Applied numerical methods with matlab for engineers and scientists

Essential MATLAB for Engineers and Scientists PHẦN 3 pdf

... vector, and uses a for loop to calculate and display the total charge for each one: 200, 500, 700, 1000, 1500 (Answers: $9, $15, $25, $40, $90) 83 Essential MATLAB for Engineers and Scientists 2. 23 ... Figures 3. 1 and 3. 2, respectively, were produced Projectile flight path, Vo ϭ 10 uo ϭ 45Њ 2.5 y 1.5 0.5 0 x Figure 3. 1 Projectile trajectory 93 10 12 Essential MATLAB for Engineers and Scientists ... radians = 180◦ 81 Essential MATLAB for Engineers and Scientists 2. 13 Set up a matrix (table) with degrees in the ﬁrst column from to 36 0 in steps of 30 , sines in the second column, and cosines in...

Essential MATLAB for Engineers and Scientists PHẦN 4 pot

... For example, the functions zeros, ones and rand generate matrices of 1’s, 0’s and random numbers, respectively With a single argument n, they generate 149 Essential MATLAB for Engineers and Scientists ... 3]) = b(:, [4 2]) replaces the ﬁrst and third columns of a by the fourth and second columns of b (a and b must have the same number of rows) 145 Essential MATLAB for Engineers and Scientists ➤ ... 123 Essential MATLAB for Engineers and Scientists 0.8 0.6 0 .4 0.2 −0.2 −0 .4 −15 −10 −5 10 15 Figure 5.2 sin(x)/x the zero with eps This MATLAB function returns the difference between 1.0 and...

Essential MATLAB for Engineers and Scientists PHẦN 6 pptx

... 2.031250000000000e-001 4.73 760 9329445558e-003 2.7790 866 665 71118e-0 06 9.583445148 564 351e-013 -4.44089209850 062 6e-0 16 Zero found at 1.21341 166 2 762 230e+000 Note: ➤ The variable y in the function ﬁles f.m and df.m ... the mean (avg) and standard deviation (stdev) of the values in the vector x Although there are 233 Essential MATLAB for Engineers and Scientists two MATLAB functions to this (mean and std), it ... 227 Essential MATLAB for Engineers and Scientists Taking a = 1, b = −107 and c = 0.001 gives x1 = 107 and x2 = The second root is expressed as the difference between two nearly equal numbers, and...

Essential MATLAB for Engineers and Scientists PHẦN 8 pptx

... Print the v and a formulae and compare with % the published results % v, a % % Step 6: Determine a from published formula and v % a2 = g - k * v; 319 Essential MATLAB for Engineers and Scientists ... engaged to close the circuit and initiate the current At this instant of time the voltage is applied to the resistor 311 Essential MATLAB for Engineers and Scientists and inductor (which are connected ... release, the speed and the distance fallen are quite different It is not surprising that quadratic friction 317 Essential MATLAB for Engineers and Scientists 140 120 Distance, y 100 80 60 40 20 0...

Essential MATLAB for Engineers and Scientists PHẦN 10 pptx

... matlab\ ops matlab\ lang matlab\ elmat - matlab\ elfun matlab\ specfun matlab\ matfun - matlab\ datafun - matlab\ audio matlab\ polyfun matlab\ funfun - matlab\ sparfun matlab\ graph2d matlab\ graph3d matlab\ specgraph ... = 100 0; for years = : 10 for months = : 12 balance = balance * 1.01; end disp( [years balance] ); end 413 Essential MATLAB for Engineers and Scientists 8.2 (a) terms = 100 ; pi = 0; sign = 1; for ... 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 N O P Q R S T U V W X Y Z [ \ ] ^ ‘ a b c d e f g 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122...

The boundary element method with programming for engineers and scientists - phần 1 pps

... 17 0 17 6 18 0 18 3 18 4 18 5 18 7 18 7 19 5 19 8 19 9 200 202 Element- by -element techniques and Parallel Programming 203 8 .1 8 .1 Introduction The Element by Element Concept 8 .1. 1 Element- by -element storage ... of nodes n n n -1 .0 1. 0 1. 0 -1 .0 0.0 1. 0 0.0 -1 .0 -1 .0 -1 .0 1. 0 1. 0 -1 .0 0.0 1. 0 0.0 N5 ( , ) N1 ( , ) 1 Figure 3.9 Shape functions for mid-side and corner nodes 39 DISCRETISATION AND INTERPOLATION ... 289 290 290 2 91 11 Multiple regions 293 11 .1 11. 2 11 .5 11 .6 11 .7 Introduction Stiffness matrix assembly 11 .2 .1 Partially coupled problems 11 .2.2 Example Computer implementation 11 .3 .1 Subroutine...

The boundary element method with programming for engineers and scientists - phần 2 pptx

... 21 T 22 (4.39) 82 The Boundary Element Method with Programming v1x 11 v3 x v1 y v2 y v3 y v1z T v2 x v2 z v3 z 2v1x v2 x 12 2v1x v3 x 2v1 y v2 y 2v2 y v3 y 2v1 y v3 y 2v1z v2 z T 2v2 x v3 x 2v2 ... DNi(1,1) - 0.5*DNi(5,1) DNi(1 ,2) = DNi(1 ,2) - 0.5*DNi(5 ,2) DNi (2, 1)= DNi (2, 1) - 0.5*DNi(5,1) DNi (2, 2)= DNi (2, 2) - 0.5*DNi(5 ,2) END IF IF(Inci(6) > 0) THEN DNi(6,1)= 0.5*(1.0 -eta*eta) DNi(6 ,2) = -eta*pxs ... ! two-dimensional element mxs= 1.0-xsi pxs= 1.0+xsi met= 1.0-eta pet= 1.0+eta DNi(1,1)= -0 .25 *met DNi(1 ,2) = -0 .25 *mxs DNi (2, 1)= 0 .25 *met DNi (2, 2)= -0 .25 *pxs DNi(3,1)= 0 .25 *pet DNi(3 ,2) = 0 .25 *pxs...

The boundary element method with programming for engineers and scientists - phần 3 doc

... % -1 16 24 32 Error % -2 -3 -4 -5 -6 -7 Number of points Figure 5 .3 Plot of error in computing the temperature versus the number of points P 104 The Boundary Element Method with Programming The ... INPUT.DAT 1.0 1.0 32 1.0 0.7 18 -5 -4 .5 -4 -3 .5 -3 -2 .5 -2 -1 .5 1 03 BOUNDARY INTEGRAL EQUATIONS 0 0 0 0 0 -1 1.5 2.5 3. 5 4.5 File OUTPUT.DAT Program : heat flow past a cylinder with Trefftz method Heat ... C1*(rB*SINThB*(LOG(rB )-1 )+ThetB*rB*COSThB & - rA*SINThA*(LOG(rA )-1 )-ThetA*rA*COSThA) 122 The Boundary Element Method with Programming dSx= C/k*(ThetB-ThetA) Fact= CosthB/CosthA IF(Fact > 0.0) THEN dSy= -C/k*LOG(Fact)...

The boundary element method with programming for engineers and scientists - phần 4 pot

... region and (-1 , 0) for sub region If a uniform subdivision is assumed the Jacobian J for the transformation from to is for all regions J K (6 .43 ) 148 The Boundary Element Method with Programming The ... 11 11 11 11 j 21 41 43 22 42 23 k 31 32 33 37 34 35 36 l 21 41 23 43 22 42 180 The Boundary Element Method with Programming We note that for mirror image number n= 1,3 ,4 and 6, the incidences have ... 182 The Boundary Element Method with Programming CASE(3) TD=(/1.0 ,-1 .0,1.0/) CASE (4) TD=(/1.0,1.0 ,-1 .0/) CASE(5) TD=( /-1 .0,1.0 ,-1 .0/) CASE(6) TD=(/1.0 ,-1 .0 ,-1 .0/) CASE(7) TD=( /-1 .0 ,-1 .0 ,-1 .0/)...

The boundary element method with programming for engineers and scientists - phần 5 pps

... 59 6 -1 0.0 0.0 0.0 -1 0.0 0.0 0.0 -1 0.0 0.0 0.0 -1 0.0 0.0 0.0 59 7 -1 0.0 0.0 0.0 -1 0.0 0.0 0.0 -1 0.0 0.0 0.0 -1 0.0 0.0 0.0 59 8 -1 0.0 0.0 0.0 -1 0.0 0.0 0.0 -1 0.0 0.0 0.0 -1 0.0 0.0 0.0 59 9 -1 0.0 ... Programming the Finite Element Method J.Wiley Beer G and Watson J.O (1992) Introduction to Finite and Boundary Elements for Engineers J.Wiley 8 Element- by -element techniques and Parallel Programming ... 10.00000 -0 .02236 0.00079 0.00079 -0 .00787 -0 .00123 0.00787 -0 .0 050 8 -0 .0 050 8 -0 .0 050 8 -0 .00787 0.00787 -0 .00123 -1 0.00000 0.00000 0.00000 -1 0.00000 0.00000 0.00000 -1 0.00000 0.00000 0.00000 -1 0.00000...

The boundary element method with programming for engineers and scientists - phần 6 pot

... 0.142E-03 0.316E-1 1-0 .532E-10 -0 .135 0.137 -0 . 365 0.000 1.20 0.00 0.00 0.127E-0 3-0 . 862 E-12 0.780E-10 -0 .134 0.111 -0 .244 0.000 1.30 0.00 0.00 0.115E-0 3-0 .209E-12 0.486E-10 -0 .121 0.091 -0 .1 76 0.000 ... 0 .60 4 0.30 -0 .107 0.421 0.40 -0 .107 -2 98.89 0.00 0.00 -6 .28 -1 1.88 -6 .28 0.000 -8 .323 0.000 -1 2 .65 8 0.000 -1 5.590 0.000 11.8 76 268 The Boundary Element Method with Programming Stress: Coordinates: ... 0.000 0.000 -0 .707 -0 .707 288 The Boundary Element Method with Programming Post-processed Results Results at Boundary Elements: Element xsi= -1 .00 eta= -1 .00 Stress: -0 .04 0.12 -0 .47 Element xsi=...

The boundary element method with programming for engineers and scientists - phần 7 ppsx

... -0 .5012 1.0140E-09 -0 .5011 Results, Element 12 u= 5.5386E-02 -0 .1582 -5 .5386E-02 -0 .1582 1. 079 2E-09 -0 .1582 t= -1 47. 7 5.933 1 47. 7 5.933 -1 .2626E-06 12.060 It can be seen that the maximum displacement ... detail with the treatment of corners in the boundary element method and the efficient analysis of problems with changing geometries 330 12.2 The Boundary Element Method with Programming CORNERS AND ... length side of the beam are the same and agree very well with the analytical solution, except for the coarse mesh with continuous elements For the discontinuous mesh with elements and for the continuous...

The boundary element method with programming for engineers and scientists - phần 8 pps

... u =-0 .171E-0 2-0 .195E-01 0.612E-0 3-0 .120E-0 1-0 .397E-0 3-0 .142E-01 t= 0.000 0.000 0.000 0.000 0.000 0.000 Results, Element u= 0.612E-0 3-0 .120E-0 1-0 .798E-0 3-0 .156E-01 0 .80 2E-0 3-0 .123E-01 t= 0.000 0.000 ... Coor -1 .00 2.50 Incidences: EL Inci EL Inci Results, Element u =-0 .471E-0 2-0 .245E-0 1-0 .171E-0 2-0 .195E-0 1-0 .323E-0 2-0 .257E-01 t= 0.000 0.000 0.000 0.000 0.000 0.000 Results, Element u =-0 .171E-0 2-0 .195E-01 ... 0.000 Results, Element u =-0 .798E-0 3-0 .156E-0 1-0 .471E-0 2-0 .245E-0 1-0 .104E-0 2-0 .251E-01 t= 0.000 0.000 0.000 0.000 0.000 0.000 13.10 CONCLUSIONS In this chapter we have dealt with the treatment...

The boundary element method with programming for engineers and scientists - phần 9 ppsx

... stress -( 1+ ( 1- 3-D -1 /8 1-2 7-5 2-1 0 -1 /30( 1- ( 1-3 - /8 The discretized form of (15.43) is E N Pa e n R e ue n n E N e n Se t e n n C N c n ˆ Ec n c 0n F Pa (15.46) 422 The Boundary Element Method ... 14.14 Boundary element mesh 406 The Boundary Element Method with Programming The boundary element mesh consists of regions and linear boundary elements, as shown in Figure 14.14 Results of the ... matrix form N N T n n u U n n n q n (14.46) 398 The Boundary Element Method with Programming If we solve for time step N, the results for the previous time steps are known and can be put to the...

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