• 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 Computational Structural Engineering Institute of Korea
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• v.14 no.4
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• pp.481-494
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• 2001

An enhanced degenerated shell finite element (FE), which has been developed for inelastic analysis of reinforced concrete structures is described in this paper. Generally, Reissner-Mindlin (RM) assumptions are adopted to develop the degenerated shell FE so that transverse shear deformation effects is considered. However, it is found that there are serious defects such as locking phenomena in RM degenerated shell FE since the stiffness matrix has been overestimated in some situations. As remedies of locking phenomena, reduced integration, incompatible mode and assumed strain method have been used. Especially, the assumed strain method has been successfully used in many FEs. But contrarily, there is a few investigation on the performance of the assumed strains in the inelastic analysis of concrete structures. Therefore, shell formulation is provided in this paper with emphasis on the terms related to the stiffness matrix based on assumed strain method and microscopic concrete material model. Finally, the performance of the present shell element is tested and demonstrated with several numerical examples. From the numerical tests, the present result shows a good agreement with experimental data or other numerical results.

• Journal of the Korean Society for Advanced Composite Structures
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• v.3 no.2
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• pp.1-10
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• 2012

In the present study, an Element-Based Lagrangian Formulation for the nonlinear analysis of shell structures is presented. 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-Based Lagrangian Formulation of a 9-node resultant-stress shell element is presented for the anisotropic composite material. 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. The arc-length control method is used to trace complex equilibrium paths in thin shell applications. Numerical examples for laminated composite curved shells presented herein clearly show the validity of the present approach and the accuracy of the developed shell element.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.3
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• pp.353-364
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• 2007

In this paper, a nonlinear finite element analysis program NUCAS, which has been developed for assessment of ultimate pressure capacity and failure mode for nuclear containment building is described. Degenerated shell element with assumed strain method and low-order solid element with enhanced assumed strain method is adapted to microscopic material and elasto-plastic material model, respectively. Finally, the performance of the developed program is tested and demonstrated with several examples. From the numerical tests, the present results show a good agreement with experimental data or other numerical results.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.33 no.2
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• pp.46-53
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• 2005

Compare to the large number of curved quadrilateral degenerated-shell elements, there are only a very few curved triangular degenerated-shell elements. Based on the assumed natural strain sampling scheme previously developed for a quadratic degenerated-shell element for linear analysis, this paper devises geometric non-linear six-node degenerated-shell element. The element can be curved and is only equipped with the standard nodal d.o.f.'s. Careful consideration has been exercised to circumvent various locking phenomena that plague degenerated-shell element. Numerical examples are presented to illustrate efficiency.

• Structural Engineering and Mechanics
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• v.18 no.5
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• pp.671-690
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• 2004

An assumed strain finite strip method(FSM) using the non-periodic B-spline for a shell is presented. In the present method, the shape function based on the non-periodic B-splines satisfies the Kronecker delta properties at the boundaries and allows to introduce interior supports in much the same way as in a conventional finite element formulation. In the formulation for a shell, the geometry of the shell is defined by non-periodic B3-splines without any tangential vectors at the ends and the penalty function method is used to incorporate the drilling degrees of freedom. In this study, new assumed strain fields using the non-periodic B-spline function are proposed to overcome the locking problems. The strip formulated in this way does not posses any spurious zero energy modes. The versatility and accuracy of the new approach are demonstrated through a series of numerical examples.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2000.11a
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• pp.173-176
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• 2000

Finite element model based on the Naghdi's shell theory in the general tensor-based form is formulated in the present study. Partial mixed variational functional for assumed strain is formulated in order to avoid the severe locking troubles known as transverse shear and membrane locking. The proposed assumed strain element in general tensor Naghdi's shell model provides very accurate solutions for thin shells in benchmark problems. In additions, linear elastic constitutive equations are given in the general curvilinear coordinate system including anisotropic layered structures. Thus laminated composited shell structures are easily analyzed in the present formulation.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.7 s.178
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• pp.1721-1730
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• 2000

An eccentric degenerated shell element with geometric non-linearity for the precise and efficient analysis of stiffened shell structures is developed. To deal with the eccentricity, we define the e ccentric shell and the master shell that constitute one combined shell. It is assumed that the sections remain plane after deformation. The internal force vector and the tangent stiffness matrix based on the virtual work principle in the natural coordinate system are derived. To enhance the robustness of the element, assumed strain method for transverse shear and membrane strains is used. Through numerical experiments the effectiveness of the proposed element is demonstrated.

• Structural Engineering and Mechanics
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• v.40 no.2
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• pp.191-213
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• 2011

This paper presents an improved 8-node shell element for the analysis of plates and shells. The finite element, based on a refined 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 different patterns of sampling points for interpolating different components of strains. 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. Further, a refined first-order shear deformation theory, which results in parabolic through-thickness distribution of the transverse shear strains from the formulation based on the third-order shear deformation theory, is proposed. This formulation eliminates the need for shear correction factors in the first-order theory. Numerical examples demonstrate that the present element perform better in comparison with other shell elements.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.59-66
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• 2001

The post-peak analysis of concrete structures is carried out using a nine-node Reissner-Mindlin(RM) shell element which is formulated by using degenerated solid concepts. In order to avoid element deficiencies inherited in the standard RM shell element, assumed strains are adopted in the present shell element. A microscopic material model is adopted to represent the inelastic characteristic of concrete material. In particular, a concrete softening model is introduced to this material model. The arc-length control method is used to trace the post-peak behaviour of concrete structures. From the numerical test of the single-edge-notched beam, the present shell element shows a reasonable agreement with experimental data.