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Euler buckling epitomises mechanical instabilities: An inextensible straight elastic line buckles under compression when the compressive force reaches a critical value $F_\ast>0$. Here, we extend this classical, planar instability to the…
Topology optimization has matured to become a powerful engineering design tool that is capable of designing extraordinary structures and materials taking into account various physical phenomena. Despite the method's great advancements in…
The classical Euler's problem on optimal configurations of elastic rod in the plane with fixed endpoints and tangents at the endpoints is considered. The global structure of the exponential mapping that parameterises extremal trajectories…
For the three-body problem, we consider the Lagrange stability. To analyze the stability, along with integrals of energy and angular momentum, we use relations by the author from Sosnitskii (2005), which band together separately squared…
We investigate the buckling under compression of a slender beam with a distributed lateral elastic support, for which there is an associated cost. For a given cost, we study the optimal choice of support to protect against Euler buckling.…
All attempts of aeroelastic explanations for the torsional instability of suspension bridges have been somehow criticised and none of them is unanimously accepted by the scientific community. We suggest a new nonlinear model for a…
We consider optimal transport based distributionally robust optimization (DRO) problems with locally strongly convex transport cost functions and affine decision rules. Under conventional convexity assumptions on the underlying loss…
We formulate and consider the problem of an inextensible, unshearable, viscoelastic rod, with evolving natural configuration, moving on a plane. We prove that the dynamic equations describing quasistatic motion of an Eulerian strut, an…
A continuous-time financial portfolio selection model with expected utility maximization typically boils down to solving a (static) convex stochastic optimization problem in terms of the terminal wealth, with a budget constraint. In…
The new linear theory of elastic shells is presented in this paper. This theory is free from various logical imperfections, that may be found in the approaches of earlier researchers. On the base of this theory the equations of shells of…
An important unresolved challenge in the theory of regularization is to set the regularization coefficients of popular techniques like the ElasticNet with general provable guarantees. We consider the problem of tuning the regularization…
Here the buckling of inextensible rods due to axial body forces is mapped to 1d, nonrelativistic, time-independent quantum mechanics. Focusing on the pedagogical case of rods confined to 2d, three simple and physically realizable…
In the seminal book M\'echanique analitique, Lagrange, 1788, the notion of a Lagrange multiplier was first introduced in order to study a smooth minimization problem subject to equality constraints. The idea is that, under some regularity…
The theory of perfect fluids is reconsidered from the point of view of a covariant Lagrangian theory. It has been shown that the Euler-Lagrange equations for a perfect fluid could be found in spaces with affine connections and metrics from…
The buckling of hyperelastic incompressible cylindrical tubes of arbitrary length and thickness under compressive axial load is considered within the framework of nonlinear elasticity. Analytical and numerical methods for bifurcation are…
We prove that, in the limit of vanishing thickness, equilibrium configurations of inhomogeneous, three-dimensional non-linearly elastic rods converge to equilibrium configurations of the variational limit theory. More precisely, we show…
We reconsider the minimization of the compliance of a two dimensional elastic body with traction boundary conditions for a given weight. It is well known how to rewrite this optimal design problem as a nonlinear variational problem. We take…
This paper describes new results linking constrained optimization theory and nonlinear contraction analysis. Generalizations of Lagrange parameters are derived based on projecting system dynamics on the tangent space of possibly…
Consider the following variational problem: among all curves in $\mathbb{R}^n$ of fixed length with prescribed end points and prescribed tangents at the end points, minimise the $L^\infty$-norm of the curvature. We show that the solutions…
The famous bifurcation analysis performed by Fl\"ugge on compressed thin-walled cylinders is based on a series of simplifying assumptions, which allow to obtain the bifurcation landscape, together with explicit expressions for limit…