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Technical Briefs

# New Concepts on Two-Dimensional Data Visualization With Applications in Engineering Analysis and Design

[+] Author and Article Information
P. A. Simionescu, Mehrube Mehrubeoglu

School of Science and Engineering,  Texas A&M University–Corpus Christi, 6300 Ocean Drive, Unit 5733, Corpus Christi, TX 78412pa.simionescu@tamucc.edu

J. Comput. Inf. Sci. Eng 12(2), 024501 (Mar 19, 2012) (10 pages) doi:10.1115/1.4006204 History: Received July 13, 2011; Revised February 04, 2012; Published March 16, 2012; Online March 19, 2012

## Abstract

The use of information visualization in engineering analysis and design has increased exponentially, making it indispensable in science and engineering education. In this paper, several new concepts on graphical representation of two-dimensional data are presented, and their implementation in a computer program called $D_2D$ detailed. Application examples include mechanism kinematics, vibrations, and optimizations. New ideas on plotting inequalities of two variables, damping ratio evaluation of single degree-of-freedom vibratory systems, and time ratio calculation of crank-driven mechanisms are presented in paper.

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## Figures

Figure 1

Multiple-curve plot with four distinct y-categories as displacement, velocity, acceleration, and transmission angle functions of a four-bar linkage. The kinematic and skeleton diagrams make for one single AUTOCAD drawing, merger facilitated by the DXF export capabilities of the D_2D program. Additional innovations include the graph legend combined with the category name and the double x axis in degrees and radians.

Figure 2

Paths of: (a) machine tool cutter and (b) the roller of a cam mechanism in a motion inversion analysis (the circle marker diameters were set to be 1.0 and 2.5 units of length, respectively). Precise control of the marker sizes and of the height and width of the plot box such that the aspect ratio equals one in both plots were essential to produce these graphs.

Figure 3

Comparison between the time ratios, TR, determined using simply bracketed limit positions (

markers), interpolated limit position (○ markers), and zero velocity positions (◊ markers), for different equally spaced positions n of the crank angle over the range of 0 deg to 360 deg

Figure 4

Time response of an underdamped spring-mass-dashpot system, showing the peak and zero-displacement values. The plot consists of 3000 data sets, and the peak values were interpolated parabolically along three points that bracket a local minimum or maximum.

Figure 5

Comparison between (a) the exact damped-period of motion, τd , and those evaluated using the average time intervals between: (b) the first 18 zeros, (c) the first 18 positive peaks and 18 negative peaks, (d) the 36 zero-peak intervals, and (e) average of (b) and (c)

Figure 6

Phase path showing an example of the chaotic response of the Duffing oscillator. Above, the arrow markers are spaced at 120 units measured along the plot line. Below, the arrow markers are placed every three data points. The second graph provides an indication of the speed at which the process takes place, comparable to an animated plot.

Figure 7

Poincaré map of the Duffing oscillator in Fig. 6. The plot box is 1080 × 690 square pixels and harbors 2 × 106 data points, of which some evidently overlap.

Figure 8

Graphical representation of inequality 17

Figure 9

Steepest Descent search over Rosenbrock’s Banana function with a secant search for the zero of the directional derivative. The level curves were produced outside D_2D with a program described in Refs. [25] and [26].

Figure 10

Conjugate gradient search over Rosenbrock’s Banana function

Figure 11

A round cantilever beam loaded with a concentrated force P [27]

Figure 12

Plot of the feasible design space of the cantilever beam problem

Figure 13

Plot of the performance space of the cantilever beam problem

Figure 14

Plot of the cantilever beam optimization problem restated in terms of one variable only

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