This paper considers structural optimization under a reliability constraint,
where the input distribution is only partially known. Specifically, when we
only know that the expected value vector and the variance-covariance matrix of
the input distribution belong to a given convex set, we require that, for any
realization of the input distribution, the failure probability of a structure
should be no greater than a specified target value. We show that this
distributionally-robust reliability constraint can be reduced equivalently to
deterministic constraints. By using this reduction, we can treat a
reliability-based design optimization problem under the distributionally-robust
reliability constraint within the framework of deterministic optimization,
specifically, nonlinear semidefinite programming. Two numerical examples are
solved to show relation between the optimal value and either the target
reliability or the uncertainty magnitude