Sandwich Beam Analysis

1972 ◽  
Vol 39 (3) ◽  
pp. 773-778 ◽  
Author(s):  
D. Krajcinovic
Keyword(s):  
Cross Section ◽  
Static Load ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Simple Algebra ◽  
Sandwich Beams ◽  
Consistent Theory ◽  
Entire Cross Section ◽  
Cross Sectional ◽  
Beam Analysis

A consistent theory of sandwich beams subjected to static load is presented. The theory is developed under the assumption that the Bernoulli’s hypothesis is valid for each lamina independently but not for the entire cross section as a whole. It is shown that the generalized displacement may be chosen in such a way that the set of equations governing the motions for which the beam remains straight on one, and a set of equations describing bending and shear types of motions on the other hand are independent. Furthermore, after some simple algebra, separate equations for each generalized displacement are derived. The normal stress is given in the from which is familiar from strength of materials with two additional terms embodying the influence of the cross-sectional distortion (deviation from classical beam theory).

Analytical and numerical investigation of the free vibration of functionally graded materials sandwich beams

2021 ◽  
Vol 2 (110) ◽  
pp. 72-85
Author(s):  
S.H. Bakhy ◽  
M. Al-Waily ◽  
M.A. Al-Shammari
Keyword(s):  
Analytical Solution ◽  
Free Vibration ◽  
Functionally Graded Materials ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Functionally Graded ◽  
Gradient Index ◽  
Sandwich Beams ◽  
Graded Materials ◽  
The Impact

Purpose: In this study, the free vibration analysis of functionally graded materials (FGMs) sandwich beams having different core metals and thicknesses is considered. The variation of material through the thickness of functionally graded beams follows the power-law distribution. The displacement field is based on the classical beam theory. The wide applications of functionally graded materials (FGMs) sandwich structures in automotive, marine construction, transportation, and aerospace industries have attracted much attention, because of its excellent bending rigidity, low specific weight, and distinguished vibration characteristics. Design/methodology/approach: A mathematical formulation for a sandwich beam comprised of FG core with two layers of ceramic and metal, while the face sheets are made of homogenous material has been derived based on the Euler–Bernoulli beam theory. Findings: The main objective of this work is to obtain the natural frequencies of the FG sandwich beam considering different parameters. Research limitations/implications: The important parameters are the gradient index, slenderness ratio, core metal type, and end support conditions. The finite element analysis (FEA), combined with commercial Ansys software 2021 R1, is used to verify the accuracy of the obtained analytical solution results. Practical implications: It was found that the natural frequency parameters, the mode shapes, and the dynamic response are considerably affected by the index of volume fraction, the ratio as well as face FGM core constituents. Finally, the beam thickness was dividing into frequent numbers of layers to examine the impact of many layers' effect on the obtained results. Originality/value: It is concluded, that the increase in the number of layers prompts an increment within the frequency parameter results' accuracy for the selected models. Numerical results are compared to those obtained from the analytical solution. It is found that the dimensionless fundamental frequency decreases as the material gradient index increases, and there is a good agreement between two solutions with a maximum error percentage of no more than 5%.

Design and Characterization of Small-Scale Sandwich Beams Fabricated by Photolithography and Electrodeposition

2000 ◽  
Author(s):  
Yuki Sugimura
Keyword(s):  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Shear Stiffness ◽  
Open Architecture ◽  
Small Scale ◽  
Sandwich Beams ◽  
The Face ◽  
Micrometer Size

Abstract Small-scale sandwich beams with core structures having cell diameters and wall widths on the order of 500 μm and 100 μm, respectively, have been produced through fabrication methods that combine photolithography and electrodeposition. Two core configurations have been examined: 1) regular hexagonal honeycomb and 2) high-aspect ratio hexagonal shells having an open architecture. The bending response of the sandwich beams has been examined and compared with the beam theory predictions. Shear stiffness of the honeycomb core was considerably high and therefore the bending behavior was dominated by the face sheets. The bending of the sandwich specimens with the hexagonal shells, on the other hand, was largely dependent on the core. The sandwich beam dimensions investigated in this study have not been optimized for weight minimization and structural efficiency. Further advances in fabrication methods to produce micrometer-size features and high-aspect ratio cores will enable realization of structurally efficient, lightweight sandwich beams and panels that can be used as multifunctional components in small-scale devices.

Velocity Field and Energy Dissipation in Viscoplastic Flow in Tubes of Non-Circular Cross-Section

2014 ◽  
Author(s):  
Mario F. Letelier ◽  
Dennis A. Siginer ◽  
Felipe Godoy
Keyword(s):  
Energy Dissipation ◽  
Velocity Field ◽  
Yield Stress ◽  
Cross Section ◽  
Mechanical Energy ◽  
Longitudinal Velocity ◽  
Circular Cross Section ◽  
Viscoplastic Flow ◽  
Entire Cross Section ◽  
Cross Sectional

An analytical method for determining the velocity field, shear stress and energy dissipation in viscoplastic flow in non-circular straight tubes is presented. Bingham’s model of fluid is used for the case of tubes with several cross-sectional contours that can be arbitrarily chosen through a shape factor imposed in the solution for the longitudinal velocity. The analysis is extended to steady flow in tubes in which the cross-section contour exhibits sharp corners. In these cases three flow zones are distinguished: stagnant, non-zero deformation, and plug zones. The method provides the expressions for determining the boundaries and characteristics of those three zones for a wide variety of cross-section shapes. In particular the dynamics of plug-zones for large values of the yield stress and for contours that markedly differ from circumferences is analyzed. Energy dissipation is determined throughout the entire cross-section, so that the effect of shape on mechanical energy loss is assessed in terms of the yield stress and viscosity of the fluid. Some general expressions that help understand energy dissipation mechanisms are derived by using natural coordinates for the velocity field and related variables. These results draw on several recent works from other researchers and the present authors, which have highlighted the significant difficulty of determining the zones of zero deformation in viscoplastic flow when the related solid boundaries are not elementary.

Calibrating and Cross-Sectional Equalizing of the Sensitivity of Ultrasonic Phased Array Inspection of Welds

NDT World ◽  
2016 ◽  
Vol 19 (3) ◽  
pp. 17-27
Author(s):  
Нурматов ◽  
Islam Nurmatov ◽  
Лапидус ◽  
Aleks Lapidus ◽  
Пасси ◽  
...  
Keyword(s):  
Cross Section ◽  
Phased Array ◽  
Flaw Detector ◽  
Practical Implementation ◽  
Flat Bottom ◽  
Entire Cross Section ◽  
Cross Sectional ◽  
Common Reference ◽  
Amplitude Correction ◽  
Ultrasonic Phased Array

Introduction. The approach and practical implementation for the sensitivity calibration and its equalizing within entire insonified cross-section of the material have been presented in the article for 3 most common reference artificial reflectors, namely the flat bottom hole (FBH) situated at parallel to the weld bevel plane, the EDM notch (N), and the side drilled hole (SDH). The method. The issue of inhomogeneous sensitivity over cross-section covered through phased array (PA) sectorial scan plan is due to several factors, which are highlighted and explained. 5 of them are independent on the reference reflector’s shape. In addition the FBH and N reference reflectors are characterized by the strong dependency of the echo amplitude on the angle, under which the ultrasonic wave hits their surface (factor 6, which differs the FBH and N from the omnidirectional SDH). The approach for equalizing the sensitivity over sectorial-scan-insonified cross-section of the material for all types of reference reflectors has been proposed and explained. It is based on the ability of ultrasonic PA flaw detector to implement each pulsing-receiving cycle among the plurality of the scan-plan-forming set of focal laws with individually and independently settled gain and other key settings including Distance Amplitude Correction / Time Corrected Gain (DAC / TCG). The Sonotron NDT’s ISONIC Series PA instruments (ISONIC 3510, ISONIC 2010, and ISONIC 2009 UPA Scope) are featured with the said ability uniquely: in the said units the DAC / TCG mechanism is used purely for compensating the dependency of echo amplitude on the material travel distance while the feature of varying Gain per Focal Law is utilized just for the forming of easy-reproducible Angle Gain Compensation (AGC) plan. Both the DAC / TCG and AGC plans are created independently on each other with use of the same reference reflectors. The results. Combining of the independent DAC / TCG and AGC mechanisms for the first time ever provides the equalizing of the sensitivity for all types of reference reflectors independently on their X, Y position over the entire cross-section of the material — this is confirmed by a number of experimental results presented. Conclusion. At last the single group sectorial scan only becomes sufficient for the complete coverage of the whole cross-section of the weld. This allows reducing the dimensions of required PA probes and wedges in use and the width of the area for the scanning along the fusion line. And finally this increases the maximal possible speed of scanning along with reducing of the inspection cost.

scholarly journals Accounting Comparability and the Accuracy of Peer-Based Valuation Models

2015 ◽  
Vol 90 (6) ◽  
pp. 2571-2601 ◽  
Author(s):  
Steven Young ◽  
Yachang Zeng
Keyword(s):  
Cross Section ◽  
Foreign Firms ◽  
Future Market ◽  
Entire Cross Section ◽  
Cross Sectional ◽  
Cross Border ◽  
Multiple Method ◽  
Empirical Tests ◽  
Accounting Comparability ◽  
Sample Window

ABSTRACT We examine the link between enhanced accounting comparability and the valuation performance of pricing multiples. Using the warranted multiple method proposed by Bhojraj and Lee (2002), we demonstrate how enhanced accounting comparability leads to better peer-based valuation performance. Empirical tests using firms from 15 European Union (EU) countries over the period 1997–2011 (with comparable peers selected from the entire cross-section of foreign firms) document significant improvement in valuation performance measured as pricing accuracy, the ability of value estimates to explain cross-sectional variation in observed price, and the ability of the pricing multiple to predict future market-to-book multiples. Findings for a series of identification tests suggest that enhanced valuation performance is the consequence of improvements in the degree of cross-border accounting comparability that occurred during the sample window, and that a significant fraction of comparability gain operates through improved peer selection.

Fully Comprehensive Geometrically Non-Linear Analysis of Anisotropic Composite Beam Systems

2007 ◽  
Author(s):  
Hemaraju Pollayi ◽  
Dineshkumar Harursampath
Keyword(s):  
Cross Section ◽  
Linear Analysis ◽  
Beam Cross Section ◽  
Reference Line ◽  
Linear Elasticity Theory ◽  
Cross Sectional ◽  
Integration Schemes ◽  
Anisotropic Composite ◽  
Beam Analysis ◽  
Non Linear

This paper describes a comprehensive approach to analyse anisotropic composite beams. Based on geometrically non-linear elasticity theory, the non-linear 3-D beam problem splits into either a linear or non-linear 2-D analysis of the beam cross-section and a non-linear 1-D analysis along the beam reference line. Usually cross-sectional analyses are linear, but there are a few exceptions, like the “trapeze effect” and “Brazier effect”. The two sub-tasks of this work (viz. non-linear analysis of the beam cross-section and non-linear beam analysis) are to be accomplished on a single platform using object-oriented framework. First, we perform a non-linear numerical cross-sectional analysis, based on the Variational-Asymptotic Method (VAM). It is capable of treating cross-sections of arbitrary geometry and generally anisotropic material. Second, we formulate the comprehensively non-linear 1-D governing equations along the beam reference line using the mixed variational method and the expressions for non-linear stiffness matrix. The dynamic response of non-linear, flexible multibody systems is thus simulated within the framework of energy-preserving and energy-decaying time integration schemes that provide unconditional stability for non-linear systems. Finally, local 3-D stress, strain and displacement fields for representative sections in the component beams are recovered, based on the stress resultants from a 1-D global beam analysis. Results from this analysis are compared with those available in the literature, both theoretical and experimental, and focus on the behavior of multi-body systems involving members with elastic couplings.

A Beam Theory for Large Global Rotation, Moderate Local Rotation, and Small Strain

1988 ◽  
Vol 55 (1) ◽  
pp. 179-184 ◽  
Author(s):  
D. A. Danielson ◽  
D. H. Hodges
Keyword(s):  
Cross Section ◽  
Variational Principles ◽  
Beam Theory ◽  
Small Strain ◽  
General Context ◽  
Equilibrium Equations ◽  
Cross Sectional ◽  
Local Rotation ◽  
Material Points

Kinematical relations are derived to account for the finite cross-sectional warping occurring in a beam undergoing large deflections and rotations due to deformation. The total rotation at any point in the beam is represented as a large global rotation of the reference triad (a frame which moves nominally with the reference cross section material points), a small rotation that is constant over the cross section and is due to shear, and a local rotation whose magnitude may be small to moderate and which varies over a given cross section. Appropriate variational principles, equilibrium equations, boundary conditions, and constitutive laws are obtained. Two versions are offered: an intrinsic theory without reference to displacements, and an explicit theory with global rotation characterized by a Rodrigues vector. Most of the formulas herein have been published, but we reproduce them here in a new concise notation and a more general context. As an example, the theory is shown to predict behavior that agrees with published theoretical and experimental results for extension and torsion of a pretwisted strip. The example also helps to clarify the role of local rotation in the kinematics.

A Study of the Effect of Geometry Changes on the Structural Stiffness of a Composite D-Spar

2010 ◽  
Author(s):  
Swaroop B. Visweswaraiah ◽  
Damiano Pasini ◽  
Larry Lessard
Keyword(s):  
Cross Section ◽  
Beam Theory ◽  
Leading Edge ◽  
Structural Stiffness ◽  
Cross Sectional ◽  
Composite Blade ◽  
The Matrix ◽  
Coupling Parameters ◽  
Laminate Theory ◽  
The Impact

The paper examines the impact of varying two geometric cross-section parameters of an advance composite D-spar on its structural stiffness. For a given blade topology, the orientation of the D-spar web with respect to the beam axis and the distance of the D-spar web from the leading edge of the blade have been selected here as the variables of study, as they govern the elastic properties of the composite cross-section. A code has been developed to calculate the matrix terms of the Euler-Bernoulli cross-sectional stiffness utilizing the closed form expressions of the structural properties formulated by assuming both Thin-Walled composite Beam theory (TWB) and Classical Laminate Theory. The code has been validated through the Variational Asymptotic Beam Sectional analysis (VABS) for the cross-sectional stiffness matrix. Two cases have been studied for a quasi-isotropic laminate D-spar. The first is for a symmetric airfoil, whereas the second is for an unsymmetrical airfoil. The variation of the stiffness parameters for the quasi-isotropic D-spar including the coupling parameters has been visualized into parametric maps. The paper also examines the impact that these geometric variables have on the stiffness-to-mass ratio to show that along with the ply orientations they play a major role in the aeroelastic tailoring and structural optimization of a composite blade.

scholarly journals Natural plant stems modelling in a three-point bending test

2019 ◽  
Vol 252 ◽  
pp. 07001
Author(s):  
Bartosz Kawecki ◽  
Jerzy Podgórski ◽  
Aleksandra Głowacka
Keyword(s):  
Numerical Modelling ◽  
Cross Section ◽  
Beam Theory ◽  
Bending Test ◽  
Basic Material ◽  
Cross Sectional ◽  
Natural Plant ◽  
Cosine Series ◽  
Three Point Bending ◽  
Miscanthus Giganteus

The paper presents an approach to natural plant stems numerical modelling in a three-point bending test. Introduced subject was connected with elaborating more efficient systems for harvesting energetic plants. There were modelled, and laboratory tested two types of stems – sida hermaphrodita and miscanthus giganteus. Course of proceedings for obtaining natural cross-sectional dimensions with graphical data processing was described in detail. Basing on dozens of stems slices from random parts of plants, three different cross-section approximations were proposed and computationally implemented – a circular pipe, an elliptical pipe (symmetrical cross-section) and a sine-cosine series pipe (asymmetrical cross-section). Analytical formulas for calculating a cross-sectional area and moments of inertia for each approximation were given. Basic material parameters as an elastic modulus and yielding stress was obtained from simply supported beam theory and laboratory force – the deflexion relation. FEM models were created in Simulia Abaqus software using C3D20R elements. Preliminary approach to modelling damage with perfect plasticity was done basing on several samples bended to failure in laboratory tests. Conclusions for future work with numerical modelling natural plant stems were drawn.

Asymptotic Approach to Oblique Cross-Sectional Analysis of Beams

2013 ◽  
Vol 81 (3) ◽  
Author(s):  
Anurag Rajagopal ◽  
Dewey H. Hodges
Keyword(s):  
Cross Section ◽  
Ad Hoc ◽  
Beam Theory ◽  
Reference Line ◽  
Cross Sectional ◽  
Cross Sectional Analysis ◽  
Variational Asymptotic ◽  
Validation Set ◽  
3D Elasticity ◽  
Sectional Analysis

Structural and aeroelastic analyses using beam theories by default choose a cross section that is perpendicular to the reference line. In several cases, such as swept wings with high AR, a beam theory that allows for the choice of a cross section that is oblique to the reference line may be more convenient. This work uses the variational asymptotic method (VAM) to develop such a beam theory. The problems addressed are the planar deformation of a strip and the full 3D deformation of a solid, prismatic, right-circular cylinder, both made of homogeneous, isotropic material. The motivation for choosing these problems is primarily the existence of 3D elasticity solutions, which comprise a complete validation set for all possible deformations and which are shown to be accurately captured by the current analysis. A secondary motivation was that the development and final results of the beam theory, i.e., the cross-sectional stiffness matrix and stress-strain-displacement recovery relations, are obtainable as closed-form analytical expressions. These results, coupled with the VAM-based beam analysis being devoid of ad hoc assumptions, culminate in what is expected to be of significance when formulating a general oblique cross-sectional analysis for beams with anisotropic material and initial curvature/twist, the detailed treatment of which will be alluded to in a later paper.

Sign in / Sign up

Export Citation Format

Share Document