• Structural Engineering and Mechanics
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• v.2 no.1
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• pp.17-34
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• 1994

This paper proposes a new four node degenerated shell element. In the formulation of the new element, the assumed covariant shear strains are used to avoid the shear locking problem, and the assumed covariant membrane strains are applied to alleviate the membrane locking problem and also to improve the membrane bending performance. The assumed covariant strains are obtained from the covariant strain field defined with respect to the element natural coordinate system. This formulation enables us to obtain a shell element, which does not produce spurious singular modes, avoids locking phenomena, and excels in calculation efficiency. Several examples in this paper indicate that, despite its simplicity, the achieved accuracy and convergence are satisfactory.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.11 no.6
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• pp.2284-2291
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• 2010

In this paper, we investigate the vibration analysis of plates, using an 8-node shell element that accounts for the transverse shear strains and rotary inertia. The forced vibration analysis of plates subjected to arbitrary loading is investigated. In order to overcome membrane and shear locking phenomena, the assumed natural strain method is used. To improve an 8-node shell element for forced vibration analysis, the new combination of sampling points for assumed natural strain method was applied. The refined first-order shear deformation theory based on Reissner-Mindlin theory which allows the shear deformation without shear correction factor and rotary inertia effect to be considered is adopted for development of 8-node assumed strain shell element. In order to validate the finite element numerical solutions, the reference solutions of plates are presented. Results of the present theory show good agreement with the reference solution. In addition the effect of damping is investigated on the forced vibration analysis of plates.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.11 no.12
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• pp.5199-5206
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• 2010

In this paper, we investigate the buckling analysis of laminated composite plates, using a improved assumed natural strain shell element. In order to overcome membrane and shear locking phenomena, the assumed natural strain method is used. The eigenvalues of the laminated composite plates are calculated by varying the width-thickness ratio and angle of fiber. To improve an shell element for buckling analysis, the new combination of sampling points for assumed natural strain method was applied and the refined first-order shear deformation theory which allows the shear deformation without shear correction factor. In order to validate the present solutions, the reference solutions are used and discussed. The results of laminated composite plates under the in-plane shear loading may be the benchmark test for the buckling analysis.

• Steel and Composite Structures
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• v.21 no.2
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• pp.373-394
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• 2016

The postbuckling behavior of laminated composite plates and shells, subjected to various shear loadings, is presented, using a modified 8-ANS method. The finite element, based on a modified first-order shear deformation theory, is further improved by the combined use of assumed natural strain method. We analyze the influence of the shell element with the various location and number of enhanced membrane and shear interpolation. Using the assumed natural strain method with proper interpolation functions, the present shell element generates neither membrane nor shear locking behavior even when full integration is used in the formulation. The effects of various types of lay-ups, materials and number of layers on initial buckling and postbuckling response of the laminated composite plates and shells for various shear loading have been discussed. In addition, the effect of direction of shear load on the postbuckling behavior is studied. Numerical results and comparisons of the present results with those found in the literature for typical benchmark problems involving symmetric cross-ply laminated composites are found to be excellent and show the validity of the developed finite element model. The study is relevant to the simulation of barrels, pipes, wing surfaces, aircrafts, rockets and missile structures subjected to intense complex loading.

• Structural Engineering and Mechanics
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• v.88 no.4
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• pp.335-354
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• 2023

In this study, analysis of wave propagation characteristics for functionally graded carbon nanotube-reinforced composite (FG-CNTRC) nanoplates is performed using first-order shear deformation theory (FSDT) and nonlocal strain gradient theory. Uniform distribution (UD) and three types of functionally graded distributions of carbon nanotubes (CNTs) are assumed. The effective mechanical properties of the FG-CNTRC nanoplate are assumed to vary continuously in the thickness direction and are approximated based on the rule of mixture. Also, the governing equations of motion are derived via the extended Hamilton's principle. In numerical examples, the effects of nonlocal parameter, wavenumber, angle of wave propagation, volume fractions, and carbon nanotube distributions on the wave propagation characteristics of the FG-CNTRC nanoplate are studied. As represented in the results, it is clear that the internal length-scale parameter has a remarkable effect on the wave propagation characteristics resulting in significant changes in phase velocity and natural frequency. Furthermore, it is observed that the strain gradient theory yields a higher phase velocity and frequency compared to those obtained by the nonlocal strain gradient theory and classic theory.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.17 no.3
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• pp.279-293
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• 2004

The analysis of linear static and free vibration problems of isotropic and laminated composite plates and shells is performed by the improved 9-node shell element with the new strain displacement relationship. In that relationship, the effect of new additional terms between the bending strain and displacement has been investigated in the warping problem. Natural co ordinate based strains, stresses and constitutive equations are used. The assumed natural strain method is used to alleviate both membrane and shear locking behavior from the element. The Lanczos method is employed in the calculation of the eigenvalues of laminated composite structures and the Gauss integration rule is adopted to evaluate the mass matrix. The numerical examples are compared with the analytical solutions to validate the current formulation and the results presented could be useful for the understanding of the behaviour of laminates under free vibration conditions.

• Structural Engineering and Mechanics
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• v.18 no.6
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• pp.807-829
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• 2004

The Element-Based Lagrangian Formulation of a 9-node resultant-stress shell element is presented for the isotropic and anisotropic composite material. The effect of the coupling term between the bending strain and displacement has been investigated in the warping problem. The strains, stresses and constitutive equations based on the natural co-ordinate have been used throughout the Element-Based Lagrangian Formulation of the present shell element which offers an advantage of easy implementation compared with the traditional Lagrangian Formulation. The element is free of both membrane and shear locking behavior by using the assumed natural strain method such that the element performs very well in thin shell problems. In composite plates and shells, the transverse shear stiffness is defined by an equilibrium approach instead of using the shear correction factor. The arc-length control method is used to trace complex equilibrium paths in thin shell applications. Several numerical analyses are presented and discussed in order to investigate the capabilities of the present shell element. The results showed very good agreement compared with well-established formulations in the literature.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.14 no.3
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• pp.349-359
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• 2001

An enhanced four-node plate element, which has been developed for explicit dynamic analysis of plate, is described in this paper. Reissner-Mind1in(RM) assumptions are adopted to consider transverse shear deformation effects in the present plate element. RM plate element produces a shear locking phenomena in thin plate so that the substitute natural strains based on assumed strain method are explicitly derived. The present plate element is applied into the explicit transient algorithm and the mass matrix of plate is formulated by using special lumping method proposed by Hinton et al. The performance of the element is verified with numerical examples.

• Journal of the Korean Society for Precision Engineering
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• v.27 no.4
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• pp.87-94
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• 2010

When occlusal force is applied to a tooth, stress concentration occurs on the dental cervical line. This study investigated to find the maximum force and strain of natural teeth using an Instron and strain gauges, comparing the strain of cervical enamel using finite element analysis(FEA). Tests were conducted with a mandibular first premolar applying the conditions of occlusion. Then, the FEA was processed with the same as conditions of the fracture test. The test showed that the maximum force, maximum compressive strain and maximum tensional strain was $278{\pm}26$ N, $0.668{\times}10^{-3}{\pm}0.678{\times}10^{-3}$ and $0.248{\times}10^{-3}{\pm}0.102{\times}10^{-3}$, respectively. It was found that six of eight measured strains were within the range of estimated strains by the FEA. Even though it was assumed that properties of FE models were isotropic, it could prove useful as a reference in understanding the tendency of dental strain.

• International Journal of Naval Architecture and Ocean Engineering
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• v.6 no.4
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• pp.763-774
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• 2014

A simple and efficient vibration analysis procedure for stiffened panels with openings and arbitrary boundary conditions based on the assumed mode method is presented. Natural frequencies and modes are determined by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange's equations of motion, where Mindlin theory is applied for plate and Timoshenko beam theory for stiffeners. The effect of stiffeners on vibration response is taken into account by adding their strain and kinetic energies to the corresponding plate energies whereas the strain and kinetic energies of openings are subtracted from the plate energies. Different stiffened panels with various opening shapes and dispositions for several combinations of boundary conditions are analyzed and the results show good agreement with those obtained by the finite element analysis. Hence, the proposed procedure is especially appropriate for use in the preliminary design stage of stiffened panels with openings.