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Topology optimization of frame structures under free-vibration eigenvalue constraints constitutes a challenging nonconvex polynomial optimization problem with disconnected feasible sets. In this article, we first formulate it as a…
Designing lightweight yet stiff structures that can withstand vibrations is a crucial task in structural optimization. Here, we present a novel framework for truss topology optimization under undamped harmonic oscillations. Our approach…
Weight optimization of frame structures with continuous cross-section parametrization is a challenging non-convex problem that has traditionally been solved by local optimization techniques. Here, we exploit its inherent semi-algebraic…
We consider the problem of optimal input design for estimating uncertain parameters in a discrete-time linear state space model, subject to simultaneous amplitude and l1/l2-norm constraints on the admissible inputs. We formulate this…
The maximum (or minimum) generalized eigenvalue of symmetric positive semidefinite matrices that depend on optimization variables often appears as objective or constraint functions in structural topology optimization when we consider…
In this paper, size-dependent dynamic responses of small-size frames are modelled by stress-driven nonlocal elasticity and assessed by a consistent finite-element methodology. Starting from uncoupled axial and bending differential…
We study the minimisation of the positive principal eigenvalue for an indefinite-weight problem under inhomogeneous Robin boundary conditions. The model is motivated by diffusive logistic equations in spatially heterogeneous environments,…
We propose an approach based on convex relaxations for certifiably optimal robust multiview triangulation. To this end, we extend existing relaxation approaches to non-robust multiview triangulation by incorporating a truncated least…
We examine robust output feedback control of discrete-time nonlinear systems with bounded uncertainties affecting the dynamics and measurements. Specifically, we demonstrate how to construct semi-infinite programs that produce gains to…
We study the reduced order modeling of a piecewise-linear, globally nonlinear flexible oscillator in which a Bernoulli-Euler beam is subjected to a position-triggered kick force and a piecewise restoring force at its tip. The nonsmooth…
A novel geometrically exact model of the spatially curved Bernoulli-Euler beam is developed. The formulation utilizes the Frenet-Serret frame as the reference for updating the orientation of a cross section. The weak form is consistently…
The design of minimum-compliance bending-resistant structures with continuous cross-section parameters is a challenging task because of its inherent non-convexity. Our contribution develops a strategy that facilitates computing all…
We investigate the dynamics of mechanical resonators subject to excitations comprising of an oscillating or harmonic part, whose amplitude decays exponentially in time. We call these complex frequency excitations and show that the resulting…
This paper studies the inverse problem related to the identification of the flexural stiffness of an Euler Bernoulli beam in order to reconstruct its profile starting from available response data. The proposed identification procedure makes…
This paper studies a downlink multiuser transmit beamforming design under spherical channel uncertainties, using a worst-case robust formulation. This robust design problem is nonconvex. Recently, a convex approximation formulation based on…
Stochastic flexural vibrations of small-scale Bernoulli-Euler beams with external damping are investigated by stress-driven nonlocal mechanics. Damping effects are simulated considering viscous interactions between beam and surrounding…
We develop a divergence-minimization (DM) framework for robust and efficient inference in latent-mixture models. By optimizing a residual-adjusted divergence, the DM approach recovers EM as a special case and yields robust alternatives…
We derive novel guaranteed lower bounds for eigenvalues of the Euler-Bernoulli beam with variable bending stiffness. While the standard finite element Rayleigh-Ritz method automatically yields upper bounds, we obtain lower bounds by…
We study the branch of semi-stable and unstable solutions (i.e., those whose Morse index is at most one) of the Dirichlet boundary value problem $-\Delta u=\frac{\lambda f(x)}{(1-u)^2}$ on a bounded domain $\Omega \subset \R^N$, which…
We use the recent theory of Spectral Submanifolds (SSM) for model reduction of nonlinear mechanical systems subject to parametric excitations. Specifically, we develop expressions for higher-order nonautonomous terms in the parameterization…