• Transactions of the Korean Society of Mechanical Engineers
• /
• v.18 no.11
• /
• pp.2922-2931
• /
• 1994

We propose a modified 6-node element, where the sampling point of Gauss quadrature moved in the thickness direction. The modified 6-node element has been applied to static problems and forced motion analyses. In this study, this method is extended to the finite element analysis of the natural frequencies of two dimensional problems. We also propose a modified 16-node element for three dimensional problems, which behaves much like a 20-node element with smaller degree of freedom. The modified 6-node and 16-node elements have been applied to the modal analyses of beams and plates, respectively. The results agree well with the results of the 8-node or 20-node element models.

• Structural Engineering and Mechanics
• /
• v.57 no.3
• /
• pp.457-471
• /
• 2016

To analyze laminated composite and sandwich beams under temperature loads, a $C^0$-type Reddy's beam theory considering transverse normal strain is proposed in this paper. Although transverse normal strain is taken into account, the number of unknowns is not increased. Moreover, the first derivatives of transverse displacement have been taken out from the in-plane displacement fields, so that the $C^0$ interpolation functions are only required for the finite element implementation. Based on the proposed model, a three-node beam element is presented for analysis of thermal responses. Numerical results show that the proposed model can accurately and efficiently analyze the thermoelastic problems of laminated composites.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.21 no.2
• /
• pp.153-160
• /
• 2008

In this study, we propose a new three-node hybrid-mixed curved beam element with the relaxed-equiribrium stress functions for static analysis. The proposed element considering shear deformation is based on the Hellinger-Reissner variational principle. The stress functions are carefully chosen from three important considerations: (i) all the kinematic deformation modes must be suppressed, and (ii) the spurious constraints must be removed in the limiting behaviors via the field-consistency, and (iii) the relaxed equilibrium conditions could be incorporated because it might be impossible to select the stress functions and parameters to fully satisfy both the equiribrium conditions and the suppression of kinematic deformation modes in the three-node curved beam hybrid-mixed formulation. Numerical examples confirm the superior and stable behavior of the proposed element regardless of slenderness ratio and curvature. Besides, the proposed element shows the outstanding performance in predicting the stress resultant distributions.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.14 no.2
• /
• pp.310-323
• /
• 1990

A three-noded, with three degree-of-freedom at each node, in-plane curved beam element is formulated and employed in eigen-analysis of constant curvature beam. The conventional quadratic shape functions used in a three noded C .deg. type curved beam element produce such an undesirable large stiffness that a significant error is introduced in displacements and stresses. These phenomena are called 'Stiffness Locking Phenomena', which result from spurious strain energy due to inappropriate assumptions on independent isoparametric quadratic interpolation functions. Stiffness locking phenomena can be alleviated by using modified interpolation functions which get rid of spurious constraints of conventional interpolation functions. Eigenvalues and their modes as well as displacements and stresses may be locked because they are related to stiffness. Using modified curved beam element in eigenvalue problem of cantilever and arch, the property and performance of modified curved beam element are examined by numerical experimentations. In these eigen-analyses, mass matrices are calculated by using both modified and unmodified curved beam element, are compared with theoretical solutions. These comparisons show that the performance of the modified curved beam element is better than that of the unmodified curved beam element.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.17 no.12
• /
• pp.3020-3027
• /
• 1993

Curved beam element has received attention because of its own usefulness and its bearing on general curved elements like shells. In conventional curved beam elements stiffness matrix is overestimated and eigensolutions are poor. To avoid this phenomenon it is necessary to use a large number of elements and, as a result, the total number of degrees of freedom is increased. In this paper the two-noded, with three degrees of freedom at each node, in-plane curvature-based curbed beam element is employed in eigen-analysis of curved beam. It is shown that the curvature-based beam element is very efficient in vibration analysis and also that it is applicable to both thin and thick curved beams.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.20 no.8
• /
• pp.2540-2545
• /
• 1996

It is well known that in typical displacement-based curved beam elements, the stiffness matrix is overestimated and as a result displacement predictions show gross error for the thin beam case. In this paper, a stain based curved beam element with 2 nodes is formulated based on shallow beam geometry. At the element level, the curvature and membrane strain fields are approximated independently and the displacement fields are obtained by integrating the strain fields. Three test problems are given to demonstrate the numerical performance of the element. Analysis results obtained reveal that the element is free for locking and very effectively applicable to deeply as well as shallowly curved beams.

• Interaction and multiscale mechanics
• /
• v.4 no.4
• /
• pp.257-271
• /
• 2011

The analysis of interfacial stresses in structural component has been the subject of several investigations but it still requires more effort and studies. In this study a general three-dimensional interface element has been formulated for stress and displacement analyses in the interfacial area between two adjacent plate bending element and brick element. Interface element has 16 nodes with 5 degrees of freedom (DOF) in each node adjacent to plate bending element and 3 DOF in each node adjacent to brick element. The interface element has ability to transfer three translations from each side of interface element and two rotations in the side adjacent to the plate element. Stiffness matrix of this element was formulated and implemented in three-dimensional finite element code. Application of this element to the reinforced concrete (RC) beam strengthened with fiber reinforced polymer (FRP) including variation of deflection, slip between plate and concrete, normal and shear stresses distributions in FRP plates have been verified using experimental and numerical work of strengthened RC beams carried out by some researchers. The results show that this interface element is effective and can be used for structural component with these types of interface elements.

• Structural Engineering and Mechanics
• /
• v.14 no.3
• /
• pp.245-262
• /
• 2002

The free vibration analysis of stiffened laminated composite plates has been performed using the layered (zigzag) finite element method based on the first order shear deformation theory. The layers of the laminated plate is modeled using nine-node isoparametric degenerated flat shell element. The stiffeners are modeled as three-node isoparametric beam elements based on Timoshenko beam theory. Bilinear in-plane displacement constraints are used to maintain the inter-layer continuity. A special lumping technique is used in deriving the lumped mass matrices. The natural frequencies are extracted using the subspace iteration method. Numerical results are presented for unstiffened laminated plates, stiffened isotropic plates, stiffened symmetric angle-ply laminates, stiffened skew-symmetric angle-ply laminates and stiffened skew-symmetric cross-ply laminates. The effects of fiber orientations (ply angles), number of layers, stiffener depths and degrees of orthotropy are examined.

• Structural Engineering and Mechanics
• /
• v.90 no.3
• /
• pp.233-252
• /
• 2024

This research explores a new finite element model for the free vibration analysis of bi-directional functionally graded (BDFG) beams. The model is based on an efficient higher-order shear deformation beam theory that incorporates a trigonometric warping function for both transverse shear deformation and stress to guarantee traction-free boundary conditions without the necessity of shear correction factors. The proposed two-node beam element has three degrees of freedom per node, and the inter-element continuity is retained using both C1 and C0 continuities for kinematics variables. In addition, the mechanical properties of the (BDFG) beam vary gradually and smoothly in both the in-plane and out-of-plane beam's directions according to an exponential power-law distribution. The highly elevated performance of the developed model is shown by comparing it to conceptual frameworks and solution procedures. Detailed numerical investigations are also conducted to examine the impact of boundary conditions, the bi-directional gradient indices, and the slenderness ratio on the free vibration response of BDFG beams. The suggested finite element beam model is an excellent potential tool for the design and the mechanical behavior estimation of BDFG structures.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.20 no.12
• /
• pp.614-621
• /
• 2019

A generalized laminated composite beam element is presented for the flexural and buckling analysis of laminated composite beams with double and single symmetric cross-sections. Based on shear-deformable beam theory, the present beam model accounts for transverse shear and warping deformations, as well as all coupling terms caused by material anisotropy. The plane stress and plane strain assumptions were used along with the cross-sectional stiffness coefficients obtained from the analytical technique for different cross-sections. Two types of one-dimensional beam elements with seven degrees-of-freedom per node, including warping deformation, i.e., three-node and four-node elements, are proposed to predict the flexural behavior of symmetric or anti-symmetric laminated beams. To alleviate the shear-locking problem, a reduced integration scheme was employed in this study. The buckling load of laminated composite beams under axial compression was then calculated using the derived geometric block stiffness. To demonstrate the accuracy and efficiency of the proposed beam elements, the results based on three-node beam element were compared with those of other researchers and ABAQUS finite elements. The effects of coupling and shear deformation, support conditions, load forms, span-to-height ratio, lamination architecture on the flexural response, and buckling load of composite beams were investigated. The convergence of two different beam elements was also performed.