Engineering Analysis with Ansys Software Episode 1 Part 1 potx

[...]... right-hand side of Equation (1. 10) is chosen as a first-order approximate solution u1 (x) = x + A1 (x 2 − x) ¯ (1. 11) the error or residual is obtained as R= 1 0 1 wi R dx = ¯ d2u − u = −A1 x 2 + (A1 − 1) x + 2A1 = 0 ¯ dx 2 1 − −A1 x 2 + (A1 − 1) x + 2A1 dx = 0 1 13 A1 − = 0 6 2 (1. 12) (1. 13) Consequently, the first-order approximate solution is obtained as u1 (x) = x + ¯ 3 x(x − 1) 13 (1. 14) ... load step) 7.2.4.8 Solution (second load step) 7.2.4.9 Postprocessing (second load step) 7.2 .1. 1 7.2 .1. 2 7.2 .1. 3 7.2 .1. 4 7.2 .1. 5 7.2 .1. 6 7.2 .1. 7 7.2.2 7.2.3 7.2.4 Index 3 31 3 31 332 332 332 333 338 339 342 347 352 359 359 360 365 368 372 374 379 382 382 385 3 91 392 398 4 01 404 410 410 412 413 423 427 436 442 444 4 51 453 This page intentionally left blank Preface This book is very much the result of a collaboration... u(0) = 0 u (1) = 1 (1. 6) The linear operator L[·] and the function f (x) in Equation (1. 6) are defined as follows: L[·] ≡ d2( · ) dx 2 f (x) ≡ u(x) (1. 7) For simplicity, let us choose the power series of x as the trial functions φi , i.e., n +1 u(x) = ¯ ci x i (1. 8) i=0 For satisfying the required boundary conditions, n +1 c0 = 0, ci = 1 (1. 9) i =1 so that n u(x) = x + ¯ Ai (x i +1 − x) (1. 10) i =1 If the second... considered 1. 1 .1 Sub-domain method (finite volume method) The choice of the following weighting function brings about the sub-domain method or finite-volume method wi (x) = 1 0 (for x ∈ D) (for x ∈ D) / (1. 5) 1. 1 Method of weighted residuals Example 1. 1 3 Consider a boundary-value problem described by the following one-dimensional differential equation: ⎧ ⎪ d2u ⎨ − u = 0 (0 ≤ x ≤ 1) dx 2 ⎪ ⎩BC: u(0) = 0 u (1) ... effective use of ANSYS in solving engineering problems Throughout the book, when we state ANSYS , we are referring to the structural FEA capabilities of the various products available from ANSYS Inc ANSYS is the original (and commonly used) name for the commercial products: ANSYS Mechanical or ANSYS Multiphysics, both general-purpose finite element analysis (FEA) computeraided engineering (CAE) software tools... Execution of the analysis 5.2.3 .1 FLOTRAN set up Execute calculation Postprocessing 5.2.5 .1 Read the calculated results of the first mode of vibration 5.2.5.2 Plot the calculated results 5.2.5.3 Plot the calculated results by path operation Analysis of flow structure in a channel with a butterfly valve 5.3 .1 5.3.2 5.3.3 5.3.4 5.3.5 Problem description Create a model for analysis 5.3.2 .1 Select kind of analysis. .. through ribbed surface 263 263 265 265 265 276 280 285 285 288 2 91 298 306 312 Contents 6.4 .1 6.4.2 6.4.3 6.4.4 Problem description Construction of the model Solution Postprocessing xi 312 313 3 21 325 Chapter 7 Application of ANSYS to contact between machine elements 7 .1 7.2 General characteristics of contact problems Example problems 7.2 .1 Pin-in-hole interference fit Problem description Construction... (CAE) software tools developed by ANSYS, Inc The company actually develops a complete range of CAE products, but is perhaps best known for the commercial products ANSYS Mechanical & ANSYS Multiphysics For academic users, ANSYS Inc provides several noncommercial versions of ANSYS Multiphysics such as ANSYS University Advanced and ANSYS University Research ANSYS Mechanical, ANSYS Multiphysics and the noncommercial... books where ANSYS is also involved xv This page intentionally left blank Chapter 1 Basics of finite-element method Chapter outline 1. 1 Method of weighted residuals 1. 2 Rayleigh–Ritz method 1. 3 Finite-element method 1. 4 FEM in two-dimensional elastostatic problems Bibliography 2 5 7 14 34 arious phenomena treated in science and engineering are often described in terms of differential equations formulated... Execution of the analysis 5.3.3 .1 FLOTRAN set up Execute calculation Postprocessing 5.3.5 .1 Read the calculated results 5.3.5.2 Plot the calculated results 5.3.5.3 Detailed view of the calculated flow velocity 5.3.5.4 Plot the calculated results by path operation 222 226 2 31 2 31 233 234 234 234 237 242 242 242 242 243 243 245 245 246 248 2 51 2 51 253 254 254 255 256 259 Chapter 6 Application of ANSYS to thermo . (1. 12)  1 0 w i Rdx =  1 0 1 −  −A 1 x 2 +(A 1 1) x +2A 1  dx = 13 6 A 1 − 1 2 = 0 (1. 13) Consequently, the first-order approximate solution is obtained as ¯u 1 (x) = x + 3 13 x(x 1) (1. 14) . w1 h0" alt="" FM-H6875.tex 28 /11 /2006 16 : 7 page i Engineering Analysis With ANSYS Software This page intentionally left blank FM-H6875.tex 28 /11 /2006 16 : 7 page iii Engineering Analysis With. Equation (1. 10) is chosen as a first-order approximate solution ¯u 1 (x) = x +A 1 (x 2 −x) (1. 11) the error or residual is obtained as R = d 2 ¯u dx 2 −¯u =−A 1 x 2 +(A 1 1) x +2A 1 = 0 (1. 12)  1 0 w i Rdx