4.4.2. Variations

In Section 4.3.4, we simply stated that the variation of a function f(b) is written as

$f′=∂f∂bδb=fδb′$

(4.110)

In fact, the variation we stated is the first variation in the calculus of variations.

4.4.2.1. Definition

In the continuum approach, sensitivity can be understood as variation of a function. Let us consider that a vector of design variable b is perturbed to b + τδb, in which τ is a scalar that measures the perturbation size and δb is the direction of design change. For simplicity, we assume for the time being material or sizing design variables that are not affecting the geometric shape of the structure. Shape sensitivity ...

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