• Structural Engineering and Mechanics
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• v.68 no.1
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• pp.17-38
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• 2018

In this paper, we compare and assess the performance of the standard 3- and 6-node MITC shell elements (Lee and Bathe 2004) with the recently developed MITC triangular elements (Lee et al. 2014, Jeon et al. 2014, Jun et al. 2018) which were based on the partitions of unity approximation, bubble node, or both. The convergence behavior of the shell elements are measured in well-known benchmark tests; four plane stress tests (mesh distortion test, cantilever beam, Cook's skew beam, and MacNeal beam), two plate tests (Morley's skew plate and circular plate), and six shell tests (curved beam, twisted beam, pinched cylinder, hemispherical shells with or without hole, and Scordelis-Lo roof). To precisely compare and evaluate the solution accuracy of the shell elements, different triangular mesh patterns and distorted element mesh are adopted in the benchmark problems. All shell finite elements considered pass the basic tests; namely, the isotropy, the patch, and the zero energy mode tests.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.33 no.2
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• pp.46-53
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• 2005

Compare to the large number of curved quadrilateral degenerated-shell elements, there are only a very few curved triangular degenerated-shell elements. Based on the assumed natural strain sampling scheme previously developed for a quadratic degenerated-shell element for linear analysis, this paper devises geometric non-linear six-node degenerated-shell element. The element can be curved and is only equipped with the standard nodal d.o.f.'s. Careful consideration has been exercised to circumvent various locking phenomena that plague degenerated-shell element. Numerical examples are presented to illustrate efficiency.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2004.10a
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• pp.69-72
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• 2004

A new three-node triangular shell element based on higher order zig-zag theory is developed for laminated composite shells with multiple delaminations. The present higher order zig-zag shell theory is described in a general curvilinear coordinate system and in general tensor notation. All the complicated curvatures of surface including twisting curvatures can be described in an exact manner in the present shell element because this element is based on geometrically exact surface representation. The displacement field of the proposed finite element includes slope of deflection, which requires continuity between element interfaces. Thus the nonconforming shape function of Specht's three-node triangular plate bending element is employed to interpolate out-of-plane displacement. The present element passes the bending and twisting patch tests in flat surface configurations. The developed element is evaluated through the eigenvalue problems of composite cylindrical shells with multiple delaminations. Through the numerical examples it is demonstrated that the proposed shell element is efficient because it has minimal degrees of freedom per node. The present shell element should serve as a powerful tool in the prediction of natural frequency and modes of multi-layered thick laminated shell structures with arbitrary-shaped multiple delaminations.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.10a
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• pp.229-236
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• 2004

A new three-node triangular shell element based on higher order zig-zag theory is developed for laminated composite shells with multiple delaminations. The present higher order zig-zag shell theory is described in a general curvilinear coordinate system and in general tensor notation. All the complicated curvatures of surface including twisting curvatures can be described in an exact manner in the present shell element because this element is based on geometrically exact surface representation. The displacement field of the proposed finite element includes slope of deflection. which requires continuity between element interfaces. Thus the nonconforming shape function of Specht's three-node triangular plate bending element is employed to interpolate out-of-plane displacement. The present element passes the bending and twisting patch tests in flat surface configurations. The developed element is evaluated through the buckling problems of composite cylindrical shells with multiple delaminations. Through the numerical examples it is demonstrated that the proposed shell element is efficient because it has minimal degrees of freedom per node. The accuracy of the present element is demonstrated in the prediction of buckling loads and buckling modes of shells with multiple delaminations. The present shell element should serve as a powerful tool in the prediction of buckling loads and modes of multi-layered thick laminated shell structures with arbitrary-shaped multiple delaminations.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.4
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• pp.451-460
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• 2007

The surface of 3D shell structure is created by using NURBS and nodes for generating finite element mesh on the surface are created by using external node offset method. In so doing the shortest distance between nodes on the top and bottom surface is searched and then the coordinates of nodes are determined by calculating the mid point of them in the middle of top and bottom surface. Triangular elements are formed on mid surface, and the average aspect ratio of the generated triangular elements are over 0.9.

• Journal of Korean Association for Spatial Structures
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• v.3 no.4 s.10
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• pp.85-92
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• 2003

In this work, a finite element model is presented for geometrically non-linear analysis of shell structures. Finite element by using a three-node flat triangular shell element is formulated. The non-linear incremental equilibrium equations are formulated by using an updated Lagrangian formulation and the solutions are obtained with the incremental/iterative Newton-Raphson method and arc length method. Some of results are presented for shell structures. The obtained results are in good agreement with the results available in existing literature.

• 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 Association for Spatial Structures
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• v.2 no.1 s.3
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• pp.93-102
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• 2002

Pressure loads caused by gas, water and wind are the most important load cases in structural analysis. Often the pressure loads are approximated by constant directional loads since it is difficult to evaluate the exact value. However, the pressure load is defined as a displacement dependent one and it is necessary to consider the follower effects of the load in analysis procedure. In this study, the large deformation analysis considering geometrical nonlinearity for shell structures under pressure loads is presented. Finite element by using a three-node flat triangular shell element is formulated and the follower effects of the pressure load are included in the formulation. Some of results are presented for cantilevered beam under uniform external pressure and thin circular ring under non-uniform external pressure. The present results are in good agreement with the results available in existing literature and commercial software ABAQUS.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.04a
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• pp.261-268
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• 2003

A first order shear deformable Loop-subdivision triangular element which can handle transverse shear deformation of moderately thick shell is developed. The developed element is general since it includes the effect of transverse shear deformation and has standard six degrees of freedom per node.(three translations and three rotations) The quartic box-spline function is employed as interpolation basis function. Numerical examples for the benchmark problems are analyzed in order to assess the performance of the newly developed subdivision shell element. Both in the uniform and in the distorted mesh configurations.

• Structural Engineering and Mechanics
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• v.15 no.1
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• pp.83-114
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• 2003

A new simple 3-node triangular flat-shell element with standard nodal DOF (6 DOF per node) is proposed for the linear and geometrically nonlinear analysis of very thin to thick plate and shell structures. The formulation of element GT9 (Long and Xu 1994), a generalized conforming membrane element with rigid rotational freedoms, is employed as the membrane component of the new shell element. Both one-point reduced integration scheme and a corresponding stabilization matrix are adopted for avoiding membrane locking and hourglass phenomenon. The bending component of the new element comes from a new generalized conforming Kirchhoff-Mindlin plate element TSL-T9, which is derived in this paper based on semiLoof constrains and rational shear interpolation. Thus the convergence can be guaranteed and no shear locking will happen. Furthermore, a simple hybrid procedure is suggested to improve the stress solutions, and the Updated Lagrangian formulae are also established for the geometrically nonlinear problems. Numerical results with solutions, which are solved by some other recent element models and the models in the commercial finite element software ABAQUS, are presented. They show that the proposed element, denoted as GMST18, exhibits excellent and better performance for the analysis of thin-think plates and shells in both linear and geometrically nonlinear problems.