By Choi K.K., Kim N.H.
Huge numerical equipment for computing layout sensitivity are integrated within the textual content for useful program and software program development. The numerical approach permits integration of CAD-FEA-DSA software program instruments, in order that layout optimization will be performed utilizing CAD geometric types rather than FEA models. This potential permits integration of CAD-CAE-CAM in order that optimized designs will be synthetic successfully.
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Broad numerical tools for computing layout sensitivity are integrated within the textual content for functional program and software program development. The numerical approach permits integration of CAD-FEA-DSA software program instruments, in order that layout optimization might be performed utilizing CAD geometric types rather than FEA types.
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Additional resources for Structural sensitivity analysis and optimization 1, Linear systems
3. 36) is independent of the design. 47) where Gu is the amount of perturbation. 36) can be differentiated with respect to design u as d ª l EIz, xx z, xx dx º G u ¼ du ¬ ³0 l ³ EIzc 0 z dx ³ , xx , xx l 0 3EI z z G u dx. 49) which yields the solution zc = dz/du. 49), following the same procedure as the finite element method. 36) by considering zg as zƍg. 3. Note that in the continuum method it is neither necessary to differentiate the stiffness matrix dK/du, nor to use any matrix multiplication procedure to calculate dK/duz, which involves a large amount of additional computational cost.
Design sensitivities of the cost and constraint functions must also be supplied to the optimization algorithm. Then, the optimization algorithms, discussed in this section, calculate the best possible design of the problem. Each algorithm has its own advantages and disadvantages. The performance of an optimization algorithm critically depends on the characteristics of the design problem and the types of cost and constraint functions. 1 Linear Programming Method The linear programming method can be used when cost and constraints are linear functions of the design variables .
23). If the explicit form of the stiffness matrix K(u) and the load vector f(u) are known, and if solution z of matrix equation Kz = f is obtained, then the design sensitivity of the displacement vector can also be obtained, as K (u ) dz du df d K z. 30) This is a discrete approach to the analytical method, since the explicit expressions of K(u) and f(u) are used to obtain design derivatives of the stiffness matrix and load vector. 30) is in the global system matrix, actual computation of these derivatives can still be carried out on the element level in order to avoid a massive amount of calculation related to global stiffness matrix K.
Structural sensitivity analysis and optimization 1, Linear systems by Choi K.K., Kim N.H.