• Structural Engineering and Mechanics
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• v.65 no.1
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• pp.33-41
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• 2018

In this paper, using modified couple stress theory in place of classical continuum theory, and using shell model in place of beam model, vibrational behavior of nanotubes is investigated via the finite element method. Accordingly classical continuum theory is unable to correctly compute stiffness and account for size effects in micro/nanostructures, higher order continuum theories such as modified couple stress theory have taken on great appeal. In the present work the mass-stiffness matrix for cylindrical shell element is developed, and by means of size-dependent finite element formulation is extended to more precisely account for nanotube vibration. In addition to modified couple stress cylindrical shell element, the classical cylindrical shell element can also be defined by setting length scale parameter to zero in the equations. The boundary condition were assumed simply supported at both ends and it is shown that the natural frequency of nano-scale shell using the modified coupled stress theory is larger than that using the classical shell theory and the results of Ansys. The results have indicated using the modified couple stress cylindrical shell element, the rigidity of the nano-shell is greater than that in the classical continuum theory, which results in increase in natural frequencies. Besides, in addition to reducing the number of elements required, the use of this type of element also increases convergence speed and accuracy.

• Structural Engineering and Mechanics
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• v.8 no.6
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• pp.623-637
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• 1999

This paper presents a four-noded quadrilateral $C^0$ strain plate element for the analysis of thick laminated composite plates. The element formulation is based on: 1) the third-order shear deformation theory; 2) assumed strain element formulation; and 3) interrelated edge displacements and rotations along element boundaries. Unlike the existing displacement-type composite plate elements based on the third-order theory, which rely on the $C^1$-continuity formulation, the present plate element is of $C^0$-continuity, and its element stiffness matrix is evaluated explicitly. Because of the third-order expansion of the in-plane displacements through the thickness, the resulting theory and hence elements do not need shear correction factors. The explicit element stiffness matrix makes the present element more computationally efficient than the composite plate elements using numerical integration for the analysis of thick layered composite plates.

• Interaction and multiscale mechanics
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• v.6 no.2
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• pp.237-255
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• 2013

In this paper, a meshfree-enriched finite element method (ME-FEM) is introduced for the large deformation analysis of nonlinear path-dependent problems involving contact. In linear ME-FEM, the element formulation is established by introducing a meshfree convex approximation into the linear triangular element in 2D and linear tetrahedron element in 3D along with an enriched meshfree node. In nonlinear formulation, the area-weighted smoothing scheme for deformation gradient is then developed in conjunction with the meshfree-enriched element interpolation functions to yield a discrete divergence-free property at the integration points, which is essential to enhance the stress calculation in the stage of plastic deformation. A modified variational formulation using the smoothed deformation gradient is developed for path-dependent material analysis. In the industrial metal forming problems, the mortar contact algorithm is implemented in the explicit formulation. Since the meshfree-enriched element shape functions are constructed using the meshfree convex approximation, they pose the desired Kronecker-delta property at the element edge thus requires no special treatments in the enforcement of essential boundary condition as well as the contact conditions. As a result, this approach can be easily incorporated into a conventional displacement-based finite element code. Two elasto-plastic problems are studied and the numerical results indicated that ME-FEM is capable of delivering a volumetric locking-free and pressure oscillation-free solutions for the large deformation problems in metal forming analysis.

• 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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1995.04a
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• pp.9-16
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• 1995

A new three-dimensional transition solid element with drilling degrees of freedom is presented. The proposed transition element is established by adding variable nodes to a basic 8-node element for an effective connection between the refined region and the coarse. The derivation of the element in this paper is based on the variational principles in which the drilling rotations are introduced as independent variables. This element was also improved through the addition of modified non-conforming modes. Numerical examples show that performance of the element and the applicability to 3D adaptations are satisfactory.

• Steel and Composite Structures
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• v.11 no.5
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• pp.359-374
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• 2011

In this paper, the influence of fibre orientation and aspect ratio on stability analysis of simply supported skew plates subjected to in plane loading is studied by using a four noded hybrid plate finite element. The formulation of the element is based on Hellinger-Reissner variational principle. The element is developed by combining a hybrid plane stress element and a hybrid plate element. Some numerical problems are solved and the effects of skew angle, aspect ratio, fibre orientation and loading type on the critical buckling loads are highlighted.

• Structural Engineering and Mechanics
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• v.3 no.4
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• pp.383-390
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• 1995

A 2-D four-noded finite element which contains a ${\lambda}$ singularity is developed. The new element is compatible with quadratic standard isoparametric elements. The element is tested on two different examples. In the first example, an edge crack problem is analyzed using two different meshes and different integration orders. The second example is a crack perpendicular to the interface problem which is solved for different material properties and in turn different singularity order ${\lambda}$. The results of those examples illustrate the efficiency of the proposed element.

• Journal of information and communication convergence engineering
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• v.8 no.3
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• pp.317-322
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• 2010

This paper presents an algorithm generating inverse element over finite fields GF($3^m$), and constructing method of inverse element generator based on inverse element generating algorithm. An inverse computing method of an element over GF($3^m$) which corresponds to a polynomial over GF($3^m$) with order less than equal to m-1. Here, the computation is based on multiplication, square and cube method derived from the mathematics properties over finite fields.

• 한국공간정보시스템학회:학술대회논문집
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• 2004.05a
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• pp.230-237
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• 2004

In this study, equation of finite element is formulated to analyze relations of large deformation-small deformation considering geometrical nonlinear for membrane structure. Total Lagrangian Formulation(TLF) is introduced to formulate theory and equation of motion considering Triangular Constant Strain(TCS) element in finite, element analysis is formulated. Finite element program is made by equation of motion considering TLF. This study analyzed a variety of examples, so compared with the past results.

• Structural Engineering and Mechanics
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• v.5 no.2
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• pp.127-135
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• 1997

Patch recovery attempts to derive a more accurate stress filed over a particular element than the finite element shape function used for that particular element. Elements that have a free edge being the boundary to the structure have particular stress relationship that can be incorporated to the stress field to improve the accuracy of the approximation.