A unified formulation of small-strain corotational finite elements: I. Theory

Felippa, Carlos A.; Haugen, Bjørn Olav

doi:10.1016/j.cma.2004.07.035

Cited by 350 publications

(281 citation statements)

References 48 publications

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“…The key idea is that we can decompose the structure motion into the rotational part and the deformation part [47,21]. Supposex 0 is a point on the axis of rotation, we can decompose the trajectory of each material particle as follows by using the rotational matrix R arising from the boundary condition (26),…”

Section: Remodeling Of the Rotational Elastic Structurementioning

confidence: 99%

Modeling and simulations for fluid and rotating structure interactions

Yang

Sun

Wang

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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In this paper, we study a dynamic fluid-structure interaction (FSI) model for an elastic structure that is immersed and spinning in the fluid. We develop a linear constitutive model to describe the motion of a rotational elastic structure which is suitable for the application of arbitrary LagrangianEulerian (ALE) method in FSI simulation. Additionally, a novel ALE mapping method is designed to generate the moving fluid mesh while the deformable structure spins in a non-axisymmetric fluid channel. The structure velocity is adopted as the principle unknown to form a monolithic saddle-point system together with fluid velocity and pressure. We discretize the nonlinear saddle-point system with mixed finite element method and Newton's linearization, and prove that the derived saddle-point problem is well-posed. The developed methodology is applied to a self-defined elastic structure and a realistic hydroturbine under a prescribed angular velocity. Both illustrate the satisfactory numerical results of an elastic structure that is deforming and rotating while interacting with the fluid. The numerical validation is also conducted to demonstrate the modeling consistency.

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Section: Remodeling Of the Rotational Elastic Structurementioning

confidence: 99%

Modeling and simulations for fluid and rotating structure interactions

Yang

Sun

Wang

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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“…Detailed comparison of various representations for rotations are given in refs. [17,18] where clear and succinct tables for comparisons are presented. Rodrigues rotation formula describes the relationship between rotation vectors and rotation matrices [19,20].…”

Section: Rotationsmentioning

confidence: 99%

Autorotation

Bohr¹,

Markvorsen

2016

Phys. Scr.

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A continuous autorotation vector field along a framed space curve is defined, which describes the rotational progression of the frame. We obtain an exact integral for the length of the autorotation vector. This invokes the infinitesimal rotation vector of the frame progression and the unit vector field for the corresponding autorotation vector field. For closed curves we define an autorotation number whose integer value depends on the starting point of the curve. Upon curve deformations, the autorotation number is either constant, or can make a jump of (multiples of) plus-minus two, which corresponds to a change in rotation of multiples of 4π. The autorotation number is therefore not topologically conserved under all transformations. We discuss this within the context of generalised inflection points and of frame revisit points. The results may be applicable to physical systems such as polymers, proteins, and DNA. Finally, turbulence is discussed in the light of autorotation, as is the Philippine wine dance, the Dirac belt trick, and the 4π cycle of the flying snake.

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“…For this reason we have opted for a finite element method based on a co-rotational formulation (introduced by Felippa in [8]) which allows for large displacements while relying on a linear expression of the stress-strain relationship. The co-rotational approach is based on decomposition of the actual element configuration into rotational and deformational components, both being quantified w. r. t. the initial position.…”

Section: Parenchyma Modelmentioning

confidence: 99%

Image-guided simulation of heterogeneous tissue deformation for augmented reality during hepatic surgery

Haouchine

Dequidt

Peterlík

et al. 2013

2013 IEEE International Symposium on Mixed and Augmented Reality (ISMAR)

119

107

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Figure 1: A sequence of images showing the superimposition of the 3D real-time biomechanical model onto the human liver, undergoing deformation due to instrument interaction during minimally invasive hepatic surgery. The liver is represented in wireframe, the tumor in purple, the hepatic vein is shown in blue and the portal vein in green. ABSTRACTThis paper presents a method for real-time augmentation of vascular network and tumors during minimally invasive liver surgery. Internal structures computed from pre-operative CT scans can be overlaid onto the laparoscopic view for surgery guidance. Compared to state-of-the-art methods, our method uses a real-time biomechanical model to compute a volumetric displacement field from partial three-dimensional liver surface motion. This permits to properly handle the motion of internal structures even in the case of anisotropic or heterogeneous tissues, as it is the case for the liver and many anatomical structures. Real-time augmentation results are presented on in vivo and phantom data and illustrate the benefits of such an approach for minimally invasive surgery.

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A unified formulation of small-strain corotational finite elements: I. Theory

Cited by 350 publications

References 48 publications

Modeling and simulations for fluid and rotating structure interactions

Modeling and simulations for fluid and rotating structure interactions

Autorotation

Image-guided simulation of heterogeneous tissue deformation for augmented reality during hepatic surgery

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