tailieunhanh - Engineering Analysis with Ansys Software Episode 1 Part 2

Tham khảo tài liệu 'engineering analysis with ansys software episode 1 part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 4 Chapter 1 Basics of finite-element method Example LI continued rvhichagrees wellwiththe hhactsolution e _ e-x u x T e - e 1 as shown by the dotted and the solid lines in Figure . Figure Comparison of the results olbtained by various kinds of discrete analyses. Galerkin method When the weighting function 1VZ in Equation is chosen equal to the trial function G the method isafleethe Galerkin method . 2dto G n z l 2 .in i and thus Equation is changed to w ộiRdv ữ JD This method determines the coefficients ữị by directly using Equation or by integrating it by parts. Example Let us solvethe sameboundasy-vahieprobfem asdescribed byEquation a the preceding tnaoion by t6e Galerkin method. The trial function ộị is chosen as the weighting function 1V in order to find the hest-order approximateaohitian wi-x n es hlh-l Rayleigh-Ritz method 5 Example continued Integrating Equation by parts du 11 Wi Xc_0 dwị du 1 dx I WjU dx 0 dx dx Jq is obtained. Choosing Ml in Equation as the upproximate solution u the substitution of Eqmuion into t gives Ị Ộ R dx Ị 0 Jo C - -xlx t Ị udx i i c 1 1 m- 1 c í da ux Jq Jq f x2-x 1 Ai x2- x px - 2- -2 0 0 s 12 o 0 Thus the following approximtte solution is obtained r- o Figure shows that the approximate solution obtained by the Galerkin method also agrees well with the exact solution throughout tho regioo of mierest. Rayleigh Ritz method When there exists the functional which is equivalent to a given differential equation theRayleiuO-Ritzmethodcan beused. Let us consider the example problem illustrated in Figure where a particle having a pomt nto lowei poixtRiainng a curve in aveafrcal plane undeithe rxdnt the particle needs for sliding from the points po to P1 vaeienwiih tha shapeof the curve deoxted byyỊx whichcosnecta the two iPe timedcanVe considered as a khndoUu-iiCn t F y .