• Structural Engineering and Mechanics
• /
• v.13 no.4
• /
• pp.437-453
• /
• 2002

In this paper, dynamic stiffness and flexibility for circular membranes are analytically derived using an efficient mixed-part dual boundary element method (BEM). We employ three approaches, the complex-valued BEM, the real-part and imaginary-part BEM, to determine the dynamic stiffness and flexibility. In the analytical formulation, the continuous system for a circular membrane is transformed into a discrete system with a circulant matrix. Based on the properties of the circulant, the analytical solutions for the dynamic stiffness and flexibility are derived. In deriving the stiffness and flexibility, the spurious resonance is cancelled out. Numerical aspects are discussed and emphasized. The problem of numerical instability due to division by zero is avoided by choosing additional constraints from the information of real and imaginary parts in the dual formulation. For the overdetermined system, the least squares method is considered to determine the dynamic stiffness and flexibility. A general purpose program has been developed to test several examples including circular and square cases.

• Structural Engineering and Mechanics
• /
• v.13 no.4
• /
• pp.355-368
• /
• 2002

In this paper, we address the numerical investigation on the effect of liquid compressibility onto the natural frequency of liquid-filled containers. Traditionally the liquid motion has been treated as an ideal fluid motion. However, from the numerical experiments for the axisymmetrical free-vibration of cylindrical liquid-storage tanks, we found that the relative difference in natural frequencies between ideal and compressible motions becomes remarkable, as the slenderness of tank or the relative liquid-fill height becomes larger. Therefore, in such cases of dynamic systems, the liquid compressibility becomes an important parameter, for the accurate vibration analysis. For the free-vibration analysis of compressible liquid-structure interaction we employed the coupled finite element formulation expressed in terms of the acoustic wave pressure and the structure deformation.

• Coupled systems mechanics
• /
• v.8 no.6
• /
• pp.537-553
• /
• 2019

In this paper we present geometrically exact Kirchhoff's initially curved planar beam model. The theoretical formulation of the proposed model is based upon Reissner's geometrically exact beam formulation presented in classical works as a starting point, but with imposed Kirchhoff's constraint in the rotated strain measure. Such constraint imposes that shear deformation becomes negligible, and as a result, curvature depends on the second derivative of displacements. The constitutive law is plasticity with linear hardening, defined separately for axial and bending response. We construct discrete approximation by using Hermite's polynomials, for both position vector and displacements, and present the finite element arrays and details of numerical implementation. Several numerical examples are presented in order to illustrate an excellent performance of the proposed beam model.

• Architectural research
• /
• v.13 no.3
• /
• pp.41-47
• /
• 2011

A study on the free vibration analysis of elastic bar is described in this paper. In order to determine the natural frequencies of bars, a bar element is developed by using isogeometric formulation. The B-spline is introduced to represent the geometry of bar and the same geometric definition is also used to define its unknown displacement field in isogeometric formulation. Therefore, the stiffness and mass matrices are derived by the order-free B-spline basis function. The efficiency and accuracy of the present isogeometric bar elementis demonstrated by using several numerical tests. From numerical results, it is found to be that the present isogeometric element produces very accurate natural frequencies of bars. Finally, the present isogeometric solutions are provided as future reference solutions.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.8 no.1
• /
• pp.67-80
• /
• 2004

In the present paper, a numerical algorithm for the kinematic analysis of a MacPherson strut motor-vehicle suspension system is developed. The kinematic analysis is carried out in terms of the rectangular Cartesian coordinates of some defined points in the links and at the joints. The presented formulation in terms of this system of coordinates is simple and involves only elementary mathematics. The resulting constraint equations are mostly either linear or quadratic in the rectangular Cartesian coordinates. The proposed formulation eliminates the need to write redundant constraints and allows to solve a reduced system of equations which leads to better accuracy and a reduction in computing time. The algorithm is applied to solve the initial positions as well as the finite displacement, velocity and acceleration problems for the MacPherson strut motor-vehicle suspension system.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1998.04a
• /
• pp.53-59
• /
• 1998

A new algorithm using meshless particle method for the analysis of crack propagation problems is presented. The meshless particle method requires only a set of nodes and the description of boundaries in its formulation. The method is particulary useful for crack propagation problems due to the absence of any predefined element connectivity. Formulation procedures for the construction of displacement and shape functions are described. A numerical integration scheme and a strategy for the consideration of crack propagation are also described. Numerical examples show that the proposed method is very convenient and efficient in modeling crack problems and can guarantee the accuracy of solution in crack propagation analysis.

• Structural Engineering and Mechanics
• /
• v.15 no.4
• /
• pp.463-476
• /
• 2003

This paper deals with nonlinear asymmetric dynamic buckling of clamped laminated angle-ply composite spherical shells under suddenly applied pressure loads. The formulation is based on first-order shear deformation theory and Lagrange's equation of motion. The nonlinearity due to finite deformation of the shell considering von Karman's assumptions is included in the formulation. The buckling loads are obtained through dynamic response history using Newmark's numerical integration scheme coupled with a Newton-Raphson iteration technique. An axisymmetric curved shell element is used to investigate the dynamic characteristics of the spherical caps. The pressure value beyond which the maximum average displacement response shows significant growth rate in the time history of the shell structure is considered as critical dynamic load. Detailed numerical results are presented to highlight the influence of ply-angle, shell geometric parameter and asymmetric mode on the critical load of spherical caps.

• Interaction and multiscale mechanics
• /
• v.6 no.2
• /
• pp.107-125
• /
• 2013

A strain smoothing meshfree formulation with stabilized conforming nodal integration is presented for modeling the consolidation process in saturated porous media. In the present method, nodal strain smoothing is consistently introduced into the meshfree approximation of strain and pore pressure gradient variables associated with the saturated porous media. Meanwhile, in order to achieve a consistent numerical implementation, a smoothing approximation of the meshfree shape function within a nodal representative domain is also proposed in the stiffness construction. The resulting discrete system of equations is all expressed in smoothed nodal measures that are very efficient for numerical evaluation. Subsequently the space-time fully discrete equations are further established by the generalized trapezoidal rule for time integration. The effectiveness of the proposed meshfree consolidation analysis method is systematically illustrated by several benchmark problems.

• Korean Journal of Optics and Photonics
• /
• v.10 no.3
• /
• pp.237-242
• /
• 1999

Taking into consideration the thermal lensing effects of laser rods, depolarization losses of laser beams induced by the thermal birefringence were calculated. The numerical model proposed for the calculation, which is based on the paraxial ray optics formulation and provides explicit expressions of optical path lengths for various optical elements, was described in detail. Calculated results were compared with those of Jones matrix formulation and experiments. The calculated results are in good agreement with experimental results.

• Computers and Concrete
• /
• v.23 no.3
• /
• pp.171-188
• /
• 2019

This study proposed a new and efficient 2D damage-plasticity model within the framework of Isogeometric analysis (IGA) for the geometrically nonlinear damage analysis of concrete. Since concrete exhibits complicated material properties, two internal variables are introduced to measure the hardening/softening behavior of concrete in tension and compression, and an implicit gradient-enhanced formulation is adopted to restore the well-posedness of the boundary value problem. The numerical results calculated by the model is compared with the experimental data of three benchmark problems of plain concrete (three-point and four-point bending single-notched beams and four-point bending double-notched beam) to illustrate the geometrical flexibility, accuracy, and robustness of the proposed approach. In addition, the influence of the characteristic length on the numerical results of each problem is investigated.