  Classical environmental contours are used in structural design in order to
obtain upper bounds on the failure probabilities of a large class of designs.
Buffered environmental contours serve the same purpose, but with respect to the
so-called buffered failure probability. In contrast to classical environmental
contours, buffered environmental contours do not just take into account failure
vs. functioning, but also to which extent the system is failing. This is
important to take into account whenever the consequences of failure are
relevant. For instance, if we consider a power network, it is important to know
not just that the power supply is failed, but how many consumers are affected
by the failure. In this paper, we study the connections between environmental
contours, both classical and buffered, and optimal structural design. We
connect the classical environmental contours to the risk measure value-at-risk.
Similarly, the buffered environmental contours are naturally connected to the
convex risk measure conditional value-at-risk. We study the problem of
minimizing the risk of the cost of building a particular design. This problem
is studied both for value-at-risk and conditional-value-at-risk. By using the
connection between value-at-risk and the classical environmental contours, we
derive a representation of the design optimization problem expressed via the
environmental contour. A similar representation is derived by using the
connection between conditional value-at-risk and the buffered environmental
contour. From these representations, we derive a sufficient condition which
must hold for an optimal design. This is done both in the classical and the
buffered case. Finally, we apply these results to solve a design optimization
problem from structural reliability.
