Logarithmic Curvature Graph as a Shape Interrogation Tool

Abstract A compact formula for Logarithmic Curvature Graph(LCG) and its gradient for planar curves has been shown which can be used as shape interrogation tool. Using these entities, the mathematical definition for a curve to be aesthetic has been introduced to overcome the ambiguity that occurs in measuring the aesthetic value of a curve. Detailed examples are shown how LCG and its gradient can be used to identify curvature extrema and measure the aesthetic value of curves. Mathematics Subject Classification: 65D17, 68U0

The Development Of Planar Curves With High Aesthetic Value

Penyelidikan terhadap lengkung satah bagi menghasilkan suatu produk yang can- tik dan pengubahsuaian lengkung bagi bidang tertentu telah dibangunkan sejak tahun 70-an. Pola penyelidikan dalam bidang ini boleh dibahagikan kepada lima cabang utama iaitu pembangungan algoritma adil, pembangunan lengkung satah melalui kaedah sintesis lengkung, pembangunan algoritma baru bagi mengubahsuai lingkaran asli untuk kegua- naan reka bentuk, pengubahsuaian lengkung °eksibel (B¶ezier dan NURBS) supaya pro¯l kelengkungan adalah monoton dan akhirnya, pembangungan algoritma dalam proses pe- myuaian dan penghampiran terhadap lingkaran asli menerusi lengkung °eksibel. The research on developing planar curves to produce visually pleasing products and modifying planar curves for special purposes has been progressing since the 1970s. The pattern of research in this ¯eld of study has branched to ¯ve major groups; the devel- opment of fairing algorithms; the development of planar curves via curve synthesis, the development of algorithms to modify natural spirals to suit design intent, the modi¯cation of °exible curves (B¶ezier and NURBS) so that the curvature pro¯le is strictly monotonic and ¯nally, the development of algorithms to ¯t natural spirals and approximation via °exible curves

Computational fluid dynamic based optimisation of an industrial axial fan for rapid prototyping

Axial air flow fans are widely used for air movement. In an increasingly international and competitive market, smaller fan companies find themselves in need of rapid preliminary design. This need is addressed in this study through the development of a first-revision, Computational Fluid Dynamics (CFD) based, optimisation tool which allows for rapid prototyping of a ducted axial fan. The result is an ElementalTM-based multi-disciplinary software tool, comprising 2D CFD, mesh movement, and constrained geometric optimisation. The analytical equation employed to represent the aerofoil significantly reduces the cost of the optimisation. A pseudo-3D fan model is generated by superimposing 2D CFD results. This is done without the general assumption of the free-vortex method, which is not a necessity for fan design and other velocity distributions may be used. For this purpose, an enhanced finite volume discretisation method was developed. A penalty function minimisation, by means of an unconstrained optimisation algorithm, is implemented thereafter. The primary objective is to deliver a specific fan static pressure rise, while optimising for fan static efficiency by means of altering the rotor blade geometry. The spherical quadratic steepest descent method is employed, which does not rely on any explicit line searches, as required by traditional steepest descent techniques. The rapid prototyping tool is finally applied to an under-performing base fan (Fan-D) which cannot meet a specified duty point. The resulting optimised fan (Fan-Optim) is manufactured and experimentally tested, in accordance with the ISO 5801 standard. The pseudo-3D model is proven to predict fan performance accurately at the target duty point, while capturing fan behaviour over a range of volumetric flow rates. The former is to within 13% of the fan static pressure rise and within 2.3% of fan static efficiency. While Fan-Optim meets the desired duty point within 2%, it offers a considerable improvement in fan static efficiency over Fan-D. Furthermore, an approximate 38% reduction in blade material is achieved as a secondary effect

Pseudoedge--a hierarchical skeletal modeler for the computer aided design of structural components

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1991.Includes bibliographical references (p. 121-122).by David Leo Bonner.M.S

Optimisation methods in structural systems reliability

Imperial Users onl