Nonlinear Deformation of Composite Beams: Unification of Cross-Sectional and Elastic Analyses

1991 ◽  
Vol 44 (11S) ◽  
pp. S9-S15 ◽  
Author(s):  
Ali R. Atilgan ◽  
Dewey H. Hodges ◽  
Mark V. Fulton
Keyword(s):  
Dynamic Behavior ◽  
Nonlinear Deformation ◽  
Small Strain ◽  
Composite Beams ◽  
Two Dimensional ◽  
Cross Sectional ◽  
One Dimensional ◽  
Local Rotation ◽  
Nonlinear Static ◽  
Sectional Analysis

A unified analysis is presented for predicting the deformation of anisotropic beams. Outlines of the derivations of both a linear, two-dimensional, cross-sectional analysis and a nonlinear, one-dimensional analysis are given from application of a general kinematical foundation, in which only small strain and small local rotation are assumed. The deformation may be arbitrary except that restrained warping effects are not treated. Predictions from the unified analysis agree quite well with published experimental results for both nonlinear static and linearized dynamic behavior about equilibrium.

Cross-sectional analysis of composite beams including large initial twist and curvature effects

AIAA Journal ◽  
1996 ◽  
Vol 34 (9) ◽  
pp. 1913-1920 ◽  
Author(s):  
Carlos E. S. Cesnik ◽  
Dewey H. Hodges ◽  
Vladislav G. Sutyrin
Keyword(s):  
Composite Beams ◽  
Cross Sectional ◽  
Curvature Effects ◽  
Cross Sectional Analysis ◽  
Sectional Analysis

Computer Simulation of Composite Beams Dynamic Behavior

2019 ◽  
Vol 974 ◽  
pp. 687-692
Author(s):  
V.S. Fyodorov ◽  
Vladimir N. Sidorov ◽  
E.S. Shepitko
Keyword(s):  
Computer Simulation ◽  
Dynamic Behavior ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Composite Beams ◽  
One Dimensional ◽  
Glass Fiber Reinforced Plastic ◽  
Finite Element Software ◽  
Dimensional Modeling ◽  
Damping Model

The paper is devoted to the computer simulation of polymer composite beams dynamic behavior. The use opportunity of one-dimensional beam models for the design of composite elements instead of three-dimensional ones is discussed. The tree-dimensional modeling is implemented using the finite-element software SIMULIA Abaqus considering the orthotropic properties of the composite material. For the one-dimensional modeling two hypothesis of the internal friction – local and nonlocal – are applied and compared. The Kelvin-Voigt hypothesis is used as a local damping model. The nonlocal model is based on the nonlocal mechanics principals and obtained using the Galerkin method. The example glass fiber reinforced plastic beam with the fixed ends is considered under an instantly applied load. The parameters of the nonlocal damping model are defined using the least squares method. The flexibility of the nonlocal damping model is shown and the use opportunity of one-dimensional beam models for the design of composite elements is justified.

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.

New Pseudo Functions To Control Numerical Dispersion

1975 ◽  
Vol 15 (04) ◽  
pp. 269-276 ◽  
Author(s):  
J.R. Kyte ◽  
D.W. Berry
Keyword(s):  
Capillary Pressure ◽  
Cross Section ◽  
Three Dimensional ◽  
Vertical Cross Section ◽  
Numerical Dispersion ◽  
Two Dimensional ◽  
Cross Sectional ◽  
One Dimensional ◽  
Sectional Model ◽  
The Cross

Abstract This paper presents an improved procedure for calculating dynamic pseudo junctions that may be used in two-dimensional, areal reservoir simulations to approximate three-dimensional reservoir behavior. Comparison of one-dimensional areal and two-dimensional vertical cross-sectional results for two example problems shows that the new pseudos accurately transfer problems shows that the new pseudos accurately transfer the effects of vertical variations in reservoir properties, fluid pressures, and saturations from the properties, fluid pressures, and saturations from the cross-sectional model to the areal model. The procedure for calculating dynamic pseudo-relative permeability accounts for differences in computing block lengths between the areal and cross-sectional models. Dynamic pseudo-capillary pressure transfers the effects of pseudo-capillary pressure transfers the effects of different pressure gradients in different layers of the cross-sectional model to the areal model. Introduction Jacks et al. have published procedures for calculating dynamic pseudo-relative permeabilities fro m vertical cross-section model runs. Their procedures for calculating pseudo functions are procedures for calculating pseudo functions are more widely applicable than other published approaches. They demonstrated that, in some cases, the derived pseudo functions could be used to simulate three-dimensional reservoir behavior using two-dimensional areal simulators. For our purposes, an areal simulator is characterized by purposes, an areal simulator is characterized by having only one computing block in the vertical dimension. The objectives of this paper are to present an improved procedure for calculating dynamic pseudo functions, including a dynamic pseudo-capillary pressure, and to demonstrate that the new procedure pressure, and to demonstrate that the new procedure generally is more applicable than any of the previously published approaches. The new pseudos previously published approaches. The new pseudos are similar to those derived by jacks et al. in that they are calculated from two-dimensional, vertical cross-section runs. They differ because (1) they account for differences in computing block lengths between the cross-sectional and areal models, and (2) they transfer the effects of different flow potentials in different layers of the cross-sectional potentials in different layers of the cross-sectional model to the areal model. Differences between cross-sectional and areal model block lengths are sometimes desirable to reduce data handling and computing costs for two-dimensional, areal model runs. For very large reservoirs, even when vertical calculations are eliminated by using pseudo functions, as many as 50,000 computing blocks might be required in the two-dimensional areal model to minimize important errors caused by numerical dispersion. The new pseudos, of course, cannot control numerical pseudos, of course, cannot control numerical dispersion in the cross-sectional runs. This is done by using a sufficiently large number of computing blocks along die length of the cross-section. The new pseudos then insure that no additional dispersion will occur in the areal model, regardless of the areal computing block lengths. Using this approach, the number of computing blocks in the two-dimensional areal model is reduced by a factor equal to the square of the ratio of the block lengths for the cross-sectional and areal models. The new pseudos do not prevent some loss in areal flow-pattern definition when the number of computing blocks in the two-dimensional areal model is reduced. A study of this problem and associated errors is beyond the scope of this paper. Our experience suggests that, for very large reservoirs with flank water injection, 1,000 or 2,000 blocks provide satisfactory definition. Many more blocks provide satisfactory definition. Many more blocks might be required for large reservoirs with much more intricate areal flow patterns. The next section presents comparative results for cross-sectional and one-dimensional areal models. These results demonstrate the reliability of the new pseudo functions and illustrate their advantages pseudo functions and illustrate their advantages over previously derived pseudos for certain situations. The relationship between two-dimensional, vertical cross-sectional and one-dimensional areal reservoir simulators has been published previously and will not be repeated here in any detail. Ideally, the pseudo functions should reproduce two-dimensional, vertical cross-sectional results when they are used in the corresponding one-dimensional areal model. SPEJ P. 269

Observation of the Full Interface of Multi-level Interconnects for Sub-Half-Micron Devices

1996 ◽  
Vol 446 ◽  
Author(s):  
Y. Hirose ◽  
T. Katayama ◽  
N. Fujiki ◽  
T. Ohno ◽  
M. Sekine ◽  
...  
Keyword(s):  
Cross Section ◽  
Electrical Resistance ◽  
Interface Layer ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Cross Sectional ◽  
Present Technique ◽  
Multi Level ◽  
Observation Method ◽  
Sectional Analysis

1. AbstractIn recent years, the problem of electrical resistance of vias and contact holes has become greater because a thin insulated layer formed at the interface of the hole has become a serious difficulty in the manufacture of ULSIs. In using conventional techniques of cross sectional analysis to examine the cause, only one cross section of the hole can be analyzed, therefore there is the problem that the two-dimensional interface layer formed cannot be analyzed exactly.In this paper, we have developed a new observation method to inspect two dimensions of the layer formed locally at the interface of the holes. This new observation method gives the configuration, coverage, and element map of the interface layer because the full interface of holes can be inspected; therefore, the process margin can be discussed. The present technique is demonstrated in failure analysis of sub-half-micron vias filled with tungsten.

A cross-sectional analysis of composite beams based on asymptotic framework

2012 ◽  
Vol 26 (1) ◽  
pp. 161-172 ◽  
Author(s):  
Joonho Jeong ◽  
Jun-Sik Kim ◽  
Yeon June Kang ◽  
Maenghyo Cho
Keyword(s):  
Composite Beams ◽  
Cross Sectional ◽  
Cross Sectional Analysis ◽  
Sectional Analysis

scholarly journals Floodplain Zoning Simulation by Using HEC-RAS and CCHE2D Models in the Sungai Maka River

2016 ◽  
Vol 9 ◽  
pp. ASWR.S36089 ◽  
Author(s):  
Ahmad ShahiriParsa ◽  
Mohammad Noori ◽  
Mohammad Heydari ◽  
Mahmood Rashidi
Keyword(s):  
Flood Damage ◽  
Complex Behavior ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Efficient Tool ◽  
Cross Sectional ◽  
One Dimensional ◽  
River Flooding ◽  
Two Dimensional Model ◽  
Analysis System

River flooding causes several human and financial casualties. It is necessary to perform research studies and implement subsequent actions consistent with the nature of the river. In order to reduce flood damage, floodplain zoning maps and river cross-sectional boundaries are important to nonstructural measures in planning and optimizing utilization of the areas around the river. Due to the complex behavior of the rivers during floods, computer modeling is the most efficient tool with the least possible cost to study and simulate the behavior of the rivers. In this study, one-dimensional model Hydrologic Engineering Centers–-River Analysis System and two-dimensional model CCHE2D were used to simulate the flood zoning in the Sungai Maka district in Kelantan state, Malaysia. The results of these two models in most sections approximately match. Most differences in the results were in the shape of the river.

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