• Structural Engineering and Mechanics
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• v.6 no.6
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• pp.711-725
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• 1998

Mixed finite element formulations for incompressible materials show pressure oscillations or pressure modes in four-node quadrilateral elements. The criterion for the stability in the pressure solution is the so-called Babu$\check{s}$ka-Brezzi stability condition, and the four-node elements based on mixed variational principles do not appear to satisfy this condition. In this study, a pressure continuity residual based on the pressure discontinuity at element edges proposed by Hughes and Franca is used to study the stabilization of pressure solutions in bilinear displacement-constant pressure four-node quadrilateral elements. Also, a solid mechanics problem is presented by which the stability of mixed elements can be studied. It is shown that the pressure solutions, although stable, are shown to exhibit sensitivity to the stabilization parameters.

• Journal of Mechanical Science and Technology
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• v.19 no.11
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• pp.2016-2024
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• 2005

In this work, a mixed beam approach that combines both the stiffness and the flexibility methods has been performed to analyze the coupled composite blades with closed, two-cell cross-sections. The Reissner's semi-complementary energy functional is used to derive the beam force-displacement relations. Only the membrane part of the shell wall is taken into account to make the analysis simple and also to deliver a clear picture of the mixed method. All the cross section stiffness coefficients as well as the distribution of shear across the section are evaluated in a closed-form through the beam formulation. The theory is validated against experimental test data, detailed finite element analysis results, and other analytical results for coupled composite blades with a two-cell airfoil section. Despite the simple kinematic model adopted in the theory, an accuracy comparable to that of two-dimensional finite element analysis has been obtained for cases considered in this study.

• Journal of the Korean Mathematical Society
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• v.51 no.2
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• pp.267-288
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• 2014

We propose and analyze two-scale product approximation for semilinear heat equations in the mixed finite element method. In order to efficiently resolve nonlinear algebraic equations resulting from the mixed method for semilinear parabolic problems, we treat the nonlinear terms using some interpolation operator and exploit a two-scale grid algorithm. With this scheme, the nonlinear problem is reduced to a linear problem on a fine scale mesh without losing overall accuracy of the final system. We derive optimal order $L^{\infty}((0, T];L^2({\Omega}))$-error estimates for the relevant variables. Numerical results are presented to support the theory developed in this paper.

• Journal of the Korean Society of Industry Convergence
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• v.7 no.4
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• pp.355-361
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• 2004

The finite element method were used to determine the stress intensity factor of cracked plate. The stress method, displacement method and J Integral are most popular finte element method. ANSYS proposed another a kind of displacement method. In this paper, it was examined that the accuracy and utility of the ANSYS method could believable to determine the stress intensity factors of centered inclined crack. Generally, inclined crack has two portion of stress intensity factors, tensile mode F1 and shear mode F2. For the purpose of increasing the accuracy of stress intensity factors, examined the effect of the numbers of nodes and elements, crack tip element size and number of partition of the crack tip vicinity. It was found that the method proposed by ANSYS is useful and has high accuracy. Accuracy of calculated stress intensity factors was increased by increase of the number of nodes and elements, and at the small size of crack tip elements can get more highly accuracy.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.3
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• pp.624-634
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• 1994

A numerical method which combines equal-order velocity-pressure formulation originated from SIMPLE algorithm and streamline upwinding method has been developed. To verify the proposed numerical method, we considered the lid-driven cavity flow and backward facing step flow. The trend of convergence history is stable up to the error criterion beyond which the maximum value of error is oscillatory due4 to the round-off error. In the present study, all results were obtained with the single precision calculation up to the given error criterion and it was found to be sufficient for our purpose. The present results were then compared with existing experimental results using laser doppler velocimetry and numerical results using finite difference method and mixed interpolation finite element method. It has been shown that the present method gives accurate results with less memories and execution time than the coventional finite element method.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.5
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• pp.120-127
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• 1998

Differential inequalities occurring in problems of obstacle contact problems are recast into variational inequalities and analyzed by finite element methods. A new a posteriori error estimator, which is essential in adaptive finite element method, is introduced to capture the errors in finite element approximations of these variational inequalities. In order to construct a posteriori error estimates, saddle point problems are introduced using Lagrange parameters and upper bounds are provided. The global upper bound is localized by a special mixed formulation, which leads to upper bounds of the element errors. A numerical experiment is performed on an obstacle contact problem to check the effectivity index both in a local and a global sense.

• Structural Engineering and Mechanics
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• v.73 no.1
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• pp.1-16
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• 2020

Finite elements based on the partition of unity (PU) approximation have powerful capabilities for p-adaptivity and solutions with high smoothness without remeshing of the domain. Recently, the PU approximation was successfully applied to the three-node shell finite element, properly eliminating transverse shear locking and showing excellent convergence properties and solution accuracy. However, the enrichment with the PU approximation results in a significant increase in the number of degrees of freedom; therefore, it requires greater computational cost, thus making it less suitable for practical engineering. To circumvent this disadvantage, we propose a new strategy to decrease the total number of degrees of freedom in the existing PU-based shell element, without loss of optimal convergence and accuracy. To alleviate the locking phenomenon, we use the method of mixed interpolation of tensorial components and perform convergence studies to show the accuracy and capability of the proposed shell element. The excellent performances of the new shell elements are illustrated in three benchmark problems.

• Composites Research
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• v.36 no.2
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• pp.117-125
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• 2023

This paper proposes a new finite element formulation based on enhanced first-order shear deformation theory including the transverse normal strain effect via the mixed formulation (EFSDTM-TN) for the effective thermo-mechanical analysis of laminated composite structures. The main objective of the EFSDTM-TN is to provide an accurate and efficient solution in describing the thermo-mechanical behavior of laminated composite structures by systematically establishing the relationship between two independent fields (displacement and transverse stress fields) via the mixed formulation. Another key feature is to consider the thermal strain effect without additional unknown variables by introducing a refined transverse displacement field. In the finite element formulation, an eight-node isoparametric plate element is newly developed to implement the advantage of the EFSDTM-TN. Numerical solutions for the thermo-mechanical behavior of laminated composite structures are compared with those available in the open literature to demonstrate the numerical performance of the proposed finite element model.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.303-310
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• 2001

We propose the framework which directly links shell finite element to the free form surface geometric modeling. For the development of a robust shell element, a first order shear deformable shell theory and partial mixed variational functional are provided. Bubble functions are included in the shape function of displacement to improve the performance of the developed element. The Spline/NURBS is used to generate the general free form of parameterized shell surfaces. The proposed shell finite element model linked with NURBS surface representation provides efficiency for design and analysis. Numerical examples are given in order to assess the accuracy of the performances of the proposed element.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.139-156
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• 2014

In this paper, we investigate the error estimates of a quadratic elliptic control problem with pointwise control constraints. The state and the co-state variables are approximated by the order k = 1 Raviart-Thomas mixed finite element and the control variable is discretized by piecewise linear but discontinuous functions. Approximations of order $h^{\frac{3}{2}}$ in the $L^2$-norm and order h in the $L^{\infty}$-norm for the control variable are proved.