• Structural Engineering and Mechanics
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• v.25 no.4
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• pp.405-421
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• 2007

A four-node hybrid stress element for analysing orthotropic folded plate structures is presented. The formulation is based on Hellinger-Reissner variational principle. The element is developed by combining a hybrid plane stress element and a hybrid plate element. The proposed element has six degree of freedom per node and permits an easy connection to other type of elements. An equilibrated stress field in each element and inter element compatible boundary displacement field are assumed independently. Static and free vibration analyses of folded plates are carried out on numerical examples to show that the validity and efficiency of the present element.

• Structural Engineering and Mechanics
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• v.33 no.5
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• pp.573-588
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• 2009

In this paper a four-node hybrid stress element is proposed for analysing arbitrarily shaped plates on a two parameter elastic foundation. The element is developed by combining a hybrid plate stress element and a soil element. The formulation is based on Hellinger-Reissner variational principle in which both inter element compatible boundary displacement and equilibrated stress fields for the plate as well as the foundation are chosen separately. This formulation also allows a low order polynomial interpolation functions. Numerical examples are presented to show that the validity and efficiency of the present element for the plate analysis resting on an elastic foundation. In these examples the effect of soil depth, interaction between closed plates on soil parameters, comparison with Winkler hypothesis is investigated.

• Structural Engineering and Mechanics
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• v.63 no.2
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• pp.225-235
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• 2017

In this paper a vibration study on orthotropic elliptic paraboloid shells with openings is carried out by using a hybrid stress finite element. The formulation of the element is based on Hellinger-Reissner variational principle. The element is developed by combining a hybrid plane stress element and a hybrid plate element. Natural frequencies of orthotropic elliptic paraboloid shells with and without openings are presented. The influence of aspect ratio, height ratio, opening ratio and material angle on the frequencies and mode shapes are investigated.

• Steel and Composite Structures
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• v.23 no.6
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• pp.737-746
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• 2017

In this paper the influence of aspect ratio, height ratio and material angle on static and free vibration behaviour of orthotropic elliptic paraboloid shells is studied by using a four-node hybrid stress finite element. The formulation of the element is based on Hellinger-Reissner variational principle. The element is developed by combining a hybrid plane stress element and a hybrid plate element. A parametric study is carried out for static and free vibration response of orthotropic elliptic paraboloid shells with respect to displacements, internal forces, fundamental frequencies and mode shapes by varying the aspect and height ratios, and material angle.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.2A
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• pp.319-326
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• 2006

A new enhanced 8-node hybrid/mixed plane stress elements based on assumed stress fields and modifed shape functions has been presented. The assumed stress fields are derived from the non-conforming displacement modes, which are less sensitive to geometric distortion. Explicit expression of shape functions is modifed so that it can represent any quadratic fields in Cartesian coordinates under the same condition as 9-node isoparametric element. The newly developed element has been designated as 'HQ8-$14{\beta}$'. The presented element is compared with existing elements to establish its accuracy and efficiency. Over a wide range of mesh distortions, the element presented here is found to be exceptionally accurate in predicting displacements.

• Structural Engineering and Mechanics
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• v.54 no.3
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• pp.393-417
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• 2015

In this paper an 8-node quadrilateral assumed stress hybrid Mindlin plate element with $39{\beta}$ is presented. The formulation is based on complementary energy principle. The proposed element is free of shear locking and is capable of passing all the patch tests, especially the non-zero constant shear enhanced patch test. To accomplish this purpose, special attention is devoted to selecting boundary displacement interpolation and stress approximation in domain. The arbitrary order Timoshenko beam function is successfully used to derive the boundary displacement interpolation. According to the equilibrium equations, an appropriate stress approximation is rationally derived. Particularly, in order to improve element's accuracy, the assumed stress field is derived by employing $39{\beta}$ rather than conventional $21{\beta}$. The resulting element can be adopted to analyze both moderately thick and thin plates, and the convergence for the very thin case can be ensured theoretically. Excellent element performance is demonstrated by a wide of experimental evaluations.

• Steel and Composite Structures
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• v.12 no.4
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• pp.275-289
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• 2012

In this paper the influence of stiffener location, rise/span ratio and fibre orientation on vibration behavior of corner supported hypar shells is studied by using a four-node hybrid stress finite element. The formulation of the element is based on Hellinger-Reissner variational principle. The element is developed by combining a hybrid plane stress element and a hybrid plate element. Benchmark problems are solved to validate the approach and free vibration response of stiffened orthotropic hypar shells is studied both with respect to fundamental frequency and mode shapes by varying the location of stiffeners, rise/span ratio and fiber orientation.

• Structural Engineering and Mechanics
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• v.29 no.6
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• pp.643-658
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• 2008

In this paper, we present a quadratic element model based on non-conforming displacement modes and modified shape functions. This new and refined 8-node hybrid stress plane element consists of two additional non-conforming modes that are added to the translational degree of freedom to improve the behavior of a membrane component. Further, the modification of the shape functions through quadratic polynomials in x-y coordinates enables retaining reasonable accuracy even when the element becomes considerably distorted. To establish its accuracy and efficiency, the element is compared with existing elements and - over a wide range of mesh distortions - it is demonstrated to be exceptionally accurate in predicting displacements and stresses.

• Structural Engineering and Mechanics
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• v.19 no.2
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• pp.199-215
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• 2005

An assumed stress quadrilateral thin/moderately thick plate element HQP4 based on the Mindlin/Reissner plate theory is proposed. The formulation is based on Hellinger-Reissner variational principle. Static and free vibration analyses of plates are carried out. Numerical examples are presented to show that the validity and efficiency of the present element for static and free vibration analysis of plates. Satisfactory accuracy for thin and moderately thick plates is obtained and it is free from shear locking for thin plate analysis.

• Structural Engineering and Mechanics
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• v.21 no.5
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• pp.571-590
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• 2005

An 8 node assumed stress hexahedral element with rotational degrees of freedom is proposed for static and free vibration analyses. The element formulation is based directly on an 8-node element. This direct formulation requires fewer computations than a similar element that is derived from an internal 20-node element in which the midside degrees of freedom are eliminated by expressing them in terms of displacements and rotations at corner nodes. The formulation is based on Hellinger-Reissner variational principle. Numerical examples are presented to show the validity and efficiency of the present element for static and free vibration analysis.