Three commonly used methods to determine the principal moments of inertia of a plane area and their directions are based on: (i) the stationarity condition for the axial moment of inertia, (ii) the eigenvalue analysis, and (iii) Mohr’s circle. In this paper we provide two new derivations, which are based on: (a) the matrix diagonalization and the invariant tensor properties, and (b) the conjuga...

The symmetric moment problem is to find a possibly unique, positive symmetric measure that will produce a given sequence of moments {Mn}. Let us assume that the (Hankel) condition for existence of a solution is satisfied, and let σn be the unique measure, supported on n points, whose first 2n moments agree with M0, . . . ,M2n−1. It is known that σ2n =⇒ σ0 (weak convergence) and σ2n+1 =⇒ σ∞, whe...

Double-angle connections are prone to fatigue cracking in old steel bridges; however, owing their complexity, there not many retrofitting solutions for these details. This study proposes a system double-angle using iron-based shape memory alloys (Fe-SMAs). An innovative connection test setup equipped with an optical 3D digital image correlation (DIC) measurement was developed. The included two ...

Model reduction by moment-matching relies upon the availability of so-called moment . If system is nonlinear, computation moments depends on an underlying specific invariance equation, which can be difficult or impossible to solve. This article presents four technical contributions related theo...