Related papers: Structural optimization of the Ziegler's pendulum:…
Two types of non-holonomic constraints (imposing a prescription on velocity) are analyzed, connected to an end of a (visco)elastic rod, straight in its undeformed configuration. The equations governing the nonlinear dynamics are obtained…
This paper presents an instability result of Hamiltonian systems associated with optimal swing-up control for a pendulum. The systems possess weak (higher-order) instability at the initial point of the swing-up control, the analysis for…
The discrete moment problem is a foundational problem in distribution-free robust optimization, where the goal is to find a worst-case distribution that satisfies a given set of moments. This paper studies the discrete moment problems with…
We consider distributionally robust optimization problems where the uncertainty is modeled via a structured Wasserstein ambiguity set. Specifically, the ambiguity is restricted to product measures $P^{\otimes N}$, where $P$ lies within a…
In this article we develop a duality principle and concerning computational method for a structural optimization problem in elasticity. We consider the problem of finding the optimal topology for an elastic solid which minimizes its…
For a given external loading on a structure we consider the optimal stresses. Ignoring the material properties the structure may have, we look for the distribution of internal forces or stresses that is in equilibrium with the external…
We consider the problem of optimal placement of concentrated masses along a massless elastic column that is clamped at one end and loaded by a nonconservative follower force at the free end. The goal is to find the largest possible interval…
In dynamical systems governed by differential equations, a guarantee that trajectories emanating from a given set of initial conditions do not enter another given set can be obtained by constructing a barrier function that satisfies certain…
This paper proposes a computational framework for the design optimization of stable structures under large deformations by incorporating nonlinear buckling constraints. A novel strategy for suppressing spurious buckling modes related to…
Flutter instability in elastic structures subject to follower load, the most important cases being the famous Beck's and Pfluger's columns (two elastic rods in a cantilever configuration, with an additional concentrated mass at the end of…
We prove that the Ziegler pendulum -- a double pendulum with a follower force -- can be integrable, provided that the stiffness of the elastic spring located at the pivot point of the pendulum is zero and there is no friction in the system.…
Optimization of large structures of multiple components is essential to many industries for minimizing mass, especially the design of aerospace vehicles. Optimizing a single primary load member independently of all other primary structures…
Robust and distributionally robust optimization are modeling paradigms for decision-making under uncertainty where the uncertain parameters are only known to reside in an uncertainty set or are governed by any probability distribution from…
We propose a kind of Bak-Sneppen dynamics as a general optimization technique to treat magnetic systems. The resulting dynamics shows self-organized criticality with power law scaling of the spatial and temporal correlations. An alternative…
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…
An elastic double pendulum subject to a force acting along a fixed straight line, the so-called "Reut's column problem", is a structure exhibiting flutter and divergence instability, which was never realized in practice and thus debated…
Non-convex optimization problems have multiple local optimal solutions. Non-convex optimization problems are commonly found in numerous applications. One of the methods recently proposed to efficiently explore multiple local optimal…
In this paper we study an optimal control problem that is affine in two-dimensional bounded control. The problem is related to the stabilization of an inverted spherical pendulum in the vicinity of the upper unstable equilibrium. We find…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
It is shown that a compound elastic structure, which displays a dynamic instability, may be designed as the union (or 'fusion') of two structures which are stable when separately analyzed. The compound elastic structure has two degrees of…