• 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.

• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.23 no.7 s.166
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• pp.1205-1214
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• 1999

A new quadrilateral plane stress element is developed for efficient and accurate analysis of thermal stress problems. It is convenient to use the same mesh and the same shape functions for thermal analysis and stress analysis. But, because of the inconsistency between deformation related strain field and thermal strain field, oscillatory responses and considerable errors in stresses are resulted in. To avoid undesired oscillations, strain approximation is enhanced by supplementing several assumed strain terms based on the variational principle. Thermal deformation is incorporated into the generalized mixed variational principle for displacement, strain and stress fields, and basic equations for the modified enhanced assumed strain method are derived. For the stress approximation of bilinear elements, the $5{\beta}$ version of Pian and Sumihara is adopted. The numerical results for several problems show that the present element behaves well and reduces oscillatory responses. it also results in almost the same magnitude of error as compared with the quadratic element.

• 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.

• 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.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.

• 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.

• 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.

• Structural Engineering and Mechanics
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• v.17 no.1
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• pp.113-140
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• 2004

A mixed eight-node hexahedral element formulated via the Hu-Washizu principle as well as the field extrapolation technique is presented. The mixed element with only three translational degrees of freedom at each node can provide extremely accurate and reliable performance for popular benchmark problems such as spacial beams, plates, shells as well as general three-dimensional elasticity problems. Numerical calculations also show that when extremely skewed and coarse meshes and nearly incompressible materials are used, the proposed mixed element can still possess excellent behaviour. The mixed formulation starts with introduction of a parallelepiped domain associated with the given general eight-node hexahedral element. Then, the assumed strain field at the nodal level is constructed via the Hu-Washizu variational principle for that associated parallelepiped domain. Finally, the assumed strain field at the nodal level of the given hexahedral element is established by using the field extrapolation technique, and then by using the trilinear shape functions the assumed strain field of the whole element domain is obtained. All matrices involved in establishing the element stiffness matrix can be evaluated analytically and expressed explicitly; however, a 24 by 24 matrix has to be inverted to construct the displacement extrapolation matrix. The proposed hexahedral element satisfies the patch test as long as the element with a shape of parallelepiped.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.30 no.2
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• pp.67-74
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• 2002

The paper deals with a fully assumed strain soild element that can be used for modeling of thin sensors and actuators. To solve fully coupled field problems, the eledtric potential is regarded as a nodal degree of freedom in addition to three translations in an eighteen node assumed strain soild element. Therefore, the induced electric potential can be calculated for a prescribed load and the actuation displacement can be computed for an input voltage. Since the assumed strain solid element can alleviate locking. A finite element code is developed based on the formulation and typical numerical examples are solved for code validation. Using the code, we have conducted parametric study for THUNDER actuator. It is found that a particular combination of materials for layer curvature of THUNDER improves the actuation displacement.