An Element Independent Corotational Procedure for the Treatment of Large Rotations

Rankin, C.; Brogan, F. A.

doi:10.1115/1.3264765

Cited by 284 publications

(129 citation statements)

References 14 publications

(42 reference statements)

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“…Linearly varying longitudinal displacement is assumed within the element and cubic Hermite polynomials are used for transverse displacements. The calculations are performed in the local element coordinate system after the finite rotation transformation 41 . We use a projector-consistent stress-stiffness matrix 42,43 to achieve a quadratic rate of convergence.…”

Section: Finite Element Modelmentioning

confidence: 99%

Finite-strain, finite-size mechanics of rigidly cross-linked biopolymer networks

et al. 2013

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The network geometries of rigidly cross-linked fibrin and collagen type I networks are imaged using confocal microscopy and characterized statistically. This statistical representation allows for the regeneration of large, three-dimensional biopolymer networks using an inverse method. Finite element analyses with beam networks are then used to investigate the large deformation, nonlinear elastic response of these artificial networks in isotropic stretching and simple shear. For simple shear, we investigate the differential bulk modulus, which displays three regimes: a linear elastic regime dominated by filament bending, a regime of strain-stiffening associated with a transition from filament bending to stretching, and a regime of weaker strain-stiffening at large deformations, governed by filament stretching convolved with the geometrical nonlinearity of the simple shear strain tensor. The differential bulk modulus exhibits a corresponding strain-stiffening, but reaches a distinct plateau at about 5 % strain under isotropic stretch conditions. The small-strain moduli, the bulk modulus in particular, show a significant size-dependence up to a network size of about 100 mesh sizes. The large-strain differential shear modulus and bulk modulus show very little size-dependence.

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Section: Finite Element Modelmentioning

confidence: 99%

Finite-strain, finite-size mechanics of rigidly cross-linked biopolymer networks

et al. 2013

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“…하지만, CR 기법은 대부분 보, 쉘 요소에 적용되었고 (Crisfield, 1990;Battini, 2007) (Rankin et al, 1986, Felippa et al, 2005. (1)과 같이 도출할 수 있다 (Battini, 2008).…”

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Development of Nonlinear Triangular Planar Element Based on Co-rotational Framework

Cho¹,

Shin²

2015

jcoseik

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This paper presents development of a geometrically nonlinear triangular planar element including rotational degrees of freedom, based on the co-rotational(CR) formulation. The CR formulation is one of the efficient geometrically nonlinear formulations and it is based on the assumptions on small strain and large rotation. In this paper, modified CR formulation is suggested for the developemnt of a triangular planar element. The present development is validated regarding the static and time transient problems. The present results are compared with the results predicted by the previous researchers and those obtained by the existing commercial software.

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“…Certain developments are essentially based on the updated Lagrangian formulation but use local reference frame attached to the structure for computation of the Cauchy stresses (Marinković et al, 2008). However, in a co-rotational approach (Rankin and Brogan, 1986;Izzuddin, 2005) the provision of such a coordinate system that is attached to the structure and performs the same rigid-body motion as the structure itself is essential. It provides means to separate the rigidbody motion from purely deformational motion.…”

Section: Introductionmentioning

confidence: 99%

Efficient Co-Rotational 3-Node Shell Element

Rama¹,

Marinković²,

Zehn³

2016

American Journal of Engineering and Applied Sciences

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Geometric nonlinear FE-analysis of thin-walled shell structures, using a co-rotational formulation and the Cell Smoothed Discrete Shear Gap triangular shell element (CS-DSG3) is presented in this study. The CS-DSG3 element formulation uses the Mindlin-Reissner kinematic hypothesis to include transverse shear effects. In order to avoid locking effects Discrete Shear Gap (DSG) method is applied. In addition, cell based smoothing technique is adopted in order to improve accuracy and stability of the element. For the purpose of comparison, the Discrete Kirchhoff-Constant strain-Triangle (DKT-CST) is also implemented and studied in the linear static analysis. In the framework of the co-rotational FE-analysis rotations and displacements are adopted as finite, while strains are infinitesimal. Large rotation theory has been utilized to take into account the non-vectorial characteristic of rotations. Several static linear and nonlinear benchmark examples are presented and compared with commercial FE software Abaqus and analytical results. The presented approach, using CS-DSG3 element in co-rotational nonlinear analysis, illustrates very good results compared to reference solution and Abaqus results. The numerical effort can be reduced compared to Lagrange formulation with a similar accuracy for the studied cases. The formulation (including CS-DSG3 shell element) has been implemented into a test program.

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An Element Independent Corotational Procedure for the Treatment of Large Rotations

Cited by 284 publications

References 14 publications

Finite-strain, finite-size mechanics of rigidly cross-linked biopolymer networks

Finite-strain, finite-size mechanics of rigidly cross-linked biopolymer networks

Development of Nonlinear Triangular Planar Element Based on Co-rotational Framework

Efficient Co-Rotational 3-Node Shell Element

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