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 paradox in curved beams

2018 ◽  
Vol 233 (8) ◽  
pp. 2830-2833 ◽  
Author(s):  
Antonio Strozzi ◽  
Enrico Bertocchi ◽  
Sara Mantovani
Keyword(s):  
Cross Section ◽  
Stress Reduction ◽  
Material Removal ◽  
Neutral Axis ◽  
Beam Cross Section ◽  
Mathematical Approach ◽  
Bending Stress ◽  
Curved Beams ◽  
Cross Sectional ◽  
Mechanical Component

It is sometimes possible to relieve the stresses in a mechanical component by removing material, where relief grooves are the commonest expedient approach. Within the rectilinear beam realm, rare situations are known in which, by removing material in the cross-sectional zones that are farthest from the neutral axis, a bending stress diminution is achieved. With regard to curved beams, selected examples are presented in which a bending stress diminution is achieved by laterally removing material from the zones close to the neutral axis. An approximate mathematical approach based on Gateaux linearization is developed that delimits the lateral zones of the beam cross-section in which material removal is accompanied by bending stress reduction. While the achievable stress diminution is generally marginal, the reduction of the beam’s cross-section is technically interesting.

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).

scholarly journals The influence of a column shape cross-section on the punching capacity

2019 ◽  
Author(s):  
Simona Sarvaicova ◽  
Viktor Borzovic ◽  
Tomas Augustin
Keyword(s):  
Cross Section ◽  
Shear Failure ◽  
Shear Crack ◽  
Rectangular Cross Section ◽  
Linear Analysis ◽  
Linear Modeling ◽  
Model Code ◽  
Eurocode 2 ◽  
Non Linear ◽  
Comparison Of The Results

The article deals with non-linear modeling of slab-column connection which represents a fragment of flat slab supported by a column and loaded up to the punching shear failure. The aim of this parametrical study is the analysis of the length of reduced control perimeters in the case of columns with significantly elongated rectangular cross-section. The non-linear analysis was performed in program Atena and calibrated by test results obtained from the laboratory experiments carried out at Slovak University of Technology in Bratislava. The results of non-linear analysis are compared with the values of shear resistance calculated according to the current Eurocode 2 model; fib Model Code 2010 and model proposed for the second generation of Eurocode 2 based on the Critical shear crack theory. The reliability of the models is evaluated by comparison of the results of numerical analyses and previously mentioned design models.

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.

scholarly journals Introducing Design Space-Independence in Beam Cross-Section Optimization

2020 ◽  
Author(s):  
Chander Sen ◽  
Jitendra Prasad
Keyword(s):  
Topology Optimization ◽  
Cross Section ◽  
Design Space ◽  
Beam Cross Section ◽  
Material Distribution ◽  
Cross Sectional ◽  
Load Carrying ◽  
Optimization Formulation ◽  
Torsional Loads ◽  
First Moment

The cross-sectional topology optimization of a slender load carrying member such as a beam typically begins with the choice of design space which is generally either a square or a rectangle. However, when subjected to bending and torsional loads, such design space may often lead to biased topologies as the material distribution is directed towards the boundaries. As it may be difficult to avoid square/rectangular design space, this work introduces a constraint which may help in decreasing the dependency on the shape of the design space. The constraint is on polar first moment of area and is different from the traditional weight constraint in a way that it simultaneously constrains the weight and enclosed volume. The outcomes from the new scheme are compared with those obtained through conventional compliance- and weight- based topology optimization formulation.

The Analysis of Shear Forces Flow around the Supports of Flat Slabs

2020 ◽  
Vol 309 ◽  
pp. 216-221
Author(s):  
Simona Šarvaicová ◽  
Viktor Borzovič
Keyword(s):  
Cross Section ◽  
Shear Resistance ◽  
Linear Analysis ◽  
Punching Shear ◽  
Shear Forces ◽  
Flat Slab ◽  
Flat Slabs ◽  
Eurocode 2 ◽  
Non Linear ◽  
Linear Shear

This paper deals with both linear and non-linear analysis of shear forces distribution in the area near the supports of the flat slabs. With a cross-section ratio of cmax / cmin > 3, the main amount of the shear stress is concentrated near the column or wall corners bases. As a consequence of this phenomenon, it is necessary to reduce the control perimeter when evaluating the punching shear resistance of a flat slab. The fragments of the flat slabs with the thickness of 200 mm supported by a wall with various loading conditions were analyzed. The results according to the Eurocode 2 were compared to a non-linear shear resistance evaluation that was calibrated based on the results from the previous experiments. Based on thus evaluated punching shear resistances, the theoretical reduced control perimeter was determined and subsequently it was compared to design model Eurocode 2. The physical basis for determining reduced control perimeters is based on the shear force concentration near the support.

scholarly journals Non-linear analysis of slab-column connections with openings

2019 ◽  
Author(s):  
Ludmila Kormosova ◽  
Tomas Augustin ◽  
Jaroslav Halvonik
Keyword(s):  
Cross Section ◽  
Linear Models ◽  
Linear Analysis ◽  
Transverse Reinforcement ◽  
Flat Slab ◽  
Analysis And Design ◽  
Non Linear ◽  
Testing Accuracy ◽  
Rectangular Columns ◽  
General Method

This paper is focused on the assessment of punching capacity of the slab-column connections without transverse reinforcement with openings located close to a column. Non-linear analysis and design equations from the relevant codes of practise are used for the prediction of the punching resistance of flat slab specimens supported by the rectangular columns with different ratio h/d of the column’s cross-section. The non-linear models were calibrated using experimental results from the laboratory tests. The main goal of the study is an investigation of the effect of the openings on the punching capacity and as well as testing accuracy of the design equations for the prediction of the punching resistance. Several methods for the reduction of the control perimeter length accounting for presence of the openings were tested in order to find the most general method for the estimation of the punching capacity. However, standard methods introduced in the relevant codes of practise provide very inconsistent results concerning of the model’s safety for different position of the openings as well as for different cross-section of the columns. Therefore modification of the methods was proposed and verified using obtained results.

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