Computer Aided Engineering Design
GEOMETRIC MODELING USING POINT CLOUDS 303 Also, the point cloud for a prismatic object is different from that of a free form obj ...
304 COMPUTER AIDED ENGINEERING DESIGN (b) Number of data points used for segmentation is small, implying that the information fr ...
GEOMETRIC MODELING USING POINT CLOUDS 305 be performed using the least square approach. In case of prismatic parts, algebraic su ...
306 COMPUTER AIDED ENGINEERING DESIGN (a) Point cloud (b) Approximating surface (c) Error plot Figure 10.13 An approximating B-s ...
GEOMETRIC MODELING USING POINT CLOUDS 307 u 1 ,.. ., uj corresponding to each data point and the knot vectors, the matrix C can ...
308 COMPUTER AIDED ENGINEERING DESIGN 10.7 Some Examples of Reverse Engineering Reverse engineering has been applied widely for ...
Chapter 11 Finite Element Method 11.1 Introduction The design procedure does not cease after accomplishing a solid model. With a ...
310 COMPUTER AIDED ENGINEERING DESIGN time taken will be more. Thus, there is a trade off involved between the average element s ...
FINITE ELEMENT METHOD 311 Writing Eq. (11.1) in the matrix form, we get kk kk u u f f pp pp i j i j = ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ ⎧ ⎨ ⎩ ⎫ ...
312 COMPUTER AIDED ENGINEERING DESIGN Adding Eqs. (11.5a) and (11.5b) yields kk kk k k kk u u u f ff f F F F pp pp q q qq i j k ...
FINITE ELEMENT METHOD 313 u k F k k k F p j p q = k (^1) + + 1⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ (11.5f) The reaction force Fi from Eq. (11 ...
314 COMPUTER AIDED ENGINEERING DESIGN constants gives c uu xx ji ji 2 = and c ux u x xx ij ji ji 1 = or = + 2 and = ...
FINITE ELEMENT METHOD 315 so that εx u x lll = = –^1 2 1 2 ∂ (^2) = – (^11) = ∂ [][] uuBu (11.7h) Herel is the length of the mem ...
316 COMPUTER AIDED ENGINEERING DESIGN whereλλλλλT = cos 0 sin 0 0 cos 0 sin θ θ θ θ ⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ . We can realize tha ...
FINITE ELEMENT METHOD 317 Example 11.1. An assemblage of truss members is shown in Figure 11.5. It is required to determine the ...
318 COMPUTER AIDED ENGINEERING DESIGN For convenience in assembly, the numbers assigned to the degrees of freedom are represente ...
FINITE ELEMENT METHOD 319 v(x) = a 1 + a 2 x + a 3 x^2 + a 4 x^3 (11.9a) where constants a 1 ,... , a 4 can be determined using ...
320 COMPUTER AIDED ENGINEERING DESIGN B = – 3 y l [12x – 6ll(6x – 4l) – (12x – 6l) l(6x – 2l)] From truss analysis, the local st ...
FINITE ELEMENT METHOD 321 The assembled matrix K is 123 45678 K = 10 12 6 – 12 6 0 0 0 0 64 –6 2 0 0 0 0 –12 –6 12+6 –6+3 –6 3 0 ...
322 COMPUTER AIDED ENGINEERING DESIGN Consistent with the definition of U for this example, the external force vector is given a ...
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