• Structural Engineering and Mechanics
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• v.2 no.1
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• pp.17-34
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• 1994

This paper proposes a new four node degenerated shell element. In the formulation of the new element, the assumed covariant shear strains are used to avoid the shear locking problem, and the assumed covariant membrane strains are applied to alleviate the membrane locking problem and also to improve the membrane bending performance. The assumed covariant strains are obtained from the covariant strain field defined with respect to the element natural coordinate system. This formulation enables us to obtain a shell element, which does not produce spurious singular modes, avoids locking phenomena, and excels in calculation efficiency. Several examples in this paper indicate that, despite its simplicity, the achieved accuracy and convergence are satisfactory.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.11 no.3
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• pp.1-10
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• 1991

The paper is concerned with the analysis of laminated composite shell structures using an improved degenerated shell element. In the formulation of the element stiffness, the combined use of three different techniques was made. They are; 1) an enhanced interpolation of transverse shear strains in the natural coordinate system to overcome the shear locking problem; 2) the reduced integration technique in in-plane strains to avoid the membrane locking behavior; and 3) selective addition of the nonconforming displacement modes to improve the element performances. This element is free of serious shear/membrane locking problems and undesirable compatible/commutable spurious kinematic deformation modes. An incremental total Lagrangian formulation is presented which allows the calculation of arbitrarily large displacements. The resulting non-linear equilibrium equations are solved by the Newton-Raphson method. The versatility and accuracy of this improved degenerated shell element are demonstrated by solving several numerical examples.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.4
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• pp.449-459
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• 2000

The original Mindlin-type degenerated shell element perform reasonably well for moderately thick shell structures. However, when full integration for analysis of thin shell is used to evaluate the stiffness matrix, the stiffness of shell element is often over-estimated due to shear or membrane locking phenomena. To correct this problem, the formulation of the new degenerated shell element is derived by the combination of two different techniques. The first type of elements(TypeⅠ) has used assumed shear strains in the natural coordinate system to overcome the shear locking problem, the reduced integration technique in in-plane strains(membrane strains) to avoid membrane locking behaviour. Another element(TypeⅡ) has applied the assumed strains to both of membrane strain and transverse shear strains. The improved degenerated shell element has been tested by several numerical problems of shell structures. Numerical results indicate that this shell element shows fast convergence and reliable solutions.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.10
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• pp.2535-2542
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• 1993

Two-noded curved beam elements, CMLC (field-consistent membrane and linear curvature) and IMLC(field-inconsistent membrane and linear curvature) are developed on the basis of Timoshenko's beam theory and curvilinear coordinate. The curved beam element is developed by the separation of the radial deflection into the bending deflection. In the CMLC element, field-consistent axial strain interpolation is adapted for removing the membrane locking. The CMLC element shows the rapid and stable convergence on the wide range of curved beam radius to thickness. The field-consistent axial strain and the separation of radial deformation produces the most efficient linear element possible.

• Structural Engineering and Mechanics
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• v.5 no.6
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• pp.853-865
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• 1997

The design of robust plate and shell elements has been a very challenging area for several decades. The main difficulty has been the shear locking phenomenon in plate elements and the shear and membrane locking phenomena together in the shell elements. Among the various artifices or devices which are used to develop elements free of these problems is the field-consistency approach. In this paper this approach is reviewed, It turns out that not only Mindlin type elements but also elements based on higher-order theories could be developed using the technique.

• Computational Structural Engineering
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• v.3 no.1
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• pp.97-107
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• 1990

The development of an improved degenerated shell element is presented in this paper. In the formulation of this element, an enhanced interpolation of transverse shear strains in the natural coordinate system is used to overcome the shear locking problem ; the reduced integration technique in in-plane strains is applied to avoid the membrane locking behavior ; and selective addition of the nonconforming displacement modes improve the element performances. This element is free of serious locking problems and undesirable compatible or commutable spurious kinematic deformation modes, and passes the patch tests. To illustrate the performance of this improved degenerated shell element, some benchmark problems are presented. Numerical results indicate that the new element shows fast convergence and reliable solutions.

• Computational Structural Engineering
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• v.3 no.3
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• pp.113-123
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• 1990

The paper is concerned with the elasto-plastic and geometrically nonlinear analysis of shell structures using an improved degenerated shell element. In the formulation of the element stiffness, the combined use of three different techniques was made. They are; 1) an enhanced interpolation of transverse shear strains in the natural coordinate system to overcome the shear locking problem ; 2) the reduced integration technique in in-plane strains to avoid the membrane locking behavior ; and 3) selective addition of the nonconforming displacement modes to improve the element performances. This element is free of serious shear/membrane locking problems and undesirable compatible/commutable spurious kinematic deformation modes. In the formulation for plastic deformation, the concept of a layered element model is used and the material is assumed von Mises yield criterion. An incremental total Lagrangian formulation is presented which allows the calculation of arbitrarily large displacements and rotations. The resulting non-linear equilibrium equations are solved by the Netwon-Raphson method combined with load or displacement increment. The versatility and accuracy of this improved degenerated shell element are demonstrated by solving several numerical examples.

• Structural Engineering and Mechanics
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• v.8 no.2
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• pp.207-231
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• 1999

A versatile 4-node shell element which is useful for the analysis of arbitrary shell structures is presented. The element is developed by flat shell approach, i.e., by combining a membrane element with a Mindlin plate element. The proposed element has six degrees of freedom per node and permits an easy connection to other types of finite elements. In the plate bending part, an improved Mindlin plate has been established by the combined use of the addition of non-conforming displacement modes (N) and the substitute shear strain fields (S). In the membrane part, the nonconforming displacement modes are also added to the displacement fields to improve the behavior of membrane element with drilling degrees of freedom and the modified numerical integration (M) is used to overcome the membrane locking problem. Thus the element is designated as NMS-4F. The rigid link correction technique is adopted to consider the effect of out-of-plane warping. The shell element proposed herein passes the patch tests, does not show any spurious mechanism and does not produce shear and membrane locking phenomena. It is shown that the element produces reliable solutions even for the distorted meshes through the analysis of benchmark problems.

• Structural Engineering and Mechanics
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• v.40 no.2
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• pp.191-213
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• 2011

This paper presents an improved 8-node shell element for the analysis of plates and shells. The finite element, based on a refined first-order shear deformation theory, is further improved by the combined use of assumed natural strain method. We analyze the influence of the shell element with the different patterns of sampling points for interpolating different components of strains. Using the assumed natural strain method with proper interpolation functions, the present shell element generates neither membrane nor shear locking behavior even when full integration is used in the formulation. Further, a refined first-order shear deformation theory, which results in parabolic through-thickness distribution of the transverse shear strains from the formulation based on the third-order shear deformation theory, is proposed. This formulation eliminates the need for shear correction factors in the first-order theory. Numerical examples demonstrate that the present element perform better in comparison with other shell elements.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1990.04a
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• pp.18-23
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• 1990

The paper is concerned with the elasto-plastic and geometrically nonlinear analysis of shell structures using an improved degenerated shell element. In the formulation of the improved degenerated shell element, an enhanced interpolation of transverse shear strains in the natural coordinate system is used to overcome the shear locking problems; the reduced integration technique in in-plane strains is applied to avoid membrane locking behavior; selective addition the nonconforming displacement modes improve the element performances. This element is free of serious locking problems and undesirable compatible or commutable spurious kinematic deformation modes and passes the patch tests. An incremental total Lagrangian formulation is presented which allows the calculation of arbitrarily large displacements and rotations. The resulting nonlinear equations are solved by the Newton-Raphson solution scheme. The versatility and accuracy of this improved degenerated shell element are demonstrated by solving several numerical examples.