Improved assumed‐stress hybrid shell element with drilling degrees of freedom for linear stress, buckling and free vibration analyses

Rengarajan, G.; Aminpour, Mohammad A.; Knight, Norman F.

doi:10.1002/nme.1620381108

Cited by 28 publications

(7 citation statements)

References 23 publications

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“…HT4R18*the hybrid stress element employing the 18 symmetric stress modes given in Equation (15); the zero-energy rotation modes are suppressed by the four skew symmetric stress modes given in Equation (24); the constant and higher order symmetric stress modes are orthogonal, see Section 6. HT4R14*same as HT4R18 except that only 14 symmetric stress modes are employed; these stress modes are obtained by subjecting the 18 modes in Equation (16) to the four constraints in Equation (16).…”

Section: Numerical Examplesmentioning

confidence: 99%

Hybrid stress tetrahedral elements with Allman's rotational D.O.F.s

Sze

Pan

2000

Int. J. Numer. Meth. Engng.

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SUMMARYThis paper presents two hybrid stress four-node tetrahedron solid elements which are equipped with the rotational d.o.f.s proposed by Allman. Inasmuch Allman's rotation is employed, the elements are plagued by zero-energy rotation modes which induce no strain. A modi"ed Hellinger}Reissner functional that treats the rotation and the skew symmetric stress as independent "elds is employed to formulate a stabilization scheme. Particular e!ort has been made to reduce the number of stress modes to minimum without sacri"cing the frame invariance and proper rank of the element. The computational cost of the element is reduced by adopting orthogonal constant and non-constant symmetric stress modes. Numerical benchmark tests indicate that accuracy of the element with the minimum number of stress modes is close to another multi-"eld element which, however, is not frame invariant and exhibits unsuppressed zero-energy deformation modes.

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Section: Numerical Examplesmentioning

confidence: 99%

Hybrid stress tetrahedral elements with Allman's rotational D.O.F.s

Sze

Pan

2000

Int. J. Numer. Meth. Engng.

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“…In general, 3D solid and shell element models are used to evaluate the lateral behaviour and instability of bridge girders supported on an elastic bearing pad. Barsoum and Gallagher (1970) solved lateral and torsional flexural stability problems using finite-element (FE) analysis, and several other researchers (Li et al, 2002;Rengarajan et al, 1985;Talbot and Dhatt, 1987) developed the FE method using shell elements for stability problems, which require geometric nonlinearity and unstable bifurcation. In the current study, for much easier modelling of the elastic support condition and application to changes in girder geometry and boundary conditions, a simplified numerical method, based on a 3D beam element, was used to evaluate the lateral instability behaviour of precast concrete girders supported on elastomeric bearings at the construction stage.…”

Section: Introductionmentioning

confidence: 99%

Rollover instability of precast girders subjected to wind load

Lee¹,

Kalkan²,

Lee³

et al. 2017

Magazine of Concrete Research

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The use of longer and deeper precast concrete girders has created concern regarding their rollover instability, particularly during construction. Current design and construction specifications do not provide any specific guidelines that can be used to evaluate the rollover instability of a girder. Therefore, analytical and simplified numerical studies were performed to evaluate the critical wind load, lateral displacement and rotational angle that would induce rollover instability of a girder supported on an elastomeric bearing pad. The influence of the length and section properties of the girder on rollover instability was also investigated. The analytical method proposed in this study can be effectively used for evaluating the lateral behaviour and rollover instability of bridge girders and can also provide management values for securing the lateral stability of girders. The paper also provides a worked problem for a long-span typical European girder to determine critical values with application of the proposed method.

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“…Analytical investigations into the lateral and torsional stability have been performed to develop a classical stability theory based on the steel structural members (Horne 1954;Salvadori 1955;Timoshenko 1956;Timoshenko and Gere 1961). Several studies (i.e., Talbot and Dhatt 1987;Rengarajan et al 1995;Li et al 2002;Darilmaz 2011;Brsoum and Gallagher 1970;Fafard et al 1987) developed finite element analysis using shell and plate elements for buckling analysis, which requires large geometric nonlinearity and bifurcation.…”

Section: Introductionmentioning

confidence: 99%

Experimental and Measurement Methods for the Small-Scale Model Testing of Lateral and Torsional Stability

Lee

Park

Jung

et al. 2017

Int J Concr Struct Mater

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Tests of the lateral and torsional stability are quite sensitive to the experimental conditions, such as support conditions and loading system. Controlling all of these conditions in a full-size test is a very challenging task. Therefore, in this paper, an experimental measurement method that can control the experimental conditions using a small-scale model was proposed to evaluate the lateral and torsional stability of beams. For this, a loading system was provided to maintain the vertical direction of the load applied to the beam, and a support frame was produced to satisfy the in-plane and out-of-plane support conditions. The experimental method using a small-scale model was applied successively to the lateral and torsional behavior and stability of I-shaped beams. The proposed experimental methods, which effectively accommodate the changes in the geometry and length of the beam, could contribute to further experimental studies regarding the lateral and torsional stability of flexural members.

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Improved assumed‐stress hybrid shell element with drilling degrees of freedom for linear stress, buckling and free vibration analyses

Cited by 28 publications

References 23 publications

Hybrid stress tetrahedral elements with Allman's rotational D.O.F.s

Hybrid stress tetrahedral elements with Allman's rotational D.O.F.s

Rollover instability of precast girders subjected to wind load

Experimental and Measurement Methods for the Small-Scale Model Testing of Lateral and Torsional Stability

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