This paper presents a numerical solution for vibration analysis of a cantilever trapezoidal thick plate. The material of the plate is considered to be graded through the thickness from a metal surface to a ceramic one according to a power law function. Kinetic and strain energies are derived based on the Reissner-Mindlin theory for thick plates and using Hamilton's principle, the governing equa...

A digital moiré technique with circular and radial gratings is proposed to measure in-plane displacement and strain distributions of soft materials in a polar coordinate system. By introducing the coordinate-transform technique, the concentric circles and radial lines in the Cartesian coordinate system are converted to cross gratings in a polar coordinate system. Then, the digital moiré fringes...

This paper describes the elements for writing hybrid and electromagnetic plasma simulation codes in generalized curvilinear coordinates. The coordinate system is described by a table giving the three-dimensional Cartesian coordinate positions of a structured curvilinear coordinate mesh. The paper shows how to calculate the geometric coefficients of the differential operators describing the elec...

This paper presents a study of generalized enrichment functions for three-dimensional curved crack fronts. Two coordinate systems used in the definition of singular curved crack front enrichment functions are analyzed. In the first one, a set of Cartesian coordinate systems defined along the crack front is used. In the second case, the geometry of the crack front is approximated by a set of cur...

We present a full Eulerian method, termed solid level set (SLS) method, for modeling of a class of fluid–structure interactions (FSI) problems soft solid body can deform significantly but remains nearly incompressible. The SLS method is based on the unified momentum equation framework in which the solid–fluid interactions are modeled by introducing a solid body force term and a solid–fluid inte...

A signiicant problem in tracking and estimation is the consistent transformation of uncertain state estimates between Cartesian and spherical coordinate systems. For example, a radar system generates measurements in its own local spherical coordinate system. In order to combine those measurements with those from other radars, however, a tracking system typically transforms all measurements to a...

In the recent years, increasing attention has been paid to the area of affective computing, which deals with the complex phenomenon of human emotion. Therefore, a model for describing, structuring, and categorizing emotional states of users is required. The dimensional emotion theory is one of widely used theoretical foundations for categorization of emotions. According to the dimensional theor...