• Journal of the Earthquake Engineering Society of Korea
• /
• v.9 no.6 s.46
• /
• pp.53-58
• /
• 2005

Semi-analytical methodology to examine the dynamic responses of a bridge is developed via the joint probability density function. The evolution of joint probability density function is evaluated by the semi-analytical procedure developed. The joint probability function of the bridge responses can be obtained by solving the path-integral solution of the Fokker-Planet equation corresponding to the stochastic differential equations of the system. The response characteristics are observed from the joint probability density function and the boundary of the envelope of the probability density function can provide the maxima ol the bridge responses.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.13 no.3
• /
• pp.479-489
• /
• 1989

The $J_{k}$ integral method for determining mixed mode stress intensity factors separately in the cracked anisotropic plate is developed. Stress intensity factors are indirectly determined from the values of $J_{1}$ and $J_{2}$. The $J_{2}$ integral can be evaluated efficiently from a finite element solution, neglecting the contribution from the portion of the integration contour along the crack faces, by selecting the integration contour in the vicinity of the crack tip. Using functions of a complex variable, the complete relations between $J_{1}$, $J_{2}$ and $K_{I}$ , $K_{II}$ for anisotropic materials are derived conveniently by selecting narrow rectangular contours shrinking to the crack tip. Compared to the existing path independent integral methods, the present method does not involve calculating the auxiliary solution and hence numerical procedures become quite simple. Numerical results to various problems are given and demonstrate the accuracy, stability and versatility of the method.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.10 no.1
• /
• pp.34-42
• /
• 1986

An interface of a circular arc formed by two isotropic, homogeneous elastic materials is investigated. It is shown that L integral satisfies the conservation law for the interface if it is perfectly bonded, in frictionless contact or separated such as in a crack with the origin of the coordinate system being located at the center of the circular arc. The property of path independence of the L integral is applied to an interfacial crack problem, to obtain the stress intensity factors, where the interfacial crack is located along the arc of the circular inclusion embedded in infinite matrix. It is assumed here that the contact zone exist as in the model proposed by Comninou, thus removing the overlapping of the materials along the interface. Another example is shown for case of a circular interfacial crack in the matrix of finite size, where the stress intensity factors are determined by computing a value of the L integral numerically along the path far from the crack tip.

• The Journal of the Acoustical Society of Korea
• /
• v.13 no.2E
• /
• pp.83-91
• /
• 1994

Three components contribute to the acoustic field propagating in a wedge or over a ridge : a direct path arrival, an image component due to reflection from the boundaries and a component diffracted by the apex. All three contributions are included in a new, exact solution of the Helmholtz equation for the three-dimensional time harmonic field from a point source in a wedge(or over a ridge) formed by two intersecting, pressure-release plane boundaries. The solution is obtained by applying three integral transforms, and consists of and infinite sum of uncoupled normal nodes. The mode coefficients are given by a finite integral involving a Gegenbauer polynomial in the integrand, which may be computed relatively efficiently. Results of the theory for propagation over a 90 degree ridge is discussed.

• Computational Structural Engineering
• /
• v.8 no.4
• /
• pp.137-148
• /
• 1995

A new path independent contour integral formulus for the distinct calculation of mode I stress intensity factors in two dimensional linear elastic fracture mechanics problems is presented. This method is based on p-convergence concepts and can be easily appended to existing finite element computer codes. In this study, the stress state at crack tip has been investigated and the path independence of J-integral values has been tested with respect to different contours expressed by normalized distance apart from the crack tip. Numerical results by p-convergence for the problems such as centrally cracked panels, single and double edged cracks in rectangular panels have been compared with those by the conventional h-convergence. The comparison demonstrates the accuracy and stability of the proposed method.