• 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.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.4
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• pp.449-459
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• 2000

The original Mindlin-type degenerated shell element perform reasonably well for moderately thick shell structures. However, when full integration for analysis of thin shell is used to evaluate the stiffness matrix, the stiffness of shell element is often over-estimated due to shear or membrane locking phenomena. To correct this problem, the formulation of the new degenerated shell element is derived by the combination of two different techniques. The first type of elements(TypeⅠ) has used assumed shear strains in the natural coordinate system to overcome the shear locking problem, the reduced integration technique in in-plane strains(membrane strains) to avoid membrane locking behaviour. Another element(TypeⅡ) has applied the assumed strains to both of membrane strain and transverse shear strains. The improved degenerated shell element has been tested by several numerical problems of shell structures. Numerical results indicate that this shell element shows fast convergence and reliable solutions.

• Journal of the Earthquake Engineering Society of Korea
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• v.5 no.3
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• pp.57-64
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• 2001

For the dynamic nonlinear analysis of stiffened plate and shell structures, total Lagrangian formulation is presented based upon the degenerated shell element considering finite rotation effects. Assumed strain concept is adopted in order to overcome shear locking phenomena and to eliminate spurious zero energy mode. In the elasto-plastic analysis, the return mapping algorithm based on the consistent elasto-plastic tangent modulus is applied to collapse analysis of shell structures. Newmark integration method is used for dynamic nonlinear analysis of shell structures under dynamic forces.

• 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.

• 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.

• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.11 no.3
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• pp.1-10
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• 1991

The paper is concerned with the analysis of laminated composite shell structures using an improved degenerated shell element. In the formulation of the element stiffness, the combined use of three different techniques was made. They are; 1) an enhanced interpolation of transverse shear strains in the natural coordinate system to overcome the shear locking problem; 2) the reduced integration technique in in-plane strains to avoid the membrane locking behavior; and 3) selective addition of the nonconforming displacement modes to improve the element performances. This element is free of serious shear/membrane locking problems and undesirable compatible/commutable spurious kinematic deformation modes. An incremental total Lagrangian formulation is presented which allows the calculation of arbitrarily large displacements. The resulting non-linear equilibrium equations are solved by the Newton-Raphson method. The versatility and accuracy of this improved degenerated shell element are demonstrated by solving several numerical examples.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.2
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• pp.197-208
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• 2000

Choi et al./sup 1)/ presented the total Lagrangian formulation based upon the degenerated shell element. Geometrically correct formulation is developed by updating the direction of normal vectors and taking into account the second order rotation terms in the incremental displacement field. Assumed strain concept is adopted in order to overcome the shear locking phenomena and to eliminate the spurious zero energy mode. In this paper, for the ultimate strength analysis of stiffened shell structures considering effects of residual stresses, the return mapping algorithm based on the consistent elasto-plastic tangent modulus is applied to anisotropic shell structures. In addition, the load/displacement incremental scheme is adopted for non-linear F.E. analysis. Based on such methodology, the computer program is developed and numerical examples to demonstrate the accuracy and the effectiveness of the proposed shell element are presented and compared with the results in literatures.

• Computational Structural Engineering
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• v.3 no.3
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• pp.113-123
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• 1990

The paper is concerned with the elasto-plastic and geometrically nonlinear analysis of shell structures using an improved degenerated shell element. In the formulation of the element stiffness, the combined use of three different techniques was made. They are; 1) an enhanced interpolation of transverse shear strains in the natural coordinate system to overcome the shear locking problem ; 2) the reduced integration technique in in-plane strains to avoid the membrane locking behavior ; and 3) selective addition of the nonconforming displacement modes to improve the element performances. This element is free of serious shear/membrane locking problems and undesirable compatible/commutable spurious kinematic deformation modes. In the formulation for plastic deformation, the concept of a layered element model is used and the material is assumed von Mises yield criterion. An incremental total Lagrangian formulation is presented which allows the calculation of arbitrarily large displacements and rotations. The resulting non-linear equilibrium equations are solved by the Netwon-Raphson method combined with load or displacement increment. The versatility and accuracy of this improved degenerated shell element are demonstrated by solving several numerical examples.

• Journal of the Korea institute for structural maintenance and inspection
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• v.14 no.3
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• pp.108-117
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• 2010

The frame element is commonly used for construction stage analysis PSC bridges. However, the frame element does not show sufficient information in the curved PSC box bridges. For the case of curved PSC bridges, the deformations in the inner and outer web are different. In this case, the different jacking forces are required in the inner and outer webs. And it is impossible to calculate different jacking forces in the inner and outer webs if we use the frame element for construction stage analysis. In order to overcome this problem, the use of shell element is essential for a three-dimensional construction stage analysis of PSC bridges. In the following, the formulation of an assumed strain shell element and its application of PSC box girder bridge analysis are presented.