• Journal of the Computational Structural Engineering Institute of Korea
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• v.33 no.5
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• pp.279-286
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• 2020

In this study, we investigate the accuracy of higher order derivatives in the moving least square (MLS) difference method. An interpolation function is constructed by employing a Taylor series expansion via MLS approximation. The function is then applied to the mixed variational theorem in which the displacement and stress resultants are treated as independent variables. The higher order derivatives are evaluated by solving simply supported beams and cantilevers. The results are compared with the analytical solutions in terms of the order of polynomials, support size of the weighting function, and number of nodes. The accuracy of the higher order derivatives improves with the employment of the mean value theorem, especially for very high-order derivatives (e.g., above fourth-order derivatives), which are important in a classical asymptotic analysis.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.3
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• pp.173-182
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• 2014

The mixed convolved action principle provides a new rigorous weak variational formalism for a broad range of initial boundary value problems in mathematical physics and mechanics in terms of mixed formulation, convolution, and fractional calculus. In this paper, its potential in the development of numerical methods for transient problems in various dynamical systems when adopting temporally second order approximation is investigated. For this, the classical single-degree-of-freedom linear elastic dynamical systems are primarily considered to investigate computational characteristics of the developed algorithms. For the undamped system, all the developed algorithms are symplectic with respect to the time step. For the damped system, they are shown to be accurate with good convergence characteristics.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.1
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• pp.37-43
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• 2014

The extended framework of Hamilton's principle provides a new rigorous weak variational formalism for a broad range of initial boundary value problems in mathematical physics and mechanics in terms of mixed formulation. Based upon such framework, a new variational numerical method of linear elasticity is provided for the classical single-degree-of-freedom dynamical systems. For the undamped system, the algorithm is symplectic with respect to the time step. For the damped system, it is shown to be accurate with good convergence characteristics.

• Computational Structural Engineering
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• v.26 no.2
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• pp.55-60
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• 2013

• Journal of the Computational Structural Engineering Institute of Korea
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• v.24 no.3
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• pp.249-257
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• 2011

In this paper, an systematic approach is presented, in which the mixed variational theorem is employed to incorporate independent transverse shear stresses into a classical higher-order shear deformation theory(HSDT). The HSDT displacement field is taken to amplify the benefits of using a classical shear deformation theory such as simple and straightforward calculation and numerical efficiency. Those independent transverse shear stresses are taken from the fifth-order polynomial-based zig-zag theory where the fourth-order transverse shear strains can be obtained. The classical displacement field and independent transverse shear stresses are systematically blended via the mixed variational theorem. Resulting strain energy expressions are named as an enhanced higher-order shear deformation theory via mixed variational theorem(EHSDTM). The EHSDTM possess the same computational advantage as the classical HSDT while allowing for improved through-the-thickness stress and displacement variations via the post-processing procedure. Displacement and stress distributions obtained herein are compared to those of the classical HSDT, three-dimensional elasticity, and available data in literature.

• Computational Structural Engineering
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• v.4 no.2
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• pp.87-94
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• 1991

In this paper, a mixed variational principle applicable to the linear elasticity of inhomogeneous anisotropic materials is presented. For derivation of the general variational principle, a systematic procedure for the variational formulation of linear coupled boundary value problems developed by Sandhu et al. is employed. Consistency condition of the field operators with the boundary operators results in explicit inclusion of boundary conditions in the governing functional. Extensions of admissible state function spaces and specialization to a certain relation in the general governing functional lead to the desired mixed variational principle. In the physical sense, the present variational principle is analogous to the Reissner's recent formulation obtained by applying Lagrange multiplier technique followed by partial Legendre transform to the classical minimum potential energy principle. However, the present one is more advantageous for the application to the general anisotropic materials since Reissner's principle contains an implicit function which is not easily converted to an explicit form.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.6
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• pp.505-512
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• 2012

In this paper, an efficient yet accurate method for the thermal stress analysis using a first order shear deformation theory(FSDT) is presented. The main objective herein is to systematically modify transverse shear strain energy through the mixed variational theorem(MVT). In the mixed formulation, independent transverse shear stresses are taken from the efficient higher-order zigzag plate theory, and the in-plane displacements are assumed to be those of the FSDT. Moreover, a smooth parabolic distribution through the thickness is assumed in the transverse normal displacement field in order to consider a transverse normal deformation. The resulting strain energy expression is referred to as an enhanced first order shear deformation theory, which is obtained via the mixed variational theorem with transverse normal deformation effect(EFSDTM_TN). The EFSDTM_TN has the same computational advantage as the FSDT_TN(FSDT with transverse normal deformation effect) does, which allows us to improve the through-the-thickness distributions of displacements and stresses via the recovery procedure. The thermal stresses obtained by the present theory are compared with those of the FSDT_TN and three-dimensional elasticity.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.19 no.4 s.74
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• pp.407-418
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• 2006

In this paper, an efficient yet accurate stress analysis based on the first-order shear deformation theory (FSDT) is presented. The transverse shear strain energy is modified via the mixed variational theorem, so that the shear correction factors are automatically involved in the formulation. In the mixed variational formulation, the transverse stresses are taken to be functions subject to variations. The transverse shear stresses based on an efficient higher order plate theory (EHOPT, Cho and Parmerter, 1993) are utilized and modified, while the transverse normal stress is assumed to be the third-order polynomial of thickness coordinates, which satisfies both zero transverse shear stresses and prescribed surface fractions in top and bottom surfaces. On the other hand, the displacements are assumed to be those of the FSDT Resulting strain energy expressions are referred to as an EFSDTM3D that stands for an enhanced first-order shear deformation theory based on the mixed formulation for three dimensional elasticity, The developed EFSDTM3D preserves the computational advantage of the classical FSDT while allowing for important local through-the-thickness variations of displacements and stresses through the recovery procedure that is based on the least square minimization of in-plane stresses. Comparisons of displacements and stresses of both laminated and sandwich plates using the present theory are made with the classical FSDT, three-dimensional exact solutions, and available data in the literature.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.2
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• pp.153-160
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• 2008

In this study, we propose a new three-node hybrid-mixed curved beam element with the relaxed-equiribrium stress functions for static analysis. The proposed element considering shear deformation is based on the Hellinger-Reissner variational principle. The stress functions are carefully chosen from three important considerations: (i) all the kinematic deformation modes must be suppressed, and (ii) the spurious constraints must be removed in the limiting behaviors via the field-consistency, and (iii) the relaxed equilibrium conditions could be incorporated because it might be impossible to select the stress functions and parameters to fully satisfy both the equiribrium conditions and the suppression of kinematic deformation modes in the three-node curved beam hybrid-mixed formulation. Numerical examples confirm the superior and stable behavior of the proposed element regardless of slenderness ratio and curvature. Besides, the proposed element shows the outstanding performance in predicting the stress resultant distributions.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.21 no.4
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• pp.53-59
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• 2022

In this study, an enhanced first-order shear deformation theory is proposed to efficiently and accurately predict the thermo-mechanical-viscoelastic coupled behavior of laminated composite structures. To this end, transverse shearstress and displacement fields are independently assumed, and the strain-energy relationship between these fields issystematically established using the mixed variational theorem (MVT). In MVT, the transverse shear stress fields are obtained from the third-order zigzag model, whereas the displacement fields of the conventional first-order model are considered to amplify the benefits of numerical efficiency. Additionally, a transverse displacement field with a smooth parabolic distribution is introduced to accurately predict the thermal behavior of composite structures. Furthermore, the concept of Laplace transformation is newly employed to simplify the viscoelastic problem, similar to the linear-elastic problem. To demonstrate the performance of the proposed theory, the numerical results obtained herein were compared with those available in the literature.