Search results for "Warping function"
showing 8 items of 8 documents
Transverse shear warping functions for anisotropic multilayered plates
2012
In this work, transverse shear warping functions for an equivalent single layer plate model are formulated from a variational approach. The part of the strain energy which involves the shear phenomenon is expressed in function of the warping functions and their derivatives. The variational calculus leads to a differential system of equations which warping functions must verify. Solving this system requires the choice of values for the (global) shear strains and their derivatives. A particular choice, which is justified for cross-ply laminates, leads to excellent results. For single layer isotropic and orthotropic plates, an analytical expression of the warping functions is given. They invol…
Two multilayered plate models with transverse shear warping functions issued from three dimensional elasticity equations
2014
Abstract A multilayered plate theory which uses transverse shear warping functions is presented. Two methods to obtain the transverse shear warping functions from three-dimensional elasticity equations are proposed. The warping functions are issued from the variations of transverse shear stresses computed at specific points of a simply supported plate. The first method considers an exact 3D solution of the problem. The second method uses the solution provided by the model itself: the transverse shear stresses are computed integrating equilibrium equations. Hence, an iterative process is applied, the model is updated with the new warping functions, and so on. Once the sets of warping functio…
Clustering and Registration of Multidimensional Functional Data
2013
In order to find similarity between multidimensional curves, we consider the application of a procedure that provides a simultaneous assignation to clusters and alignment of such functions. In particular we look for clusters of multivariate seismic waveforms based on EM-type procedure and functional data analysis tools.
Normalizing temporal patterns to analyze sit-to-stand movements by using registration of functional data
2004
Functional data analysis techniques provide an alternative way of representing movement and movement variability as a function of time. In particular, the registration of functional data provides a local normalization of time functions. This normalization transforms a set of curves, records of repeated trials, yielding a new set of curves that only vary in terms of amplitude. Therefore, main events occur at the "same time" for all transformed curves and interesting features of individual recordings remain after averaging processes. This paper presents an application of the registration process to the analysis of the vertical forces exerted on the ground by both feet during the sit-to-stand …
Statistical Approach for Biomarker Discovery Using Label-Free LC-MS Data: An Overview
2016
The identification of new diagnostic, prognostic, or theranostics biomarkers is one of the main aims of clinical research. Technologies like mass spectrometry (MS) focus on the discovery of proteins as biomarkers and are commonly being used for this purpose. Mass spectrometry consists in the separation by gas of charged molecules, based on their mass-over-charge. Liquid chromatography coupled to tandem mass spectrometry (LC-MS/MS) first involves a separation by liquid chromatography (LC) followed by mass spectrometry in the MS and MS/MS modes.
A Multilayered Plate Theory with Transverse Shear and Normal Warping Functions
2016
A multilayered plate theory which takes into account transverse shear and normal stretching is presented. The theory is based on a seven-unknowns kinematic field with five warping functions. Four warping functions are related to the transverse shear behaviour, the fifth is related to the normal stretching. The warping functions are issued from exact three-dimensional solutions. They are related to the variations of transverse shear and normal stresses computed at specific points for a simply supported bending problem. Reddy, Cho-Parmerter and (a modified version of) Beakou-Touratier theories have been retained for comparisons. Extended versions of these theories, able to manage the normal s…
A multilayer anisotropic plate model with warping functions for the study of vibrations reformulated from Woodcock's work
2013
Abstract In this paper, a suitable model for static and dynamic analysis of inhomogeneous anisotropic multilayered plates is described. This model takes into account the variations of the transverse shear strains through the thickness of the plate by means of warping functions. Warping functions are determined by enforcing kinematic and static assumptions at the interfaces. This model leads to: a 10×10 stiffness matrix coupling to each other the membrane strains, the bending and torsion curvatures, and the x and y-derivatives of the transverse shear strains; and a classical 2×2 transverse shear stiffness matrix. This model has been proven to be very efficient, especially when high ratios be…
Shear Effects in Elastic Nanobeams
2020
Small-scale, shear deformable nanobeams, subjected to quasi-static loads, are analyzed by a nonlocal (integral) elasticity model with the main goal to evaluate the influence of shear deformation on size effects. To this aim a warping parametric model is considered in order to obtain a continuous family of shear deformable beam models which span from the Euler-Bernoulli to the Thimoshenko beam model, passing from the Reddy model. The strain difference based nonlocal elasticity theory is applied under the hypotheses of small displacements and isotropic material. The results, obtained by analysing a cantilever nonlocal nanobeam, indicate that shear deformation has a considerable influence upon…