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Abstract This paper presents an analytical solution for the free vibration behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) doubly curved shallow shells with integrated piezoelectric layers. Here, linear distribution electric potential across thickness layer and five different types nanotube (CNT) distributions through direction are considered. Based on four-varia...

This study presents a finite element method (FEM) based three-dimensional laser forming process design methodology for thin plates to determine the laser scanning paths and heating conditions. The strain fields were first calculated via FEM. The laser scanning paths were chosen perpendicular to the averaged principal minimum strain direction. The ratios of in-plane and bending strain were calcu...

A focused beam total X-ray fluorescence technique was developed based on doubly curved crystal optics. This technique provides good detection sensitivity and spatial resolution for localized detection of surface deposits. Compact low power X-ray sources were used to demonstrate the benefit of the X-ray optics for focusing Cr Ka, Cu Ka and Mo Ka radiation. The detection capability of the focused...

In this paper, a novel algorithm for computing Physical Optics (PO) integrals is introduced. In this method, the integration problem is converted to an inverse problem by Levin’s integration algorithm. Furthermore, the singularities, that are possible to occur in the applications of Levin’s method, are handled by employing trapezoidal rule together with Levin’s method. Finally, the computationa...