Early attempts to derive curved beam and shell elements in a curvilinear system were dramatically unsuccessful. This was wrongly attributed to the failure of these elements to recover strain-free rigid body displacement modes in a curvilinear co-ordinate description. Recent evidence points to a ‘membrane locking’ phenomenon that arises when constrained strain fields corresponding to inextension...

In this article we derive the deflection equation of a simple beam using screw theory. The effects of tension, torsion and bending of the beam can be unified into a single equation. We begin by looking at the compliance matrix for small elements of the beam. This is loosely based on work by von Mises in the 1920s. We reproduce von Mises results for the compliance matrix of the entire beam by in...

Nomenclature L y spanwise coordinate q net beam loading S shear M bending moment θ deflection angle (= dw/dx) w deflection κ local beam curvature ′ lift/span distribution ′ S η normalized spanwise coordinate (= 2y/b) c local wing chord wing wing area b wing span λ taper ratio E Young's modulus δ tip deflection N load factor m wing mass/span distribution I bending inertia i spanwise station inde...

In this paper, a displacement-based, variationally consistent, two variable refined theory for shear deformable beams is presented. The beam is assumed to be of linearly elastic, homogeneous, isotropic material and has a uniform rectangular cross-section. In this theory, the beam axial displacement and beam transverse displacement consist of bending components and shearing components. The assum...

Thorough understanding of steel rail response to wheel load is a key step towards design and evaluation of the railway track structure. In current practice, maximum vertical deflection and bending moment are calculated using the theory of infinite beam on continuous elastic foundation (Winkler model), in which the foundation stiffness is assumed as constant. However, variation of track modulus ...

A bent Laue double-crystal monochromator system has been designed for vertically expanding the X-ray beam at the Canadian Light Source's BioMedical Imaging and Therapy beamlines. Expansion by a factor of 12 has been achieved without deteriorating the transverse coherence of the beam, allowing phase-based imaging techniques to be performed with high flux and a large field of view. However, preli...

The paper investigates the shape recovery behavior of a simple beam and a tape spring made of LDPE under prescribed deformation history at room temperature. The linear viscoelastic material properties of LDPE were measured via creep tests. An analysis of a LDPE beam under four-point bending with an imposed history of vertical deflection and reaction force was performed. A theoretical solution w...

Abstract: A structure of micro-electro-mechanical system (MEMS) linear phased array based on “multi-cell” element is designed to increase radiation sound pressure of transducer working in bending vibration mode at high frequency. In order to more accurately predict the resonant frequency of an element, the theoretical analysis of the dynamic equation of a fixed rectangular composite plate and f...

Laser micro bending process of Ti6Al4V square bar are carried out using a 3D thermo-mechanical finite element analytical model (FEM). The transient temperature fields, displacement fields, stress fields and strain fields are obtained and analyzed. The results show that the bending angel during laser micro bending process is in good agreement with experimental measurements. The effects of proces...