Mohamed Nassar

Natural frequencies of a functionally graded cracked beam using the differential quadrature method

The present work is concerned with the free vibration analysis of an elastically supported cracked beam. The beam is made of a functionally graded material and rested on a Winkler–Pasternak foundation. The line spring model is employed to formulate the problem. The method of differential quadrature is applied to solve it. The obtained results agreed with the previous similar ones. Further, a parametric study is introduced to investigate the effects of the geometric and elastic characteristics of the problem on the values of natural frequencies and mode shape functions.

Vibration analysis of structural elements using differential quadrature method

The method of differential quadrature is employed to analyze the free vibration of a cracked cantilever beam resting on elastic foundation. The beam is made of a functionally graded material and rests on a Winkler–Pasternak foundation. The crack action is simulated by a line spring model. Also, the differential quadrature method with a geometric mapping are applied to study the free vibration of irregular plates. The obtained results agreed with the previous studies in the literature. Further, a parametric study is introduced to investigate the effects of geometric and elastic characteristics of the problem on the natural frequencies.

Analysis of composite plates using moving least squares differential quadrature method

Abstract In this work, the moving least squares differential quadrature method (MLSDQM) is employed to analyze bending problems of composite plates. Based on a transverse shear theory, the governing equations of the problem are derived. The transverse deflection and two rotations of the plate are independently approximated with MLS approximations. The weighting coefficients used in the MLSDQ approximation are obtained through the fast computation of the MLS shape functions and their partial derivatives. The obtained results are compared with the previous analytical and numerical ones. Further a parametric study is introduced to investigate the effects of elastic and geometric characteristics on the values of transverse deflection of the plate.

Prediction of Ratchet Boundary for 90-Degree Smooth and Mitred Pipe Bends

The present paper attempts to predict ratchet boundary for 90-degree mitred and smooth pipe bends subjected to sustained pressure and cyclic in-plane bending. The methodology utilizes a recently published technique known as the “Uniform Modified Yielding” (UMY) technique, which relies on generation of a virtual structure with inhomogeneous reduced yield strength, whose magnitude and distribution depend on the elastic stress field due to the cyclic load. The collapse load of this virtual structure determines the threshold steady load necessary for commencement of “incremental collapse”. The technique is applied first to predict ratchet boundaries for two benchmark problems possessing analytical descriptions of ratchet boundary and uni-axial states of stress; the two-bar structure problem and the Bree cylinder. Predicted ratchet boundaries exactly coincided with the corresponding published analytical descriptions, and reasons for this correlation were discussed in this paper. The technique was then applied to three 90-degree pipe bends with similar geometries as follows: smooth pipe bend (SPB), single mitred pipe bend (SMPB), and three weld mitred pipe bend (3WMPB). Certain assumptions are adopted to enable treatment of the problem as a quasi-uniaxial one. Conservative estimates are obtained for ratchet boundaries in pipe bends that correlates well with elastic shakedown/ratchet boundary of the same problems as predicted by a recently developed non-cyclic direct technique.Copyright

Dynamic snap-through of a negative shallow arch resting on a fluid layer

In this paper, we study the snap-through stability of a negative shallow arch resting on a fluid layer foundation under a point load moving at a constant speed. The deformation of the arch is expressed in the Fourier series. By studying the fluid layer separately, it is noted that the back pressure of the fluid is directly proportional to the density of the fluid and depth of the fluid layer. We are interested only when the point load is downward. In quasi-static manner, it is so obvious that the arch will not snap. When the point load moves with a significant speed, we used the first four modes in the Fourier series to predict the response of the arch.