• Structural Engineering and Mechanics
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• v.13 no.4
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• pp.387-410
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• 2002

Formulation of an 8 nodes assumed strain shell element is presented for the analysis of shells. The stiffness matrix based on the Mindlin-Reissner theory is analytically integrated through the thickness. The element is free of membrane and shear locking behavior by using the assumed strain method such that the element performs very well in modeling of thin shell structures. The material is assumed to be isotropic and laminated composite. The element has six degrees of freedom per node and can model the stiffened plates and shells. A great number of numerical testing carried out for the validation of present 8 node shell element are in good agreement with references.

• 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 Computational Structural Engineering Institute of Korea
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• v.13 no.2
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• pp.209-220
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• 2000

For non-linear analysis of stiffened shell structures, the total Lagrangian formulation is presented based upon the degenerated shell element. Geometrically correct formulation is developed by updating the direction of normal vectors and taking into account second order rotational terms in the incremental displacement field. Assumed strain concept is adopted in order to overcome shear locking phenomena and to eliminate spurious zero energy mode. The post-buckling behaviors of stiffened shell structures are traced by modeling the stiffener as a shell element and considering general transformation between the main structure and the stiffener at the connection node. Numerical examples to demonstrate the accuracy and the effectiveness of the proposed shell element are presented and compared with references' results.

• Structural Engineering and Mechanics
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• v.37 no.2
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• pp.253-256
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• 2011

• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.6
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• pp.925-932
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• 1997

Two shear-flexible curved axisymmetric shell elements with two nodes, LCCS(linear curvature and constant strain) and CCCS(constant curvature and constant strain) are designed based on the assumed meridional strain fields and shallow shell geometry. At the element level, meridional curvature, membrane strain and shear strain fields are assumed by using polynomials and the displacement fields are obtained by integrating the assumed strain fields along the shallowly curved meridian. The formulated elements have high order displacement fields consistent with the strain field. Several test problems are given to demonstrate the performance of the two elements. Analysis results obtained reveal that the elements are very accurate in the displacement and the stress predictions.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.728-732
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• 2004

In the FE analysis of sheet metal forming, efficient results can be obtained by using shell elements rather than using solid elements. However, shell elements have some limitations to describe three-dimensional material laws. In the recent years, solid-shell element, which has only translational degree of freedom like solid element, has been presented. The assumed nature strain (ANS) and enhanced assumed strain (EAS) methods can be used to remove several solid-shell locking problems. In this paper, ANS method was used for diminish transverse shear locking and EAS method for thickness locking. Using the element, the steel pipe making process from flat plate analyzed effectively, which is including bending and welding.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.31 no.2
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• pp.25-34
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• 2003

In the present paper, formulation of a nine-node assumed strain shell element is modified and extended for analysis of actuator embedded/attached structures. The shell element can alleviate locking and has sic DOFs per node by discarding assumption of no thickness change. In modeling of the physicalquantities, we have assumed linear strain field through the whole thickness direction. The electric and mechanical quantities have been coupled through the constitutive equations. Unlike typical shell element, the present shell element allows thickness change. Thus, three-dimensional piezoelasticity can be accurately simulated. Base on the formulation, a finite element program is generated and the code is validated by solving numerical examples. The results from the present work are well agreed with those from other references.

• Structural Engineering and Mechanics
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• v.15 no.2
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• pp.199-223
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• 2003

The formulation of a non-linear shear deformable shell element is presented for the solution of stability problems of stiffened plates and shells. The formulation of the geometrical stiffness presented here is exactly defined on the midsurface and is efficient for analyzing stability problems of thick plates and shells by incorporating bending moment and transverse shear resultant force. As a result of the explicit integration of the tangent stiffness matrix, this formulation is computationally very efficient in incremental nonlinear analysis. The element is free of both membrane and shear locking behaviour by using the assumed strain method such that the element performs very well in the thin shells. By using six degrees of freedom per node, the present element can model stiffened plate and shell structures. The formulation includes large displacement effects and elasto-plastic material behaviour. The material is assumed to be isotropic and elasto-plastic obeying Von Mises's yield condition and its associated flow rules. The results showed good agreement with references and computational efficiency.

• Architectural research
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• v.16 no.1
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• pp.27-35
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• 2014

Nonlinear analysis of reinforced concrete structures is carried out by using Reissner-Mindlin (RM) shell finite element (FE). The brittle inelastic characteristic of concrete material is represented by using the elasto-plastic fracture (EPF) material model with the relevant material models such as cracking criteria, shear transfer model and tension stiffening model. In particular, assumed strains are introduced in the formulation of the present shell FE in order to avoid element deficiencies inherited in the standard RM shell FE. The arc-length control method is used to trace the full load-displacement path of reinforced concrete structures. Finally, four benchmark tests are carried out and numerical results are provided as future reference solutions produced by RM shell element with assumed strains.