• Structural Engineering and Mechanics
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• v.40 no.3
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• pp.393-410
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• 2011

The eight-node 3D solid element is one of the most extensively used elements in computational mechanics. This is due to its simple shape and easy of discretization. However, due to the parasitic shear locking, it should not be used to simulate the behaviour of structural members in bending dominant conditions. Previous researches have indicated that the introduction of incompatible mode into the displacement field of the solid element could significantly reduce the shear locking phenomenon. In this study, an incompatible mode eight-node solid element, which considers both geometric and material nonlinearities, is developed for modelling of structural members at elevated temperatures. An algorithm is developed to extend the state determination procedure at ambient temperature to elevated temperatures overcoming initially converged stress locking when the external load is kept constant. Numerical studies show that this incompatible element is superior in terms of convergence, mesh insensitivity and reducing shear locking. It is also showed that the solid element model developed in this paper can be used to model structural behaviour at both ambient and elevated temperatures.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.7
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• pp.2078-2086
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• 1996

This paper introduces two three-dimensional eight-node hexagonal elements obtained by using multivariable variational mehtod. Both of them are based on the modified hellinger-reissner principle to employ incompatible displacements and assumed stresses of assumed strains. The internal functions of element are introduced to as element formulation through two different methods : the first one uses the functions determined directly from the element boundary condition of the incompatible displacements ; while the second, being a kind of B-bar mehtod, employs the modification technique of strain-displacement matrix to pass the patch test. The elements are evaluated on the selective problems of bending and material incompressibility with regular and distorted meshes. The results show that the new elements perform with good accuracy in both of deformation and stress calculation and they are insensitive to distorted geometry of element.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.2
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• pp.486-494
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• 1995

This paper introduces two kinds of new four-node quadrilateral axisymmetric elements with independently-assumed strains. They are formulated by the modified Hellinger-Reissner principle so as to employ incompatible displacements and assumed strains. In one of the present elements, the strains from incompatible displacements are corrected to pass the constant strain patch test. The other contains incompatible functions that are obtained from the element boundary condition. The elements are evaluated on the several problems of bending and material incompressibility with regular and distorted meshes. The results show that the new element performs excellently in deformation and stress calculation.

• Structural Engineering and Mechanics
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• v.17 no.1
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• pp.87-97
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• 2004

In gradient-dependent plasticity theory, the yield strength depends on the Laplacian of an equivalent plastic strain measure (hardening parameter), and the consistency condition results in a differential equation with respect to the plastic multiplier. The plastic multiplier is then discretized in addition to the usual discretization of the displacements, and the consistency condition is solved simultaneously with the equilibrium equations. The disadvantage is that the plastic multiplier requires a Hermitian interpolation that has four degrees of freedom at each node. Instead of using a Hermitian interpolation, in this article, a 3-node incompatible (trigonometric) interpolation is proposed for the plastic multiplier. This incompatible interpolation uses only the function values of each node, but it is continuous across element boundaries and its second-order derivatives exist within the elements. It greatly reduces the degrees of freedom for a problem, and is shown through a numerical example on localization to yield good results.

• Economic and Environmental Geology
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• v.29 no.2
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• pp.171-182
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• 1996

Quaternary Jungok basalts are distributed along the old Hantan river in Mid-Korean Peninsula. They were flowed out from Mt. Ori and Upland (680 m), and they formed narrow and long basalt plateau showing the layers of 10 to 20 meters in thickness and about 95 km in length. Fifty seven samples were collected from the study area, and sixteen rock samples were selected and analysed for major and trace elements. The analyzed samples have alkalic composition and show a relatively restricted variation in major element chemistry (except MgO), as comparing to the that of trace element. Based on major element chemistry, a quantitative modelling of fractional crystallization by multiple linear regression method suggests that the chemical evolution of the evolved rocks can be generated by fractionation of olivine, plagioc1ase, clinopyroxene, and magnetite in proportion of 56 : 25 : 17 : 2, respectively. The calculated trace element abundances by mineral proportions estimated from major element modelling, however, underestimate the incompatible element concentrations in the evolved rocks. According to the incompatible element abundances, simple fractional crystallization process has difficulty to explain the chemical variation of the evolved rocks. It seems that the other processes, which enrichment of incompatible elements can occure without concomitant changes in major element compositions, are needed in order to explain the chemical variation of the Jungok basalts. Thus, the major elements and compatible trace elements variations of the Jungok basalts are due to fractional crystallization, but the incompatible elements variation is due to fractional crystallization superimposed on already varying concentrations caused by slightly different degrees of melting of the same source, and/or due to periodic replenishment, tapping and fractionation(RTF) processes.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.22 no.2
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• pp.365-371
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• 1998

In the present study, we attempted to add the incompatible functions as additional variable terms to the conventional u-p formulation. It is derived from the four-field generalized variational principle that encompasses velocity, pressure, velocity strains and stress fields as independent interpolated variables. As a severe test of the present formulation, we have investigated the driven cavity with the corner velocity singularity like leaky lid. Through the test, the present element performs very well without unstable oscillation of pressure distribution.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.4
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• pp.1133-1145
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• 1996

A method is proposed to predict the deformed shape of the structure subjected to the unknown external loads using the signal from the piezoceramic sensors. Such a shape estimation is based on the linear relationship between the deformation of structure and the signal from sensor, which is calculated using finite element method. The deformed shape is, then calculated using the linear matrix and the signals from the piezoceramic sensors attached to the structures. For the purpose, a structural analysis program is developed using a multi-layerd finite element of 8 nodes with 3 displacement and one voltage degrees of freedom at each node. The multiple layers with the different material properties can be layered within the element. The incompatible mode with the element is found to be crucial to catch the bending behavior accurately. The accuracy of the program is, then, verified by being compared with the experimental results performed by Crawley. The proposed shape estimation method is also verified for the different loads and sensor size. It is shown that the results of shape estimation method using the linear matrix well predicts the deflections compared with those of finite element method.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2000.11a
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• pp.135-140
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• 2000

A numerical method fur performance evaluation of LIPCA is proposed using a finite element method. Fully coupled formulations for piezo-electric material are introduced and eight-node incompatible element is used. After verifying the developed code, the behaviors of LIPCA and $THUNDER^{TM}$ are investigated.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.12 no.3
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• pp.363-370
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• 1999

This study presented an modeling method for the connections in mixed structure with reinforced concrete columns and steel beam using finite element method. The contacting surfaces between concrete and steel are modeled using master-slave contact algorithm and the incompatible mode elements were used in the steel tube subjected to bending. The characteristics of mixed structure was that diaphragm was used for transferring force from beam to column. The three dimensional nonlinear analysis was performed and the analytical results compared with experimental results in order to prove modeling method.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.729-734
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• 2001

A 3-dimentional finite element model for vibration analysis of steam-turbine blade groups is presented, employing the 3-dimentional incompatible brick element with 8 nodes. The skew coordinate system is introduced in the model for considering multi-axis symmetry and specialty of displacement constrain condition of blade groups. Vibration characteristics of blade groups are analyzed, and compared with experimental results.