The result is in .NET Development barcode data matrix in .NET The result is

How to generate, print barcode using .NET, Java sdk library control with example project source code free download:
The result is use .net ecc200 maker toassign gs1 datamatrix barcode on .net GS1 Glossary x = 0.6556 7.6265 1.

1393. 10.3 Powell s Method EXAMPLE 10.5 u2 P The displacem barcode data matrix for .NET ent formulation of the truss shown results in the following simultaneous equations for the joint displacements u: A3 u1 0 2 2A 2 + A 3 A 3 E A 3 A3 A 3 u2 = P 2 2L A3 A 3 2 2A 1 + A 3 u3 0 where E represents the modulus of elasticity of the material and A i is the crosssectional area of member i. Use Powell s method to minimize the structural volume (i.

e., the weight) of the truss while keeping the displacement u2 below a given value . Solution Introducing the dimensionless variables vi = the equations become 2 2x2 + x3 1 x3 2 2 x3 ui xi = E Ai PL.

x3 x3 x3 x3 v1 0 x3 v2 = 1 2 2x1 + x3 v3 0 The structura l volume to be minimized is P L2 (x1 + x2 + 2x3 ) V = L(A 1 + A 2 + 2A 3 ) = E In addition to the displacement constraint . u2 . , we shou ld also prevent the crosssectional areas from becoming negative by applying the constraints A i 0. Thus the optimization problem becomes: minimize F = x1 + x2 + 2x3 with the inequality constraints . v2 . 1 xi 0 (i = 1, 2, 3). Introduction to Optimization Note that in order to obtain v2 we must solve Eqs. (a). Here is the program:.

function exam .NET DataMatrix ple10_5 % Example 10.5 (Powell s method of minimization) xStart = [1;1;1]; [x,fOpt,nCyc] = powell(@fex10_5,xStart); fprintf( x = %8.

4f %8.4f %8.4f\n ,x) fprintf( v = %8.

4f %8.4f %8.4f\n ,u) fprintf( Relative weight F = %8.

4f\n ,x(1)+ x(2) ...

+ sqrt(2)*x(3)) fprintf( Number of cycles = %2.0f\n ,nCyc). function F = fex10_5(x) mu = 100; c = 2*sqrt(2); A = [(c*x(2) + x(3)) -x(3) x(3) b = [0;-1;0]; u = gauss(A,b); F = x(1) + x(2) + sqrt(2)*x(3) ...

+ mu*((max(0,abs(u(2)) - 1)) 2 ...

+ (max(0,-x(1))) 2 ...

+ (max(0,-x(2))) 2 ...

+ (max(0,-x(3))) 2); end end -x(3) x(3) -x(3) x(3); -x(3); (c*x(1) + x(3))]/c;. The subfuncti VS .NET DataMatrix on fex10 5 returns the penalized merit function. It includes the code that sets up and solves Eqs.

(a). The displacement vector v is called u in the program. The rst run of the program started with x = [ 1 1 1 ]T and used = 100 for the penalty multiplier.

The results were. x = v = 3.7387 -0.2675.

3.7387 -1.0699.

5.2873 -0.2675 14.

9548. Relative weight F = Number of cycles = 10 Since the mag gs1 datamatrix barcode for .NET nitude of v2 is excessive, the penalty multiplier was increased to 10 000 and the program run again using the output x from the last run as the input. As seen below, v2 is now much closer to the constraint value.

. 10.4 Downhill Simplex Method x = v = 3.999 .NET gs1 datamatrix barcode 7 -0.

2500 3.9997 -1.0001 5.

6564 -0.2500 15.9987.

Relative weight F = Number of cycles = 17 In this problem the use of = 10 000 at the outset would not work. You are invited to try it. 10.4 Downhill Simplex Method The downhill VS .NET Data Matrix simplex method is also known as the Nelder Mead method. The idea is to employ a moving simplex in the design space to surround the optimal point and then shrink the simplex until its dimensions reach a speci ed error tolerance.

In n-dimensional space a simplex is a gure of n + 1 vertices connected by straight lines and bounded by polygonal faces. If n = 2, a simplex is a triangle; if n = 3, it is a tetrahedron..

2d Original simplex Reflection Hi 0.5d Expansion Lo Contraction Shrinkage Figure 10.4. A simplex in two dimensions illustrating the allowed moves. The allowed m oves of the simplex are illustrated in Fig. 10.4 for n = 2.

By applying these moves in a suitable sequence, the simplex can always hunt down the minimum point, enclose it and then shrink around it. The direction of a move is determined by the values of F (x) (the function to be minimized) at the vertices. The vertex with the highest value of F is labeled Hi and Lo denotes the vertex with the lowest value.

The magnitude of a move is controlled by the distance d measured from the Hi vertex to the centroid of the opposing face (in the case of the triangle, the middle of the opposing side)..
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