A NURBS-based isogeometric finite element formulation is developed and adopted to the free vibration analysis of finite square and skew laminated plates. Variable stiffness plies are assumed due to implementation of curvilinear fiberreinforcements. It is assumed due to employment of tow placement technology, in each ply of variable stiffness composite laminated plate the fiber reinforceme...

2 Vector Analysis 6 2.1 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Scalar Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 The Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 The Divergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.5 The Curl . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

The contravariant form of the Navier–Stokes equations in a fixed curvilinear coordinate system is well known. However, when the curvilinear coordinate system is time-varying, such as when a body-fitted grid is used to compute the flow over a compliant surface, considerable care is needed to handle the momentum term correctly. The present paper derives the complete contravariant form of the Navi...

We present an algorithm for efficiently computing ray intersections with multi-resolution global terrain which is partitioned by spheroidal height-augmented quadtrees. While previous methods support terrain defined on a Cartesian coordinate system, our methods support terrain defined on a two-parameter ellipsoidal coordinate system. This curvilinear system is necessary for an accurate model of ...

Abstract China Geodetic Coordinate System 2000 (CGCS2000), as the formal national coordinate reference frame, has been used for 20 years. The coordinates of all Global Navigation Satellite (GNSS) stations in need referring to this system. To end, first step is align stations, usually included a regional GNSS network, with given International Terrestrial Reference Frame (ITRF), then these are co...