Finite Element Modeling for Materials Engineers Using MATLAB®

... Finite Element Modeling for Materials Engineers Using MATLABÒ Oluleke Oluwole Finite Element Modeling for Materials Engineers Ò Using MATLAB 123 Dr Oluleke Oluwole ... Oluwole, Finite Element Modeling for Materials Engineers Using MATLABÒ, DOI: 10.1007/978-0-85729-661-0_1, Ó Springer-Verlag London Limited 2011 Chapter The Weak Formulation 2.1 Nodal F...

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... MATHEMATICAL and COMPUTATIONAL TOOLS for ELECTRICAL and COMPUTER ENGINEERS USING MATLAB ® © 2001 by CRC Press LLC ELEMENTARY MATHEMATICAL and COMPUTATIONAL TOOLS for ELECTRICAL and COMPUTER ENGINEERS USING ... Elementary mathematical and computational tools for electrical and computer engineers using MATLAB/ Jamal T Manassah p cm Includes bibliogra...

Ngày tải lên: 31/03/2014, 16:19

... (x1(n+1) ^2) ); x2(n+1)=b2*y2(n)+a*x2(n) +2* (1-a)*(x2(n)) ^2/ (1+ (x2(n) ^2) ); y2(n+1)=-x2(n)+a*x2(n+1) +2* (1-a)*(x2(n+1) ^2) /(1+ (x2(n+1) ^2) ); end subplot (2, 1,1); plot(x1,y1,'.') title('a =-0 .99 b=1') ... y1(n+1)=b*x1(n)+a*(y1(n )-( x1(n)) ^2) ; x2(n+1)=a*x2(n)-b*(y2(n )-( x2(n)) ^2) ; y2(n+1)=b*x2(n)+a*(y2(n )-( x2(n)) ^2) ; end plot(x1,y1,'ro',x2,y2,'bx') 2. 8 .2. 1 Demon...

Ngày tải lên: 13/08/2014, 02:21

... theory © 2001 by CRC Press LLC FIGURE 3. 4 Profile of the signal of Pb 3. 31 FIGURE 3. 5 Profile of the first input to Pb 3. 32 Pb 3. 33 In DSB-AM (double-sideband amplitude modulation), the amplitude ... following sub-units: mF = 10 3 F (milli-Farad); nF = 10 −9 F (nano-Farad); fF = 10 −15 F (femto-Farad); µF = 10 –6 F (micro-Farad); pF = 10 −12 F (pico-Farad); aF = 10 −18 F (atto-Farad)...

Ngày tải lên: 13/08/2014, 02:21

... +a*D2(k-1)+u(k)); D(k)=(2/dt)*(y(k)-y(k-1))-D(k-1); D2(k)= (4/ dt^2)*(y(k)-y(k-1) )-( 4/ dt)*D(k-1)-D2 (k-1); end plot(t,y,t,u,' ') The dashed curve is the temporal profile of the source term In-Class ... D2(1)=(1/a(1))*(-b(1)*D(1)-c(1)*y(1)+u(1)); for k=2:N y(k)=( (4* a(k)/dt^2+2*b(k)/dt+c(k))^ (-1 ))* (y(k-1)* (4* a(k)/dt^2+2*b(k)/dt)+D(k-1) * (4* a(k)/dt+b(k))+a(k)*D2(k-1)+u(k)); D(k...

Ngày tải lên: 13/08/2014, 02:21

... a(1)) (5. 25) a(2) = c(1) = a(1) + r(b(1) − a(1)) (5. 26) b(2) = b(1) (5. 27) Now, replacing the values of a(2) and b(2) from Eqs (5. 26) and (5. 27) into Eq (5. 25) , we are led to a second-degree ... The command is poly poly(r) In-Class Exercise Pb 5. 14 Find the roots of the polynomial p = [1 pute their sum and product 3], and com- Pb 5. 15 Consider the two polynomials: p1 = [1...

Ngày tải lên: 13/08/2014, 02:21

... LLC (6. 67) and where ˜ ˜ ˜ Vtot = Atot e jφtot = V1 + V2 (6. 68) Preparatory Exercise Pb 6. 35 Write the analytical expression for Atot and φtot in Eq (6. 68) as functions of the amplitudes and phases ... signals? Pb 6. 42 Two- and three-phase power can be extended to N-phase power In such a scheme, the N-110-V /60 -Hz signals are given by: © 2001 by CRC Press LLC πn   Vn = 110...

Ngày tải lên: 13/08/2014, 02:21

... Replacing l by l – in Eq (7. 94) and eliminating Pl′ ( x) from Eq − (7. 95), we find that: (1 − x ) dPl ( x) = lPl−1 ( x) − lxPl ( x) dx (7. 97) Differentiating Eq (7. 97) and using Eq (7. 95), we obtain: ... unique For example, in 4-D space, the canonical four-unit orthonormal basis vectors are given, respectively, by: ê1 = [1 0 0] (7. 15) ê2 = [0 0] (7. 16) ê3 = [0 0] (7. 17) ê4 = [0...

Ngày tải lên: 13/08/2014, 02:21

... n v m = λ n v m (8. 83) On the other hand, if we dotted Eq (8. 78) on the left with the bra-vector , we obtain: H v m = λ m v m = λ m v m (8. 84) Now compare Eqs (8. 83) and (8. 84) They are equal, ... ilamp=circuit872(RL) M=[1 0 0 0;1 -1 -5 0 0;0 -1 -1 00 0; 0 -3 00;0 -RL 0;0 0 -1 -1 ]; Vs=[5;0;0;0;0;0]; VI=M\Vs; ilamp=VI(5); Then, from the command window, we proceed b...

Ngày tải lên: 13/08/2014, 02:21

... transformations, in 2-D, are respectively: s Sx =  x 0 0 1  (9. 8) 1 Sy =  0 0 sy   (9. 9) In-Class Exercises Pb 9. 12 Find the transformation matrix for simultaneously compressing the x-coordinate ... 2, while expanding the y-coordinate by a factor of Apply this transformation to the trapezoid of Example 9. 1 and plot the result Pb 9. 13 Find the inverse matrices for Sx...

Ngày tải lên: 13/08/2014, 02:21

... Solution: The number of ways of selecting 10 items from a batch of 100 items is: N= 100 ! 100 ! 100 = = C10 10! (100 − 10) ! 10! 90! n where Ck is the binomial coefficient and represents the number of combinations ... (10. 43) Again, using Eqs (10. 37) and (10. 43), we have: P( Ai B) = P(B Ai )P( Ai ) (10. 44) P(B) Now, substituting Eq (10. 41) in the denominator of Eq (10. 44),...

Ngày tải lên: 13/08/2014, 02:21

... DISCRETE ELEMENT MODELING FOR FLOWS OF GRANULAR MATERIALS BY LIM WEE CHUAN ELDIN (M.Eng., B.Eng (Hons.), NUS) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF CHEMICAL ... University for helpful discussions via video-conferencing on the subject of granular attrition which subsequently led to the formulation of a theoretical approach for...

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