• Steel and Composite Structures
• /
• v.47 no.3
• /
• pp.365-374
• /
• 2023

This paper presents a new scheme for constructing locking-free finite elements in thick and thin plates, called Discrete Shear Gap element (DSG), using multiphase material topology optimization for triangular elements of Reissner-Mindlin plates. Besides, common methods are also presented in this article, such as quadrilateral element (Q4) and reduced integration method. Moreover, when the plate gets too thin, the transverse shear-locking problem arises. To avoid that phenomenon, the stabilized discrete shear gap technique is utilized in the DSG3 system stiffness matrix formulation. The accuracy and efficiency of DSG are demonstrated by the numerical examples, and many superior properties are presented, such as being a strong competitor to the common kind of Q4 elements in the static topology optimization and its computed results are confirmed against those derived from the three-node triangular element, and other existing solutions.

• Computational Structural Engineering
• /
• v.3 no.1
• /
• pp.97-107
• /
• 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
• /
• v.3 no.3
• /
• pp.113-123
• /
• 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
• /
• v.8 no.1
• /
• pp.19-26
• /
• 1999

Superior performance of field consistent eight-node hexahedron element in static bending problems has already been demonstrated in literature. In this paper, its performance in free vibration is investigated. Free vibration frequencies of typical test problems have been computed using this element. The results establish its superior performance in free vibration, particularly in thin plate application and near incompressibility regimes, demonstrating that shear locking, Poisson's stiffening and volumetric locking have been eliminated.

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

• Proceedings of the KSME Conference
• /
• 2004.04a
• /
• pp.728-732
• /
• 2004

In the FE analysis of sheet metal forming, efficient results can be obtained by using shell elements rather than using solid elements. However, shell elements have some limitations to describe three-dimensional material laws. In the recent years, solid-shell element, which has only translational degree of freedom like solid element, has been presented. The assumed nature strain (ANS) and enhanced assumed strain (EAS) methods can be used to remove several solid-shell locking problems. In this paper, ANS method was used for diminish transverse shear locking and EAS method for thickness locking. Using the element, the steel pipe making process from flat plate analyzed effectively, which is including bending and welding.

• Architectural research
• /
• v.16 no.2
• /
• pp.57-65
• /
• 2014

A study on the static analysis of Timoshenko beams is presented. A beam element is developed by using isogeometric approach based on Timoshenko beam theory which allows the transverse shear deformation. The identification of transverse shear locking is conducted by three refinement schemes such as h-, p- and k-refinement and compared to other reference solutions. From numerical examples, the present beam element does not produce any shear locking in very thin beam situations even with full Gauss integration rule. Finally, the benchmark tests described in this study is provided as future reference solutions for Timoshenko beam problems based on isogeometric approach.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.11 no.5
• /
• pp.1785-1790
• /
• 2010

To study the vortex induced vibrations the wind tunnel and the two story shear building were designed and built. The wind tunnel was designed to generate the wind speed up to 24 m/s, and the building was designed to have the two lowest natural frequencies within the range of the vortex frequencies generated by the wind tunnel. The resonance behaviors by the locking-on phenomena were observed during the wind tunnel tests of the shear building with the cylinder attached. From the locking-on phenomena observed it is found that the effects of the amplitudes and the frequencies of the cylinders should be considered on the forces generated by the vortex shedding.

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

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.17 no.11
• /
• pp.2694-2703
• /
• 1993

In the vibration analysis of Timoshenko beams by the finite element method, it is necessary to use a large number of elements or higher-order elements in modeling thin beams. This is because the overestimated stiffness matrix due to the shear locking phenomenon when lower-order displacement-based elements are used yields poor eigensolutions. As a result, the total number of degrees of freedom becomes critical in view of computational efficiency. In this paper, the curvature-based formulation is applied to the vibration problem. It is shown that the curvaturebased beam elements are free of shear locking and very efficient in the vibration analysis.