I. Elishakoff

TL;DR: In this paper, a set-theoretical, convex description of uncertainty is discussed in detail, where uncertainty is described as a set of constraints unlike the classical probabilistic approach, and instead of conventional optimization studies, where the minimum possible responses are sought, here an uncertainty modeling is developed as an "anti-optimization" problem of finding the least favorable response under the constraints within the set theoretical description.

TL;DR: In this paper, it was shown that the bending, buckling and vibration problems of a microstructured beam can be modeled by Eringen's nonlocal elasticity model, which is composed of rigid periodic elements elastically connected by rotational springs.

TL;DR: In this paper, a generalized interval eigenvalue problem is pursued by taking into account the actual variability and dependencies of uncertain structural parameters affecting the mass and stiffness matrices, and it is shown that the upper and lower bounds of the natural frequencies of truss and beam structures with uncertain-but-bounded parameters can be evaluated as solution of two appropriate deterministic eigen value problems without requiring any combinatorial procedure.

TL;DR: In this article, the authors investigated three different kinds of nonlocal plate theories for capturing the small length scale effect of microstructured plates in elasticity and derived exact lattice solution for the discrete micro-structured plate model via the resolution of a linear difference boundary value problem.

TL;DR: A new method combining PIA and IIA-EUI overcomes their limits and by optimization and anti-optimization problem solutions allows to efficiently solve the set of governing algebraic interval equations in statics.