction structures with the use of non-linear deformation model (NLDM) qualifies as check-and-control or testing method. In this case the calculation according to NLDM will be performed with definite force (external or internal) values, reinforcement (of concrete) and member geometrical dimensions (Boujelben, Ibrahimbegovic, 2017;Jagtap et al, 2018).…”