Sequential Buckling: A Variational Analysis

Sequential Buckling: A Variational Analysis

We examine a variational problem from elastic stability theory: a thin elastic strut on an elastic foundation. The strut has infinite length, and its lateral deflection is represented by u : R→ R. Deformation takes place under conditions of prescribed total shortening, leading to the variational problem inf { 1 2 ∫ u′′ 2 + ∫ F (u) : 1 2 ∫ u′ 2 = λ } . (0.1) Solutions of this minimization proble...

Sequential Optimality Conditions and Variational Inequalities

In recent years, sequential optimality conditions are frequently used for convergence of iterative methods to solve nonlinear constrained optimization problems. The sequential optimality conditions do not require any of the constraint qualications. In this paper, We present the necessary sequential complementary approximate Karush Kuhn Tucker (CAKKT) condition for a point to be a solution of a ...

Numerical Variational Methods Applied to Cylinder Buckling

Abstract. We review and compare different computational variational methods applied to a system of fourth order equations that arises as a model of cylinder buckling. We describe both the discretization and implementation, in particular how to deal with a 1 dimensional null space. We show that we can construct many different solutions from a complex energy surface. We examine numerically conver...

Variational Sequential Monte Carlo

Many recent advances in large scale probabilistic inference rely on variational methods. The success of variational approaches depends on (i) formulating a flexible parametric family of distributions, and (ii) optimizing the parameters to find the member of this family that most closely approximates the exact posterior. In this paper we present a new approximating family of distributions, the v...

Buckling Analysis