A Higher Order Finite Element Model for the Vibration Analysis of Laminated Beams

1998 ◽  
Vol 120 (3) ◽  
pp. 822-824 ◽  
Author(s):  
S. R. Marur ◽  
T. Kant
Keyword(s):  
Axial Strain ◽  
Element Model ◽  
Order Theory ◽  
Higher Order ◽  
Transverse Shear Strain ◽  
Normal Strain ◽  
Laminated Beams ◽  
First Order Theory ◽  
Displacement Model ◽  
Transverse Normal Strain

A higher order displacement model based on a cubic axial strain, cubic transverse shear strain and quadratic transverse normal strain across the thickness of the beam, to model exactly the warping of the cross section is proposed which maintains zero stress at the top and bottom of the beam with out the aid of any shear correction factor. Numerical experiments carried out clearly bring out the efficacy of this model over the first order theory for laminated beams.

Analysis of three-layer composite plates with a new higher-order layerwise formulation

2014 ◽  
Vol 21 (3) ◽  
pp. 401-404
Author(s):  
Dalal A. Maturi ◽  
Antonio J.M. Ferreira ◽  
Ashraf M. Zenkour ◽  
Daoud S. Mashat
Keyword(s):  
Composite Plates ◽  
Order Theory ◽  
Higher Order ◽  
Basis Functions ◽  
Numerical Accuracy ◽  
First Order ◽  
The Core ◽  
First Order Theory ◽  
Layer Composite ◽  
Vibration Problems

AbstractIn this paper, we combine a new higher-order layerwise formulation and collocation with radial basis functions for predicting the static deformations and free vibration behavior of three-layer composite plates. The skins are modeled via a first-order theory, while the core is modeled by a cubic expansion with the thickness coordinate. Through numerical experiments, the numerical accuracy of this strong-form technique for static and vibration problems is discussed.

A Simple Higher-Order Theory for Laminated Composite Plates

1984 ◽  
Vol 51 (4) ◽  
pp. 745-752 ◽  
Author(s):  
J. N. Reddy
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Order Theory ◽  
Higher Order ◽  
Laminated Composite Plates ◽  
First Order ◽  
First Order Theory

A higher-order shear deformation theory of laminated composite plates is developed. The theory contains the same dependent unknowns as in the first-order shear deformation theory of Whitney and Pagano [6], but accounts for parabolic distribution of the transverse shear strains through the thickness of the plate. Exact closed-form solutions of symmetric cross-ply laminates are obtained and the results are compared with three-dimensional elasticity solutions and first-order shear deformation theory solutions. The present theory predicts the deflections and stresses more accurately when compared to the first-order theory.

A Noncanonically Shape Laminated Plate Subjected to Impact Loading: Theory and Experiment

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
Natalia V. Smetankina ◽  
Alexander N. Shupikov ◽  
Sergei Yu. Sotrikhin ◽  
Vladimir G. Yareshchenko
Keyword(s):  
Order Theory ◽  
Transverse Shear Strain ◽  
Laminated Plate ◽  
Immersion Method ◽  
Plan View ◽  
First Order Theory ◽  
Wide Range ◽  
Normal Element ◽  
Straight Lines ◽  
Theoretical Results

This paper suggests an analytical approach to investigating vibrations of a laminated plate with a noncanonical shape in plan view under impact with an impactor having a semispherical end. The approach suggested is based on the immersion method. The dynamic behavior of the plate is described by the first-order theory accounting for transverse shear strain, thickness reduction, and normal element rotation inertia in each layer. Impact has been analyzed for different points of the plate whose contour consists of straight lines and circle arcs. The theoretical results are consistent with experimental data obtained with the dynamic wide-range strain measurement technique.

scholarly journals HOL-λσ: an intentional first-order expression of higher-order logic

2001 ◽  
Vol 11 (1) ◽  
pp. 21-45 ◽  
Author(s):  
GILLES DOWEK ◽  
THERESE HARDIN ◽  
CLAUDE KIRCHNER
Keyword(s):  
Order Theory ◽  
Higher Order ◽  
Search Method ◽  
Order Logic ◽  
Automated Deduction ◽  
Higher Order Logic ◽  
First Order ◽  
Proof Search ◽  
First Order Theory ◽  
Explicit Substitutions

We give a first-order presentation of higher-order logic based on explicit substitutions. This presentation is intentionally equivalent to the usual presentation of higher-order logic based on λ-calculus, that is, a proposition can be proved without the extensionality axioms in one theory if and only if it can be in the other. We show that the Extended Narrowing and Resolution first-order proof-search method can be applied to this theory. In this way we get a step-by-step simulation of higher-order resolution. Hence, expressing higher-order logic as a first-order theory and applying a first-order proof search method is a relevant alternative to a direct implementation. In particular, the well-studied improvements of proof search for first-order logic could be reused at no cost for higher-order automated deduction. Moreover, as we stay in a first-order setting, extensions, such as equational higher-order resolution, may be easier to handle.

Effects of higher-order nonlinearity and finite geometry on the propagation of KdV solitons

1988 ◽  
Vol 40 (3) ◽  
pp. 545-552 ◽  
Author(s):  
B. Ghosh ◽  
K. P. Das
Keyword(s):  
Planar Waveguide ◽  
Electron Plasma ◽  
Finite Geometry ◽  
Order Theory ◽  
Higher Order ◽  
Ion Acoustic Wave ◽  
Electron Plasma Wave ◽  
First Order ◽  
First Order Theory ◽  
Ion Acoustic

Using reductive perturbation theory and a planar waveguide geometry, the effects of higher-order nonlinearity and finite boundaries on the propagation of electron plasma and ion-acoustic KdV solitons are investigated by taking into account finite electron and ion temperatures. For an electron plasma wave, the higher-order nonlinearity is found to increase the amplitude of the soliton and slightly decrease the width of the soliton compared with that predicted by the first-order theory. For an ion-acoustic wave the higher-order-nonlinearity and finite-boundary effects give rise to a W-shaped soliton.

A Finite Element Model for Thick-Walled Axisymmetric Shells

1982 ◽  
Vol 104 (3) ◽  
pp. 215-222 ◽  
Author(s):  
D. J. Barrett ◽  
A. Soler
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Finite Element Model ◽  
Thin Shell ◽  
Element Model ◽  
Order Theory ◽  
Higher Order ◽  
Shells Of Revolution ◽  
Geometric Conditions ◽  
Higher Order Theory

The symmetrically loaded moderately thick-walled shell of revolution can be treated by general finite elements, or for certain geometric conditions, by extended thin shell finite elements that have incorporated transverse shear deformation. In this work, we develop a higher order theory finite element model for symmetrically loaded shells of revolution which is useful for configurations which are out of the range of validity of the extended thin shell elements. Legendre polynomial series expansions are key features of the development and lead to nonlinear distributions of both stress and deformation in the thickness variable. Problems are solved to yield some initial data for comparison of the cost and accuracy of the higher order theory finite element model to other shell element models.

Sign in / Sign up

Export Citation Format

Share Document