The Application of Newton’s Method to the Problem of Elastic Stability

Riks, E.

doi:10.1115/1.3422829

Cited by 679 publications

(277 citation statements)

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“…To construct the entire branch of ceased states, namely, both the stable and unstable equilibrium states, we use the Riks method of arclength continuation. 28 Because the length of a crease is unknown, to be determined as part of the solution, the simulation often does not converge. To enable these calculations, we therefore place a much softer material on top of the film, which prevents surface self-contact and facilitates convergence of the simulation.…”

mentioning

confidence: 99%

Controlled formation and disappearance of creases

et al. 2014

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mentioning

confidence: 99%

Controlled formation and disappearance of creases

et al. 2014

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“…The basis of GMNIA analysis is the Risk method. This method was developed by Wempner (1971) [10], Riks (1972Riks ( , 1979 [11,12] and later supplemented by other several authors. In the Riks method, nonlinear static equilibrium solution is to produced for unstable phenomena.…”

Section: Geometrically and Materially Nonlinear Imperfection Analysismentioning

confidence: 99%

Resistance of Door Openings in Towers for Wind Turbines

Tran¹,

Veljković²,

Rebelo³

et al. 2014

Proceedings of the 3rd South-East European Conference on Computational Mechanics (SEECCM III)

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Abstract. In this paper, a study of resistance of a lower part of a wind tower including a door opening is presented. Nonlinear 3-D shell element models with real geometry of lower tower segment have been used to simulate the thin walled shell structure in order to study the influence of door opening on the strength of the tower. Two possible alternatives for strengthening the door openings were considered: (i) increasing thicknesses of plate around the opening and (ii) stiffening the opening by a stiffener. Buckling analysis and nonlinear analysis were performed to obtain critical buckling modes and strength of the tower segment. Nominal material properties of different steel grades were considered to investigate possibility of using higher strength steels. A parametric study considering possible local shell imperfections according to EN1993-1-6 has been considered. Additionally, comparative studies have been performed based on the FE model without door opening.

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“…Linear eigenvalue buckling analyses are also performed to generate perturbations in the form of the linear eigen modes to be used in subsequent response analyses. Geometric nonlinearity is included in the response analysis through the RIKS [Riks 1972] option available in ABAQUS. Elastic material properties for the AS4/3501-6 [Soden et al 1998] material system are described in Table 3, which are consistent with the lamina properties derived from the fiber and matrix properties described in [Basu 2005].…”

Section: Numerical Simulationsmentioning

confidence: 99%

A macroscopic model for kink banding instabilities in fiber composites

Basu¹,

Waas

Ambur

2006

JOMMS

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In this paper, a mechanism-based lamina level modeling approach is used as the basis for developing a macroscopic (lamina level) model to capture the mechanisms of kink banding. Laminae are modeled as inelastic degrading homogenized layers in a state of plane stress according to Schapery Theory (ST). However, the principal orthotropic material axes are allowed to rotate as a function of deformation. In ST, each lamina degrades as characterized through laboratory scale experiments. In the fiber direction, elastic behavior prevails; however, in this work, the phenomenon of fiber microbuckling leading to kink banding, which is responsible for the sudden degradation of the axial lamina properties under compression, is explicitly accounted for by allowing the fiber rotation at a material point to be a variable in the problem. These features are built into a user-defined material subroutine that is implemented through the commercial finite element (FE) software ABAQUS. Thus, in this model we eschew the notion of a fixed compressive strength of a lamina and instead use the mechanics of the failure process to provide the in situ compression strength of a material point in a lamina, the latter being dictated strongly by the current local stress state, the current state of the lamina transverse material properties, and the local fiber rotation. The inputs to this model are laboratory scale, coupon level test data (at the lamina level) that provide information on the lamina transverse property degradation (that is, appropriate, measured, strain-stress relations of the lamina transverse properties), the elastic lamina orthotropic properties and the geometry of the lamina. The validity of the approach advocated is demonstrated through numerical simulations of unidirectional lamina with initial fiber imperfections. The predictions of the simulations reported in this paper are compared against previously reported results from micromechanical analyses. Good agreement between the present macroscopic modeling approach and the previous micromechanical observations are reported.

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The Application of Newton’s Method to the Problem of Elastic Stability

Cited by 679 publications

References 0 publications

Controlled formation and disappearance of creases

Controlled formation and disappearance of creases

Resistance of Door Openings in Towers for Wind Turbines

A macroscopic model for kink banding instabilities in fiber composites

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