Download Structural Sensitivity Analysis and Optimization 1 by Kyung K. Choi, Nam-Ho Kim PDF
By Kyung K. Choi, Nam-Ho Kim
Wide numerical equipment for computing layout sensitivity are integrated within the textual content for sensible program and software program development. The numerical strategy permits integration of CAD-FEA-DSA software program instruments, in order that layout optimization should be performed utilizing CAD geometric types rather than FEA models. This strength permits integration of CAD-CAE-CAM in order that optimized designs should be synthetic successfully.
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Large numerical equipment for computing layout sensitivity are incorporated within the textual content for sensible software and software program development. The numerical process permits integration of CAD-FEA-DSA software program instruments, in order that layout optimization may be conducted utilizing CAD geometric versions rather than FEA versions.
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Extra info for Structural Sensitivity Analysis and Optimization 1
39) with respect to the design. Consider height u of the cross-sectional dimension as a design variable. 39) as dK du 3EI ª 12 6A º . 42) as dz du 3p A ª 4A 2 6A º ª« º» u 12 EI «¬ 6A 12 »¼ « » ¬ 0 ¼ ª pA 3 º « EIu » . 34) is valid for displacement sensitivity. Thus, the displacement function sensitivity can be obtained as dz ( x) du NT dz du p 2 x ( x 3A). 41). 4 Continuum Method In the continuum method, the design derivative of the variational equation (the continuum model of the structure) is taken before discretization.
16), u = [b1, b2, b3]T denotes the design variable vector, which is the cross-sectional area of each truss element. Note that the global stiffness matrix Kg is singular, since it has a rigid body motion that can be removed by applying boundary conditions. As shown in Fig. 8, the displacement variables z3 and z4 are fixed. In addition, z5 and z6 are dependent on each other. Solution candidates must satisfy these conditions. 17) and Kg(u) is the positive definite in Zh, although it is not positive definite in all of R6.
7 Design Optimization 33 the previous iteration. 57). 57). This method tends to select the descent direction as a diagonal of two orthogonal steepest descent directions, such that a zigzagging pattern can be eliminated. This method always has better convergence than the steepest descent method. Newton Method The previous methods we have examined use first-order information (first-order design sensitivity) of the cost function to find the optimum design, which is called linear approximation. The Newton method uses second-order information (second-order design sensitivity) to approximate the cost function as a quadratic function of the design.