A consistent co-rotational formulation for non-linear, three-dimensional, beam-elements
01 Aug 1990-Computer Methods in Applied Mechanics and Engineering (North-Holland)-Vol. 81, Iss: 2, pp 131-150
TL;DR: In this paper, a co-rotational formulation for three-dimensional beams is presented, in which both the internal force vector and tangent stiffness matrix are consistently derived from the adopted "strain measures".
About: This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 1990-08-01. It has received 496 citations till now. The article focuses on the topics: Tangent stiffness matrix & Timoshenko beam theory.
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TL;DR: A unified theoretical framework for the corotational (CR) formulation of finite elements in geometrically nonlinear structural analysis is presented in this paper, which permits the derivation of a set of CR variants through selective simplifications.
389 citations
TL;DR: The status and some recent developments in computational modeling of flexible multibody systems are summarized in this article, where a number of aspects of flexible multi-body dynamics including: modeling of the flexible components, constraint modeling, solution techniques, control strategies, coupled problems, design, and experimental studies.
Abstract: The status and some recent developments in computational modeling of flexible multibody systems are summarized. Discussion focuses on a number of aspects of flexible multibody dynamics including: modeling of the flexible components, constraint modeling, solution techniques, control strategies, coupled problems, design, and experimental studies. The characteristics of the three types of reference frames used in modeling flexible multibody systems, namely, floating frame, corotational frame, and inertial frame, are compared. Future directions of research are identified. These include new applications such as micro- and nano-mechanical systems; techniques and strategies for increasing the fidelity and computational efficiency of the models; and tools that can improve the design process of flexible multibody systems. This review article cites 877 references. @DOI: 10.1115/1.1590354#
360 citations
TL;DR: In this paper, the issue of discretization of the strain configuration relationships in the geometrically exact theory of 3D beams has been discussed, which has been at the heart of most recent work.
Abstract: The paper discusses the issue of discretization of the strainconfiguration relationships in the geometrically exact theory of threedimensional (3D) beams, which has been at the heart of most recent...
305 citations
Cites background or methods from "A consistent co-rotational formulat..."
...We now repeat the computations, having first superimposed the rigid-body rotation on the nodal rotation matrices so that, from Λ1 = ΛRΛ1 and Λ2 = ΛRΛ2, we extract the rotational vectors (see Spurrier (1978), Simo & Vu-Quoc (1986), and Crisfield (1997) for the actual algorithm to extract the rotational vector from a rotation matrix)...
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...Other formulations based on the interpolation of incremental and iterative rotations, such as those due to Jelenić & Saje (1995) and Jelenić & Crisfield (1998), are also non-objective and path-dependent....
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...It is worth emphasizing a strong link between the proposed procedure and the ‘co-rotational method’ (Crisfield 1990)....
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TL;DR: In this article, a hierarchical displacement interpolation was proposed for the beam theory of Reissner, which is capable of eliminating both shear and membrane locking phenomena in the finite element beam theory.
302 citations
TL;DR: In this paper, a finite element formulation of the geometrically exact 3D beam theory is proposed to preserve the objectivity of the adopted strain measures, and the current local rotations are interpolated in a manner similar to that adopted in co-rotational approaches.
300 citations
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996 citations
TL;DR: In this article, a variational formulation and computational aspects of a three-dimensional finite-strain rod model, considered in Part I, are presented, which bypasses the singularity typically associated with the use of Euler angles.
Abstract: The variational formulation and computational aspects of a three-dimensional finite-strain rod model, considered in Part I, are presented. A particular parametrization is employed that bypasses the singularity typically associated with the use of Euler angles. As in the classical Kirchhoff-Love model, rotations have the standard interpretation of orthogonal, generally noncommutative, transformations. This is in contrast with alternative formulations proposed by Argyris et al. [5–8], based on the notion of semitangential rotation. Emphasis is placed on a geometric approach, which proves essential in the formulation of algorithms. In particular, the configuration update procedure becomes the algorithmic counterpart of the exponential map. The computational implementation relies on the formula for the exponential of a skew-symmetric matrix. Consistent linearization procedures are employed to obtain linearized weak forms of the balance equations. The geometric stiffness then becomes generally nonsymmetric as a result of the non-Euclidean character of the configuration space. However, complete symmetry is recovered at an equilibrium configuration, provided that the loading is conservative. An explicit condition for this to be the case is obtained. Numerical simulations including postbuckling behavior and nonconservative loading are also presented. Details pertaining to the implementation of the present formulation are also discussed.
986 citations
01 Jan 1986
968 citations
TL;DR: In this paper, a finite element procedure is introduced for the analysis of nearly-incompressible media, which is applicable to arbitrary anisotropic and/or nonlinear media.
Abstract: A new finite element procedure is introduced for the analysis of nearly-incompressible media. The approach may be simply implemented by a small change of the standard technique, and is applicable to arbitrary anisotropic and/or nonlinear media. The procedure is shown to specialize to the selective integration and mean-dilatation formulations under appropriate hypothesis.
839 citations
TL;DR: In this article, an improved algorithm is presented for integrating rate constitutive equations in large deformation analysis, and the algorithm is shown to be "objective" with respect to large rotation increments.
Abstract: An improved algorithm is presented for integrating rate constitutive equations in large-deformation analysis. The algorithm is shown to be ‘objective’ with respect to large rotation increments.
755 citations