• Structural Engineering and Mechanics
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• v.11 no.3
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• pp.325-340
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• 2001

This paper addresses an efficient modification method that eliminates the undesirable effects of strains due to various non-conforming modes so that the non-conforming element can pass the patch test unconditionally. The scheme is incorporated in the element formulation to establish new types of non-conforming hexahedral elements designated as NHx and NVHx for the regular element and variable node element, respectively. Non-conforming displacement modes are selectively added to the ordinary (conforming) element displacement assumptions to improve the bending behavior of the distorted solid element. To verify the validation of proposed direct modification method and the improvement of element behavior, several numerical tests are carried out. Test results show that the proposed method is effective and its applications to non-conforming solid elements guarantee for the element to pass the patch test.

• Structural Engineering and Mechanics
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• v.14 no.5
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• pp.595-610
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• 2002

This paper presents an efficiency of various non-conforming (NC) modes in development of a series of new finite elements with the special emphasis on 4-node quadrilateral elements. The NC modes have been used as a key scheme to improve the behaviors of various types of new finite elements, i.e., Mindlin plate bending elements, membrane elements with drilling degrees of freedom, flat shell elements. The NC modes are classified into three groups according to the 'correction constants' of 'Direct Modification Method'. The first group is 'basic NC modes', which have been widely used by a number of researchers in the finite element communities. The basic NC modes are effective to improve the behaviors of regular shaped elements. The second group is 'hierarchical NC modes' which improve the behaviors of distorted elements effectively. The last group is 'higher order NC modes' which improve the behaviors of plate-bending elements. When the basic NC modes are combined with hierarchical or higher order NC modes, the elements become insensitive to mesh distortions. When the membrane component of a flat shell has 'hierarchical NC modes', the membrane locking can be suppressed. A number of numerical tests are carried out to show the positive effect of aforementioned various NC modes incorporated into various types of finite elements.

• 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.4 no.5
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• pp.569-586
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• 1996

A new three-dimensional 8-node solid element with rotational degrees of freedom is presented. The proposed element is established by adding rotational degrees of freedom to the basic 8-node solid element. Thus the element has three translations and three rotational degrees of freedom per node. The corner rotations are introduced by transforming the hierarchical mid-edge displacements which are parabolic shape along an edge. The derivation of the element is based on the mixed variational principles in which the rotations are introduced as independent variables. Several types of non-conforming modes are selectively added to the displacement fields to obtain a series of improved elements. The resulting elements do not have the spurious zero energy modes and Poisson's ratio locking and pass patch test. Numerical examples show that presented non-conforming solid elements with rotational degrees of freedom show good performance even in the highly distorted meshes.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.10a
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• pp.3-17
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• 2003

This paper deals with the problems and their possible solutions in the development of finite element for analysis of shell. Based on these solution schemes, a series of flat shell elements are established which show no signs of membrane locking and other defects even though the coarse meshes are used. In the element formulation, non-conforming displacement modes are extensively used for improvement of element behaviors. A number of numerical tests are performed to prove the validity of the solutions to the problems involved in establishing a series of high performance flat shell elements. The test results reveal among others that the high accuracy and fast convergence characteristics of the elements are obtainable by the use of various non-conforming modes and that the ‘Direct Modification Method’ is a very useful tool for non-conforming elements to pass the patch tests. Furthermore, hierarchical and higher order non-conforming modes are proved to be very efficient not only to make an element insensitive to the mesh distortion but also to remove the membrane locking. Some numerical examples are solved to demonstrate the validity and applicability of the presented elements to practical engineering shell problems.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.10a
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• pp.27-34
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• 1998

A versatile flat shell element has been developed by combining a membrane element with drilling degree-of-freedom and a plate bending element. This element is formulated by the enhanced displacement field with the additional non-conforming displacement modes. Thus the element possesses six degrees-of-freedom (DOF) per node which permits an easy connection to other six DOF elements as well as the improvement of the element behavior. In plate bending part, this element is established by the combined use of the addition of non-conforming modes, the reduced (or selective) integration scheme, and the construction of the substitute shear strain fields. The achieved improvement may be attributable to the fact that the merits of these individual techniques are merged into the new element in a complementary manner. In membrane part, this element shows better membrane behavior as the nonconforming displacement mode is added to drilling mode.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.18 no.3
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• pp.311-320
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• 2005

In this paper an enhanced quadratic finite element for static and dynamic analysis of plate structures is presented. The performance of a proposed plate element is improved by the coupled use of non conforming displacement modes, the selective integration scheme, and the assumed shear strain fields. An efficient direct modification method is also applied to this element to solve the problem such as failure of the patch test due to the adoption of non conforming modes. The proposed quadratic finite element does not show any spurious mechanism and does not produce shear locking phenomena even with distorted meshes. It is shown that the results obtained by this element converged to analytical solutions very rapidly tough numerical tests for standard benchmark problems. It is also noted that this element is applicable to transient dynamic analysis of Mindlin plates.

• 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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1995.04a
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• pp.9-16
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• 1995

A new three-dimensional transition solid element with drilling degrees of freedom is presented. The proposed transition element is established by adding variable nodes to a basic 8-node element for an effective connection between the refined region and the coarse. The derivation of the element in this paper is based on the variational principles in which the drilling rotations are introduced as independent variables. This element was also improved through the addition of modified non-conforming modes. Numerical examples show that performance of the element and the applicability to 3D adaptations are satisfactory.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.409-416
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• 2001

The present work is concerned with the development of new variable-node Mindlin plate bending elements. The proposed variable-node elements pass the patch tests, do not show spurious zero-energy modes, and do not produce shear locking phenomena. It is also shown that the elements produce reliable solutions through numerical tests for standard benchmark problems.