• Structural Engineering and Mechanics
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• v.68 no.4
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• pp.385-398
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• 2018

In the present paper, we offer a new flat shell finite element. It is the result of the combination of a membrane element and a bending element, both based on the strain-based formulation. It is known that $C^{\circ}$ plane membrane elements provide poor deflection and stress for problems where bending is dominant. In addition, they encounter continuity and compliance problems when they connect to C1 class plate elements. The reach of the present work is to surmount these problems when a membrane element is coupled with a thin plate element in order to construct a shell element. The membrane element used is a triangular element with four nodes, three nodes at the vertices of the triangle and the fourth one at its barycenter. Each node has three degrees of freedom, two translations and one rotation around the normal. The coefficients related to the degrees of freedom at the internal node are subsequently removed from the element stiffness matrix by using the static condensation technique. The interpolation functions of strain, displacements and stresses fields are developed from equilibrium conditions. The plate element used for the construction of the present shell element is a triangular four-node thin plate element based on Kirchhoff plate theory, the strain approach, the four fictitious node, the static condensation and the analytic integration. The shell element result of this combination is robust, competitive and efficient.

• Journal of Korean Society of Steel Construction
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• v.16 no.3 s.70
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• pp.295-303
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• 2004

In this paper, an improved four-node Reissner-Mindlin plate-bending element with enhanced assumed strain field is presented for the analysis of isotropic and laminated composite plates. To avoid the shear locking and spurious zero energy modes, the transverse shear behavior is improved by the addition of a new enhanced shear strain based on the incompatible displacement mode approach and bubble function. The "standard" enhanced strain fields (Andelfinger and Ramm, 1993) are also employed to improve the in-plane behaviors of the plate elements. The four-node quadrilateral element derived using the first-order shear deformation theory is designated as "14EASP". Several applications are investigated to assess the features and the performances of the proposed element. The results are compared with other finite element solutions and analytical solutions. Numerical examples show that the element is stable, invariant, passes the patch test, and yields good results especially in highly distorted regimes.

• Structural Engineering and Mechanics
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• v.39 no.3
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• pp.339-360
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• 2011

In the h-type adaptive analysis, when an element is refined or subdivided, new nodes are added. Among them are the transition nodes which are the corner nodes of the new elements formed by subdivision and, simultaneously, the mid-side nodes of the adjacent non-subdivided elements. To secure displacement compatibility, the slave-node approach in which the DOFs of a transition node are constrained by those of the adjacent nodes had been used. Alternatively, transition elements which possess the transition nodes as active mid-side/-face nodes can be used. For C0 plate analyses, the conventional slave-node constraints and the previously derived ANS transition elements are implemented. In both implementations, the four-node element is the ANS element. With reference to the predictions of the transition elements, the slave-node approach not only delivers erroneous results but also fails the patch test. In this paper, the patch test failure is resolved by developing a set of new constraints with which the slave-node approach surpasses the transition-element approach. The accuracy of the slave-node approach is further improved by developing a hybrid four-node element in which the assumed moment and shear force modes are in strict equilibrium.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.14 no.3
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• pp.349-359
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• 2001

An enhanced four-node plate element, which has been developed for explicit dynamic analysis of plate, is described in this paper. Reissner-Mind1in(RM) assumptions are adopted to consider transverse shear deformation effects in the present plate element. RM plate element produces a shear locking phenomena in thin plate so that the substitute natural strains based on assumed strain method are explicitly derived. The present plate element is applied into the explicit transient algorithm and the mass matrix of plate is formulated by using special lumping method proposed by Hinton et al. The performance of the element is verified with numerical examples.

• Structural Engineering and Mechanics
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• v.30 no.4
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• pp.387-402
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• 2008

The Integrated Force Method (IFM) has been developed in recent years for the analysis of civil, mechanical and aerospace engineering structures. In this method all independent or internal forces are treated as unknown variables which are calculated by simultaneously imposing equations of equilibrium and compatibility conditions. The solution by IFM needs the computation of element equilibrium and flexibility matrices from the assumed displacement, stress-resultant fields and material properties. This paper presents a general purpose code for the automatic generation of element equilibrium and flexibility matrices for plate bending elements using the Integrated Force Method. Kirchhoff and the Mindlin-Reissner plate theories have been employed in the code. Paper illustrates development of element equilibrium and flexibility matrices for the Mindlin-Reissner theory based four node quadrilateral plate bending element using the Integrated Force Method.

• International Journal of Naval Architecture and Ocean Engineering
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• v.7 no.2
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• pp.324-345
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• 2015

A new procedure for determining properties of thick plate finite elements, based on the modified Mindlin theory for moderately thick plate, is presented. Bending deflection is used as a potential function for the definition of total (bending and shear) deflection and angles of cross-section rotations. As a result of the introduced interdependence among displacements, the shear locking problem, present and solved in known finite element formulations, is avoided. Natural vibration analysis of rectangular plate, utilizing the proposed four-node quadrilateral finite element, shows higher accuracy than the sophisticated finite elements incorporated in some commercial software. In addition, the relation between thick and thin finite element properties is established, and compared with those in relevant literature.

• Structural Engineering and Mechanics
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• v.49 no.6
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• pp.793-810
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• 2014

This research work deals with the development of a new Triangular finite element for the linear analysis of plate bending with transverse shear effect. It is developed in perspective to building shell elements. The displacements field of the element has been developed by the use of the strain-based approach and it is based on the assumed independent functions for the various components of strain insofar as it is allowed by the compatibility equations. Its formulation uses also concepts related to the fourth fictitious node, the static condensation and analytic integration. It is based on the assumptions of tick plate.s theory (Reissner-Mindlin theory). The element possesses three essential external degrees of freedom at each of the four nodes and satisfies the exact representation of the rigid body modes of displacements. As a result of this approach, a new bending plate finite element (Pep43) which is competitive, robust and efficient.

• Structural Engineering and Mechanics
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• v.59 no.6
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• pp.1071-1094
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• 2016

We employ the so-called problem-dependent linked interpolation concept to develop two cubic 4-node quadrilateral plate finite elements with 12 external degrees of freedom that pass the constant bending patch test for arbitrary node positions of which the second element has five additional internal degrees of freedom to get polynomial completeness of the cubic form. The new elements are compared to the existing linked-interpolation quadratic and nine-node cubic elements presented by the author earlier and to the other elements from literature that use the cubic linked interpolation by testing them on several benchmark examples.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.855-859
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• 2004

We develop a new four-node flat shell element which is accurate, efficient, and suitable to be used on general purpose. The new element has a hybrid Trefftz element with drilling degrees of freedom as a membrane part. We define the two independent displacement field: the internal displacement field that satisfies governing equations in the domain a priori and the boundary displacement field that is usually used as a conventional finite element method. The hybrid Trefftz variational formulation connects these two displacement fields on the boundary of the domain. To add drilling degrees of freedom, we introduce the Allman's quadratic displacement field to the boundary displacement field. As a result, our flat shell element has 6 degrees of freedom per a node. We also use the well-known DKMQ plate bending element for the plate part of the proposed element. The DKMQ element satisfies Mindlin-Reissner‘s plate theory along the edge of the element and gives proper behavior regardless of the thickness. A series of numerical experiments shows that the performance of the new element such as accuracy, rate of convergence, robustness to mesh quality, and so on.

• Structural Engineering and Mechanics
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• v.57 no.3
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• pp.473-506
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• 2016

The aim of this work is the development of a 2D quadrilateral isoparametric finite element model, based on a layerwise approach, for the bending analysis of sandwich plates. The face sheets and the core are modeled individually using, respectively, the first order shear deformation theory and the third-order plate theory. The displacement continuity condition at the interfaces 'face sheets-core' is satisfied. The assumed natural strains method is introduced to avoid an eventual shear locking phenomenon. The developed element is a four-nodded isoparametric element with fifty two degrees-of-freedom (52 DOF). Each face sheet has only two rotational DOF per node and the core has nine DOF per node: six rotational degrees and three translation components which are common for the all sandwich layers. The performance of the proposed element model is assessed by six examples, considering symmetric/unsymmetric composite sandwich plates with different aspect ratios, loadings and boundary conditions. The numerical results obtained are compared with the analytical solutions and the numerical results obtained by other authors. The results indicate that the proposed element model is promising in terms of the accuracy and the convergence speed for both thin and thick plates.