On the uniqueness of large deflections of a uniform cantilever beam under a tip-concentrated rotational load

Mutyalarao, M.; Bharathi, Divya; Rao, B. Nageswara

doi:10.1016/j.ijnonlinmec.2009.12.015

Cited by 24 publications

(16 citation statements)

References 18 publications

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“…Asymptotic effectivity indexes are obtained for large number of degrees of freedom n V h,p . (29) and (30), while for ∆ i,2h,p and ∆ i,h,p+1 , also the enhanced primal ones (33) and (34) need to be solved, with consequent increased computational costs.…”

Section: Error Estimatorsmentioning

confidence: 99%

“…[3] and the references therein. Also, different approaches have been considered in the literature for the analysis of elastic thin beams: (i) the elliptic integral approach first proposed by [9], which gives closed-form solutions only for simple loading cases and boundary conditions [33], (ii) the numerical integration approach with iterative shooting techniques (e.g. [29,32,13]), and (iii) the incremental Finite Element method with Newton-Raphson iteration techniques [43,22,21].…”

Section: Introductionmentioning

confidence: 99%

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B-spline goal-oriented error estimators for geometrically nonlinear rods

Dedè¹,

Santos²

2011

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Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. AbstractWe consider goal-oriented a posteriori error estimators for the evaluation of the errors on quantities of interest associated with the solution of geometrically nonlinear curved elastic rods. For the numerical solution of these nonlinear one-dimensional problems, we adopt a B-spline based Galerkin method, a particular case of the more general Isogeometric Analysis. We propose error estimators using higher order "enhanced" solutions, which are based on the concept of enrichment of the original B-spline basis by means of the "pure" k-refinement procedure typical of Isogeometric Analysis. We provide several numerical examples for linear and nonlinear output functionals, corresponding to the rotation, displacements and strain energy of the rod, and we compare the effectiveness of the proposed error estimators.

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Section: Error Estimatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

B-spline goal-oriented error estimators for geometrically nonlinear rods

Dedè¹,

Santos²

2011

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“…In another approach, two point boundary value problem is converted to an initial value problem by estimating slope of beam at particular position as one of the required initial condition for a particular load step. The initial value problem is then solved using several iterative shooting techniques [77,78]. The problem associated with such iterative process is convergence of the solution.…”

Section: Analytical Methodmentioning

confidence: 99%

“…Presence of multiple solutions for similar boundary value problem is another frequently encountered problem in nonlinear analysis of beam structures [79][80][81]. However, most widely used numerical methods [82][83][84][85][86] for solution of nonlinear governing equations of beam problems are Newton iterative method [82], Runge-Kutta-Fehlberg method [83], Runge-Kutta method [77,78,85,86], etc.…”

Section: Analytical Methodmentioning

confidence: 99%

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A Review on Stress and Deformation Analysis of Curved Beams under Large Deflection

Ghuku

Saha

2017

IJET

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Abstract. The paper presents a review on large deflection behavior of curved beams, as manifested through the responses under static loading. The term large deflection behavior refers to the inherent nonlinearity present in the analysis of such beam system response. The analysis leads to the field of geometric nonlinearity, in which equation of equilibrium is generally written in deformed configuration. Hence, the domain of large deflection analysis treats beam of any initial configuration as curved beam. The term curved designates the geometry of center line of beam, distinguishing it from the usual straight or circular arc configuration. Different methods adopted by researchers, to analyze large deflection behavior of beam bending, have been taken into consideration. The methods have been categorized based on their application in various formats of problems. The nonlinear response of a beam under static loading is also a function of different parameters of the particular problem. These include boundary condition, loading pattern, initial geometry of the beam, etc. In addition, another class of nonlinearity is commonly encountered in structural analysis, which is associated with nonlinear stress-strain relations and known as material nonlinearity. However the present paper mainly focuses on geometric nonlinear analysis of beam, and analysis associated with nonlinear material behavior is covered briefly as it belongs to another class of study. Research works on bifurcation instability and vibration responses of curved beams under large deflection is also excluded from the scope of the present review paper.

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B-spline goal-oriented error estimators for geometrically nonlinear rods

Dedè

Santos

2011

Comput Mech

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We consider goal-oriented a posteriori error estimators for the evaluation of the errors on quantities of interest associated with the solution of geometrically nonlinear curved elastic rods. For the numerical solution of these nonlinear one-dimensional problems, we adopt a B-spline based Galerkin method, a particular case of the more general isogeometric analysis. We propose error estimators using higher order "enhanced" solutions, which are based on the concept of enrichment of the original B-spline basis by means of the "pure" k-refinement procedure typical of isogeometric analysis. We provide several numerical examples for linear and nonlinear output functionals, corresponding to the rotation, displacements and strain energy of the rod, and we compare the effectiveness of the proposed error estimators. © 2011 Springer-Verlag

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On the uniqueness of large deflections of a uniform cantilever beam under a tip-concentrated rotational load

Cited by 24 publications

References 18 publications

B-spline goal-oriented error estimators for geometrically nonlinear rods

B-spline goal-oriented error estimators for geometrically nonlinear rods

A Review on Stress and Deformation Analysis of Curved Beams under Large Deflection

B-spline goal-oriented error estimators for geometrically nonlinear rods

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