Vibration Analysis of Thin/Thick, Composites/Metallic Spinning Cylindrical Shells by Refined Beam Models

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
E. Carrera ◽  
M. Filippi
Keyword(s):  
Composite Materials ◽  
Initial Stress ◽  
Cylindrical Shells ◽  
Three Dimensional ◽  
Point Of View ◽  
Displacement Fields ◽  
Previous Theory ◽  
Cross Sectional ◽  
Computational Point ◽  
Thick Composites

This paper evaluates the vibration characteristics of thin/thick rotating cylindrical shells made of metallic and composite materials. A previous theory of the authors is extended here to include the effects of geometrical stiffness due to rotation. To this end, variable kinematic one-dimensional (1D) models obtained by applying the Carrera Unified Formulation (CUF) were used. The components of the displacement fields are x, z polynomials of arbitrary order N, making it possible to go beyond the rigid cross section assumptions of the classical beam theories. A significant contribution of this formulation consists in the possibility to include the in-plane cross-sectional deformations allowing the introduction of the in-plane initial stress effects, e.g., the effect of the geometrical stiffness. Equations of motions, including both Coriolis and in-plane initial stress contributions, were solved through the finite element method. Several analyses were carried out on both thin and thick cylinders made of either metallic or composite materials with different boundary conditions. The results are compared with analytical and numerical shell formulations and three-dimensional solutions available in the literature. Various laminate lay-up have been considered in the case of composites shells. Numerical evaluations of the effect of geometric stiffness are provided, demonstrating its importance in the analyses presented. The 1D models appear very effective to investigate the dynamics of spinning shells and, contrary to shell theories, they do not require any amendments with thick shell geometry. From the computational point of view, the present refined beam models are less expensive than the shell and solid counterparts.

Three-Dimensional Solutions for Rotor Blades Using High-Order Geometrical Nonlinear Beam Finite Elements

2019 ◽  
Vol 64 (3) ◽  
pp. 1-10
Author(s):  
Matteo Filippi ◽  
Alfonso Pagani ◽  
Erasmo Carrera
Keyword(s):  
Finite Elements ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
High Order ◽  
Rotor Blades ◽  
Constitutive Law ◽  
Displacement Fields ◽  
Cross Sectional ◽  
The Cross

This paper proposes a geometrically nonlinear three-dimensional formalism for the static and dynamic study of rotor blades. The structures are modeled using high-order beam finite elements whose kinematics are input parameters of the analysis. The displacement fields are written using two-dimensional Taylor- and Lagrange-like expansions of the cross-sectional coordinates. As far as the Taylor-like polynomials are concerned, the linear case is similar to the first-order shear deformation theory, whereas the higher-order expansions include additional contributions that describe the warping of the cross section. The Lagrange-type kinematics instead utilizes the displacements of certain physical points as degrees of freedom. The inherent three-dimensional nature of the Carrera unified formulation enables one to include all Green–Lagrange strain components as well as all coupling effects due to the geometrical features and the three-dimensional constitutive law. A number of test cases are considered to compare the current solutions with experimental and theoretical results reported in terms of large deflections/rotations and frequencies related to small amplitude vibrations.

Algorithms for the calculation of X-ray diffraction patterns from finite element data

2010 ◽  
Vol 43 (6) ◽  
pp. 1287-1299 ◽  
Author(s):  
E. Wintersberger ◽  
D. Kriegner ◽  
N. Hrauda ◽  
J. Stangl ◽  
G. Bauer
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Point Of View ◽  
X Ray Diffraction ◽  
Displacement Fields ◽  
X Ray ◽  
Si Substrates ◽  
Diffraction Patterns ◽  
Simulation Point ◽  
Ccd Detectors

A set of algorithms is presented for the calculation of X-ray diffraction patterns from strained nanostructures. Their development was triggered by novel developments in the recording of scattered intensity distributions as well as in simulation practice. The increasing use of two-dimensional CCD detectors in X-ray diffraction experiments, with which three-dimensional reciprocal-space maps can be recorded in a reasonably short time, requires efficient simulation programs to compute one-, two- and three-dimensional intensity distributions. From the simulation point of view, the finite element method (FEM) has become the standard tool for calculation of the strain and displacement fields in nanostructures. Therefore, X-ray diffraction simulation programs must be able to handle FEM data properly. The algorithms presented here make use of the deformation fields calculated on a mesh, which are directly imported into the calculation of diffraction patterns. To demonstrate the application of the developed algorithms, they were applied to several examples such as diffraction data from a dislocated quantum dot, from a periodic array of dislocations in a PbSe epilayer grown on a PbTe pseudosubstrate, and from ripple structures at the surface of SiGe layers deposited on miscut Si substrates.

Two‐point ray tracing in a three‐dimensional medium consisting of homogeneous nonisotropic layers separated by plane interfaces

Geophysics ◽  
1984 ◽  
Vol 49 (6) ◽  
pp. 767-770 ◽  
Author(s):  
R. F. Stöckli
Keyword(s):  
Point Source ◽  
Travel Time ◽  
Ray Tracing ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Point Of View ◽  
Wave Surface ◽  
Computational Point ◽  
Time Problem

The ray‐tracing problem is considered the solution to a minimum travel time problem for media where each layer may be regarded as a transversely isotropic homogeneous solid. The wave surface‐wavefront at t = 1 s, corresponding to a wave generated at the point source, associated with each layer’s anisotropy is approximated by surfaces which are not more difficult to handle, from a computational point of view, than ellipsoidal surfaces. These approximating surfaces are those used in ray‐tracing computation; a ray being a true ray approximation is thus obtained.

Construction of Dynamic Fundamental Solutions for Piezoelectric Solids

1995 ◽  
Vol 48 (11S) ◽  
pp. S222-S229 ◽  
Author(s):  
Naum Khutoryansky ◽  
Horacio Sosa
Keyword(s):  
Three Dimensional ◽  
Transversely Isotropic ◽  
Fundamental Solutions ◽  
Point Of View ◽  
Integral Representations ◽  
Computational Point ◽  
Plane Wave Decomposition ◽  
Piezoelectric Solid ◽  
Piezoelectric Solids ◽  
Wave Decomposition

Fundamental solutions are derived within the framework of transient dynamic, three-dimensional piezoelectricity. The purpose of the article is to show alternate integral representations for such solutions. Thus, a representation over the unit sphere in accordance to a methodology based on the plane wave decomposition is provided. It is shown, however, that more efficient representations from a computational point of view can be achieved through appropriate coordinate transformations. Hence, representations of the fundamental solutions over surfaces of slowness are provided as novel alternatives to more classical approaches. The computational benefits of these new representations are displayed through a numerical example involving a transversely isotropic piezoelectric solid.

Singular Behavior of Laminated Skew Composite Materials with Cross-Ply Stacking

2012 ◽  
Vol 538-541 ◽  
pp. 1640-1645 ◽  
Author(s):  
Jae Seok Ahn ◽  
Kwang Ik Son ◽  
Kwang Sung Woo ◽  
Young Shik Shin
Keyword(s):  
Composite Materials ◽  
Physical Meaning ◽  
Order Approximation ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Higher Order ◽  
Point Of View ◽  
Shape Functions ◽  
Laminated Composite Materials ◽  
Dimensional Shape

This study deals with effects depending on skew angles in skewed-laminated composite materials in macroscopic point of view. Based on higher-order approximation of displacements, subparametric layer-wise finite elements are used to analyze skewed-laminated composite systems. The elements have higher-order shape functions derived from the Lobatto shape functions. The modes of the elements are classified into three groups such as vertex, side, and internal modes. The vertex modes have physical meaning, while side and internal modes with respect to the increase of order of the Lobatto shape functions do not have physical meaning but improve accuracy of analysis. Therefore, fixing mesh arrangement of present analysis, the quality of the analysis can be enhanced without re-meshing work. The approach based on p-version of finite element method is implemented with three-dimensional elasticity theory, while shape functions are developed by combination of one- and two-dimensional shape functions, not using three-dimensional shape functions. Using the accurate and practical proposed technique, macroscopic behavior of skewed-laminated composite materials is investigated.

An enhancement of the warping shear functions of Refined Zigzag Theory

2021 ◽  
pp. 1-15
Author(s):  
Matteo Sorrenti ◽  
Marco Di Sciuva
Keyword(s):  
Coupling Effect ◽  
Three Dimensional ◽  
Composite Plates ◽  
Laminated Plates ◽  
Point Of View ◽  
Multilayered Structures ◽  
Computational Point ◽  
Multilayered Plates ◽  
Elasticity Solutions ◽  
Zigzag Theory

Abstract The paper presents an enhancement in Refined Zigzag Theory (RZT) for the analysis of multilayered composite plates. In standard RZT, the zigzag functions cannot predict the coupling effect of in-plane displacements for anisotropic multilayered plates, such as angle-ply laminates. From a computational point of view, this undesirable effect leads to a singular stiffness matrix. In this work, the local kinematic field of RZT is enhanced with the other two zigzag functions that allow the coupling effect. In order to assess the accuracy of these new zigzag functions for RZT, results obtained from bending of angle-ply laminated plates are compared to the three-dimensional exact elasticity solutions and other plate models used in the open literature. The numerical results highlight that the enhanced zigzag functions extend the range of applicability of RZT to the study of general angle-ply multilayered structures, maintaining the same seven kinematic unknowns of standard RZT.

scholarly journals Effects of the Inlet Endwall Boundary Layer on 3-D Flows and Loss Evolution in a Linear Turbine Cascade

1995 ◽  
Author(s):  
J. Tominaga ◽  
E. Outa ◽  
Atsumasa Yamamoto
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Test Data ◽  
Three Dimensional ◽  
Internal Flow ◽  
Point Of View ◽  
Navier Stokes ◽  
Turbine Cascade ◽  
Computational Point ◽  
Flow Phenomena

A three-dimensional Navier-Stokes computation was made for investigating internal flow phenomena of a linear turbine cascade, and the results were compared with the test data obtained inside the cascade passage. The present code was found to fairly well simulate the experimental data, as well as various vortices being generated in the cascade passage. In this paper, detailed mechanisms of the loss generation are discussed mainly from the computational point of view.

COMBINATORIAL POLYNOMIALLY COMPUTABLE CHARACTERISTICS OF SUBSTITUTIONS AND THEIR PROPERTIES

2020 ◽  
Vol 7 (2) ◽  
pp. 34-41
Author(s):  
VLADIMIR NIKONOV ◽  
◽  
ANTON ZOBOV ◽  
Keyword(s):  
Mathematical Expectation ◽  
Point Of View ◽  
Small Range ◽  
Computational Point ◽  
Wide Range ◽  
Bijective Function ◽  
The Difference ◽  
Element Base ◽  
Selection Of

The construction and selection of a suitable bijective function, that is, substitution, is now becoming an important applied task, particularly for building block encryption systems. Many articles have suggested using different approaches to determining the quality of substitution, but most of them are highly computationally complex. The solution of this problem will significantly expand the range of methods for constructing and analyzing scheme in information protection systems. The purpose of research is to find easily measurable characteristics of substitutions, allowing to evaluate their quality, and also measures of the proximity of a particular substitutions to a random one, or its distance from it. For this purpose, several characteristics were proposed in this work: difference and polynomial, and their mathematical expectation was found, as well as variance for the difference characteristic. This allows us to make a conclusion about its quality by comparing the result of calculating the characteristic for a particular substitution with the calculated mathematical expectation. From a computational point of view, the thesises of the article are of exceptional interest due to the simplicity of the algorithm for quantifying the quality of bijective function substitutions. By its nature, the operation of calculating the difference characteristic carries out a simple summation of integer terms in a fixed and small range. Such an operation, both in the modern and in the prospective element base, is embedded in the logic of a wide range of functional elements, especially when implementing computational actions in the optical range, or on other carriers related to the field of nanotechnology.

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