1. INTRODUCTION. A rotation in two dimensions (or other even dimensions) does not in general leave any direction fixed, and even in three dimensions it is not immediately obvious that the composition of rotations about distinct axes is equivalent to a rotation about a single axis. However, in 1775–1776, Leonhard Euler [8] published a remarkable result stating that in three dimensions every rota...

The goal of this note is to present some new results on the application of AVI algorithms to the Simo-Marsden-Krishnaprasad beam model based on a description using rotation matrices. This follows our earlier work on the Euler-Bernoulli beam and thin-shell models with Kirchhoff-Love constraints and various boundary conditions. We consider the effect of large deflections, when the beam is subject...

The stochastic behaviour of materials and loading is great importance for buckling analysis prestressed beam frame structures. In this paper, the stiffness stress matrices are developed analysis. bending rigidity load modelled as fields. spectral decomposition known Karhunen–Loéve expansion has been used to expand random Using expansion, closed-form formulated in terms discrete parameters. cons...

in this paper, the concept of k-regular fuzzy matrix as a general- ization of regular matrix is introduced and some basic properties of a k-regular fuzzy matrix are derived. this leads to the characterization of a matrix for which the regularity index and the index are identical. further the relation between regular, k-regular and regularity of powers of fuzzy matrices are dis- cussed.

A general mathematical formulation of the n × n proper Orthogonal matrix, that corresponds to a rigid rotation in n-dimensional real Euclidean space, is given here. It is shown that a rigid rotation depends on an angle (principal angle) and on a set of (n−2) principal axes. The latter, however, can be more conveniently replaced by only 2 Orthogonal directions that identify the plane of rotation...

Abstract. In this work an alternative beam finite element for rapid time-domain flutter analysis of wings equipped with trailing edge control surfaces, generally distributed along the span, is presented. The aeroelastic proposed based on Euler-Bernoulli theory, De St. Venant torsion theory and two-dimensional unsteady aerodynamics. developed model attractive preliminary aero-servo-elastic analy...

the accuracy and efficiency of the elements proposed by finite element method (fem) considerably depend on the interpolating functions namely shape functions used to formulate the displacement field within the element. in the present study, novel functions, namely basic displacements functions (bdfs), are introduced and exploited for structural analysis of nanobeams using finite element method ...

Let $a, b, k,in K$ and $u, v in U(K)$. We show for any idempotent $ein K$, $(a 0|b 0)$ is e-clean iff $(a 0|u(vb + ka) 0)$ is e-clean and if $(a 0|b 0)$ is 0-clean, $(ua 0|u(vb + ka) 0)$ is too.