Download Structural sensitivity analysis and optimization 1, Linear by Choi K.K., Kim N.H. PDF
By Choi K.K., Kim N.H.
Broad numerical equipment for computing layout sensitivity are integrated 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 should be conducted utilizing CAD geometric types rather than FEA models. This potential permits integration of CAD-CAE-CAM in order that optimized designs might be synthetic successfully.
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Broad numerical equipment for computing layout sensitivity are incorporated within the textual content for useful program and software program development. The numerical technique permits integration of CAD-FEA-DSA software program instruments, in order that layout optimization might be performed utilizing CAD geometric versions rather than FEA types.
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Extra info for Structural sensitivity analysis and optimization 1, Linear systems
Third, the exact solution (and not a numerical solution) of the finite element matrix equation and the adjoint equation should be used to compare these two methods. Fourth, the movement of discrete grid points must be consistent with the design parameterization method used in the continuum method. 5 Structural Design Sensitivity Analysis 29 For the sizing design variable, it is shown in  that the discrete and continuum-discrete methods are equivalent under the conditions given above, using a beam as the structural component.
As a remedy, Olhoff et al.  proposed an exact numerical differentiation method when the analytical form of the element stiffness matrix is available. 2. Three-Bar Truss (Discrete Method). To obtain discrete design sensitivity with respect to sizing design variables, consider the three-bar truss problem. More complicated design variables, namely, shape and configuration, will be considered in Chapters 6 and 7. 19). 31) and load vector f is independent of the design, that is, df/du = 0. 29) for each design variable.
21). 3. Cantilever Beam (Discrete Method). Consider the cantilever beam in Fig. 15 with point load p at x = l. If one finite element is used to discretize the structure, as shown in Fig. 34) where z1 and z2 are nodal displacement, T1 and T2 are nodal rotations, and Ni’s are corresponding shape functions of the approximation, defined as N1 N3 3x 2 2 x3 3 , l2 l 2 3x 2 x3 3 , l2 l 1 N2 N4 2 x 2 x3 2, l l 2 3 x x 2. 36) 26 1. 15. Cantilever beam. where E is Young’s modulus, I = bu3/12 is the second moment of inertia, G(x – l) is the Dirac delta measure, which has a value of infinity at x = l and zero otherwise, and Z is the space of kinematically admissible displacements.