โ Scribed by Yoshihiro Kanno; Izuru Takewaki
No coin nor oath required. For personal study only.
This paper presents a method for computing a minimal bound that contains the solution set to the uncertain linear equations. Particularly, we aim at finding a bounding ellipsoid for static response of structures, where both external forces and elastic moduli of members are assumed to be imprecisely known and bounded. By using the S-lemma, we formulate a semidefinite programming (SDP) problem which provides an outer approximation of the minimal bounding ellipsoid. Bounding ellipsoids are computed for nodal displacements of uncertain braced frames as the solutions of the presented SDP problems by using the primal-dual interior-point method.
๐ SIMILAR VOLUMES
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are i.i.d. Gaussian variables, we compute the distribution of the
The probabilistic analysis of FE discretized uncertain linear structures in the static and dynamic domain is the goal of this paper. In particular, a procedure able to give the exact relationship between the response and the random variables representing the structural uncertainties is presented, un