• 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.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.17 no.12
• /
• pp.3007-3019
• /
• 1993

For the same configuration, the stiffness of 6-node two dimensional isoparametric is stiffer than that of 8-node two dimensional isoparametric element. This phenomenon may be called 'Relative Stiffness Stiffening Phenomenon.' In this paper, the relative stiffness stiffening phenomenon was studied, and could be corrected by modifying the position of Gauss integral points used in the numerical integration of the stiffness matrix. For the same deformation (bending) energy of 6-node and 8-node two dimensional isoparametric elements, Gauss integral points of 6-node element have to move closer, in comparison with those of 8-node element, in the case of numerical integration along the thickness direction.

• Structural Engineering and Mechanics
• /
• v.18 no.6
• /
• pp.731-744
• /
• 2004

Modified virtual crack closure integral (MVCCI) technique has become very popular for computation of strain energy release rate (SERR) and stress intensity factor (SIF) for 2-D crack problems. The objective of this paper is to propose a numerical integration procedure for MVCCI so as to generalize the technique and make its application much wider. This new procedure called as numerically integrated MVCCI (NI-MVCCI) will remove the dependence of MVCCI equations on the type of finite element employed in the basic stress analysis. Numerical studies on fracture analysis of 2-D crack (mode I and II) problems have been conducted by employing 4-noded, 8-noded (regular & quarter-point), 9-noded and 12-noded finite elements. For non-singular (regular) elements at crack tip, NI-MVCCI technique generates the same results as MVCCI, but the advantage for higher order regular and singular elements is that complex equations for MVCCI need not be derived. Gauss numerical integration rule to be employed for 8-noded singular (quarter-point) element for accurate computation of SERR and SIF has been recommended based on the numerical studies.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.19 no.4
• /
• pp.990-1004
• /
• 1995

A modified 16-node element for composite plate has been proposed and compared with the 20-node element to check the validity of it. The fields of numerical inspection include mode analysis and specific damping analysis. By symetrizing the conventional unsymmetric damping matrix in the analysis of specific damping capacity, we could compute the specific damping capacity and make a program, effectively. In addition, we could predict the errors caused by reduction of integration order in thickness direction depending upon the number of layers.