Evaluation of overhauser splines as boundary elements in linear elastostatics

Walters, Harold G.; Gipson, G. Steven

doi:10.1016/0955-7997(94)90093-0

Cited by 8 publications

(6 citation statements)

References 4 publications

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“…In Boundary Elements Method (BEM), Overhauser quadrilateral elements were first applied by Hibbs (1987, 1988). Later, Walters and Gipson (1994) demonstrated that Overhauser elements give more accurate results then the standard quadratic and cubic elements based on Lagrange interpolation in BEM and Hadavinia et al (2000) developed generalized parabolic blending C 1 elements using Overhauser concept enhancing the accuracy of the solution over non-uniform meshing in BEM. Archer (2006) proposed continuous solutions from the Green element method using Overhauser elements, as an effective alternative to the Hermitian approach presented by Taigbenu (1998).…”

Section: Latin American Journal Of Solids and Structures 14 (2017) 92mentioning

confidence: 99%

A C1 Beam Element Based on Overhauser Interpolation

Lima

Faria

2017

Lat. Am. j. solids struct.

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A new C 1 element is proposed to model Euler-Bernoulli beams in one and two-dimensional problems. The proposed formulation assures C 1 continuity requirement without the use of rotational degrees of freedom, used in traditional elements, through the use of an Overhauser interpolation scheme for bending displacements. The principle of virtual displacements is used to determine the equilibrium equations and boundary conditions for one and twodimensional Euler-Bernoulli beams. The Overhauser interpolation is introduced and the new bending interpolation functions are defined. Finally, beam and frame problems are solved with the new formulation and the results are compared to the traditional Euler-Bernoulli element and exact solutions.

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Section: Latin American Journal Of Solids and Structures 14 (2017) 92mentioning

confidence: 99%

A C1 Beam Element Based on Overhauser Interpolation

Lima

Faria

2017

Lat. Am. j. solids struct.

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“…For the other internal nodes x 3 ; : : : ; x N −1 the value of s i is given by equation (9). This set of equations can be written in the form…”

Section: Singular-ended Splinesmentioning

confidence: 99%

“…Various types of splines, such as cubic splines [4], B-splines [6] and Overhauser splines [8], have been used to solve these di erent kinds of problems. It is claimed that the continuity up to the ÿrst (C 1 ) or even second (C 2 ) derivative across the elements boundaries provided by these functions leads to superior accuracy when compared with the standard linear or higher order polynomial elements [9]. The cost of this added continuity is the extended in uence of the nodal values on the interpolation function.…”

Section: Introductionmentioning

confidence: 98%

Singular-ended spline interpolation for two-dimensional boundary element analysis

Barros

Mesquita

2000

Int. J. Numer. Meth. Engng.

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SUMMARYA method of interpolation of the boundary variables that uses spline functions associated with singular elements is presented. This method can be used in boundary element method analysis of 2-D problems that have points where the boundary variables present singular behaviour. Singular-ended splines based on cubic splines and Overhauser splines are developed. The former provides C 2 -continuity and the latter C 1 -continuity across element edges. The potentialities of the methodology are demonstrated analysing the dynamic response of a 2-D rigid footing interacting with a half-space. It is shown that, for a given number of elements at the soil-foundation interface, the singular-ended spline interpolation increases substantially the displacement convergence rate and delivers smoother traction distributions.

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“…Accordingly, they are the most suitable interpolation form for the ÿnite element contact problem involving exible bodies. These splines have also been used to develop smooth boundary elements [21] and to evaluate contact between gear teeth [22]. Other cubic spline interpolation schemes possessing the same properties as Overhauser splines were also developed [23; 24].…”

Section: Interpolation Of Contact Surfacementioning

confidence: 99%

On the modelling of smooth contact surfaces using cubic splines

El-Abbasi

Meguid

Czekanski

2001

Int. J. Numer. Meth. Engng.

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In this paper, a new strategy for the smooth representation of 2D contact surfaces is developed and implemented. The contact surfaces are modelled using cubic splines which interpolate the finite element nodes. These splines provide a unique surface normal vector and do not require prior knowledge of surface tangents and normals. C2‐continuous cubic splines are suitable for representing rigid contact surfaces, while C1‐continuous Overhauser splines are shown to be most suitable for representing flexible contact surfaces. A consistent linearization of the kinematic contact constraints, based on the spline interpolation, is derived. The new spline‐based contact surface interpolation scheme does not influence the element calculations. Consequently, it can be easily implemented in standard FE codes. Several numerical examples are used to illustrate the advantages of the proposed smooth representation of contact surfaces. The results show a significantimprovement in accuracy compared to traditional piecewise element‐based surface interpolation. The predicted contact stresses are also less sensitive to the mismatch in the meshes of the different contacting bodies. This property is useful for problems where the contact area is unknown a priori and when there is significant tangential slip. Copyright © 2001 John Wiley & Sons, Ltd.

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Evaluation of overhauser splines as boundary elements in linear elastostatics

Cited by 8 publications

References 4 publications

A C1 Beam Element Based on Overhauser Interpolation

A C1 Beam Element Based on Overhauser Interpolation

Singular-ended spline interpolation for two-dimensional boundary element analysis

On the modelling of smooth contact surfaces using cubic splines

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