Numerical solution of the curved rigid line problem in an infinite plate

Summary This paper deals with the problem of evaluating the stress singularity coefficients at the tips of a rigid line in an infinite plate. If the traction difference between the upper and lower borders of the rigid line is taken as an unknown function and the displacement of the curved rigid line as the right-hand term of the integral equation, then a new integral equation for the curved rigid line problem is obtained which is presented in this paper. The newly obtained integral equation has a logarithmic singular kernel. To solve the integral equation an interpolation equation for the traction difference functions (the undetermined functions in the integral equation) is proposed. A numerical examination is carried out to demonstrate the efficiency of the proposed technique. Also two numerical examples are given in this paper.

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Numerische lösung des problems einer gekrümmten linie als starrer einschlu\ in einer unendlichen platte

Übersicht Vorgeführt wird die Bestimmung von Spannungssingularitätsfaktoren an den Enden einer starren Kurve in einer unendlichen Platte. Wenn die Spannungsdifferenz an beiden Seiten der starren Linie als unbekannte Funktion und die Verschiebung dieser Linie als rechte Seite der Integralgleichung gewählt werden, erhält man eine neue Integralgleichung, die hier vorgestellt wird. Diese enthält einen logarithmisch singulären Kern. Um sie zu lösen, wird eine Interpolationsfunktion für die unbekannten Funktionen der Spannungsdifferenzen vorgeschlagen und ein numerischer Test zur Demonstration der Leistungsfähigkeit der Methode durchgeführt. Zwei numerische Beispiele werden vorgestellt.

     

An equivalent polynomial approximation technique in nonlinear structural dynamics

Summary A new technique is proposed to obtain an approximate probability density for the response of a general nonlinear system under Gaussian white noise excitations. In this new technique, the original nonlinear system is replaced by another equivalent nonlinear system, structured by the polynomial formula, for which the exact solution of stationary probability density function is obtainable. Since the equivalent nonlinear system structured in this paper originates directly from certain classes of real nonlinear mechanical systems, the technique is applied to some very challenging nonlinear systems in order to show its power and efficiency. The calculated results show that applying the technique presented here can yield exact stationary solutions for the nonlinear oscillators. This is obtained by using an energy-dependent system, and for a nonlinearity of a more complex type. A more accurate approximate solution is then available, and is compared with the approximation. Application of the technique is illustrated by examples.     

NORMAL EXPANSION THEORY FOR PENETRATION OF PROJECTILE AGAINST CONCRETE TARGET

Based on the equations which describe the dynamic behavior of material under high-velocity and high-pressure shock, corresponding equations at shock front whose surface is general space curve surface were established. For concrete material, a normal expansion theory was proposed by which some deceleration about time history of the projectile can be analytically given. This normal expansion theory is not only suitable for spherical and cylindrical-nose projectile, but also suitable for other general nose projectile, for example conical nose or ogive-nose. And it is not only suitable for perpendicular shock but also for oblique shock.     

NUMERICAL SIMULATION OF OIL MIGRATION-ACCUMULATION OF MULTILAYER AND ITS APPLICATION

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