scholarly journals General non-uniform quadrilateral cross-sections for thin-walled FG sandwich beams

2021 ◽  
Vol 15 (2) ◽  
pp. 90-100
Author(s):  
Tan-Tien Nguyen ◽  
Quoc-Hung Nguyen ◽  
Thang D. Le ◽  
Hiep D. Le
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Higher Order ◽  
Functionally Graded ◽  
Sandwich Beams ◽  
Finite Element Package ◽  
Fg Beam ◽  
Thin Walled ◽  
The Cross ◽  
Beam Frame

The paper aims at introducing an analysis of thin-walled functionally graded sandwich beams for general non-uniform quadrilateral cross-sections. Generally, the materials are assumed to be graded through the thickness following a predefined shape while Poisson's ratio kept as a constant due to its less domination. The cross-section linearly varies from one end to another end of the beam. In order to relax the difficulties in modeling as well as capturing the behaviors of thin-walled functionally graded beams, a higher-order approach has been applied including warping, coupling distortions as well as Poisson's distortion. A multi-separated beam on each edge of the cross-section which is an application of the so-called beam-frame-modal method is adopted. Subsequently, the effects of these major importance along with anisotropy of materials are then fully considered. As a consequence, the analysis is able to extensively applied to closed-section beam-shells with different curvatures. In order to illustrate the accuracy and computational efficiency of the method, various examples have been conducted in which the results obtained from finite element package as ABAQUS are employed. Keywords: quadrilateral cross-section; thin-walled FG beam; higher-order coupling; beam frame modal.

Vibration analysis of thin-walled functionally graded sandwich beams with non-uniform polygonal cross-sections

2021 ◽  
pp. 114723
Author(s):  
Tan-Tien Nguyen ◽  
Ngoc-Linh Nguyen ◽  
Jaehong Lee ◽  
Quoc-Hung Nguyen
Keyword(s):  
Cross Sections ◽  
Vibration Analysis ◽  
Functionally Graded ◽  
Sandwich Beams ◽  
Thin Walled

Design variation of thin-walled composite beam cross-section properties

2016 ◽  
Vol 12 (3) ◽  
pp. 558-576 ◽  
Author(s):  
Aníbal J.J. Valido ◽  
João Barradas Cardoso
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Laminated Composite ◽  
Adjoint System ◽  
Design Sensitivity ◽  
Content Type ◽  
Design Elements ◽  
Thin Walled ◽  
The Cross ◽  
Cross Section Geometry

Purpose The purpose of this paper is to present a design sensitivity analysis continuum formulation for the cross-section properties of thin-walled laminated composite beams. These properties are expressed as integrals based on the cross-section geometry, on the warping functions for torsion, on shear bending and shear warping, and on the individual stiffness of the laminates constituting the cross-section. Design/methodology/approach In order to determine its properties, the cross-section geometry is modeled by quadratic isoparametric finite elements. For design sensitivity calculations, the cross-section is modeled throughout design elements to which the element sensitivity equations correspond. Geometrically, the design elements may coincide with the laminates that constitute the cross-section. Findings The developed formulation is based on the concept of adjoint system, which suffers a specific adjoint warping for each of the properties depending on warping. The lamina orientation and the laminate thickness are selected as design variables. Originality/value The developed formulation can be applied in a unified way to open, closed or hybrid cross-sections.

Cross-section optimization of thin-walled open-section composite column for maximizing its ultimate strength

2021 ◽  
pp. 146442072110462
Author(s):  
Prashant K Choudhary ◽  
Prashanta K Mahato ◽  
Prasun Jana
Keyword(s):  
Finite Element ◽  
Ultimate Strength ◽  
Cross Section ◽  
Cross Sections ◽  
Ultimate Load ◽  
Material Failure ◽  
Element Analysis ◽  
Composite Column ◽  
Thin Walled ◽  
The Cross

This paper focuses on the optimization of thin-walled open cross-section laminated composite column subjected to uniaxial compressive load. The cross-section of the column is parameterized in such a way that it can represent a variety of shapes including most of the regular cross-sections such as H, C, T, and I sections. The objective is to obtain the best possible shape of the cross-section, by keeping a constant total material volume, which can maximize the ultimate load carrying capacity of the column. The ultimate strength of the column is determined by considering both buckling instability and material failure. For material failure, Tsai-Wu composite failure criterion is considered. As analytical solutions for these parameterized column models are not tractable, the ultimate loads of the composite columns are computed through finite-element analysis in ANSYS. And, the optimization is carried out by coupling these finite-element results with a genetic algorithm based optimization scheme developed in MATLAB. The optimal result obtained through this study is compared with an equivalent base model of cruciform cross-section. Results are reported for various lengths and boundary conditions of the columns. The comparison shows that a substantial increase of the ultimate load, as high as 610%, can be achieved through this optimization study. Thus, the present paper highlights some important characteristics of open cross-sections that can be useful in the design of thin-walled laminated column structures.

On the cross-section distortion of thin-walled beams with multi-cell cross-sections subjected to bending

2005 ◽  
Vol 42 (3-4) ◽  
pp. 901-925 ◽  
Author(s):  
R. Pavazza ◽  
B. Blagojević
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Thin Walled ◽  
The Cross

Material tailoring in functionally graded rods under torsion

2014 ◽  
Vol 228 (18) ◽  
pp. 3283-3295 ◽  
Author(s):  
F Liaghat ◽  
MR Hematiyan ◽  
A Khosravifard
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Torsional Rigidity ◽  
Optimization Methods ◽  
Arbitrary Cross Section ◽  
Functionally Graded ◽  
Material Tailoring ◽  
Graded Material ◽  
The Cross ◽  
Torsional Analysis

Material tailoring in functionally graded isotropic hollow rods of arbitrary cross section under torsion is studied. The purposes of material tailoring pursued in this paper are divided into two categories. In the first category, we find the variation of the volume fractions of constituents of a functionally graded member under torsion to obtain an appropriate distribution of shear stress over the cross section. In the second category, the torsional rigidity of a rod with a pre-defined mass is maximized by appropriate determination of the variation of constituents of the functionally graded material. Hollow rods are studied in this paper since they have higher torsional rigidity compared to solid members with the same mass. Meshless numerical methods are used for torsional analysis of the cross sections. Moreover, numerical optimization methods are used for material tailoring of the rods. Several examples with different cross sections are presented to investigate the usefulness of the proposed technique on achieving the mentioned purposes.

Converting Helicopter Rotor Blades From D-Spar to C-Spar: Allowing for Aeromorphing Structures

2014 ◽  
Author(s):  
Nathan S. Hosking ◽  
Zahra Sotoudeh
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Leading Edge ◽  
Honeycomb Structure ◽  
Rotor Blades ◽  
Cross Sectional ◽  
Helicopter Blades ◽  
Helicopter Rotor Blades ◽  
Thin Walled ◽  
The Cross

Modern helicopter blades are designed as thin-walled hollow structures in form of either C-spar or D-spar cross-sections. With the advent of new materials hollow designs have been implemented to reduce the overall weight of the structure. A D-spar is a rotor blade cross-section that is hollow in nature with a single vertical spar used to carry a large portion of the stresses otherwise carried by the skin [1]. The vertical spar is normally located between the leading edge and half of the chord length. The remaining volume aft of the vertical spar can either be hollow or filled with a honeycomb structure. The honeycomb structure increases the cross-sectional stiffness. Figure 1. shows an example of a common D-spar with a honeycomb structure aft of the vertical spar [2]. Due to new manufacturing methods the D-spar has now become common place in helicopter design [3]. A C-spar cross-section is very similar to the D-spar cross-section in design and construction. The C-spar cross-section does not have the honeycomb structure and the spar. The structural load is offset by more lamina layers towards the leading edge of the cross-section [4,5]. The thin-walled structure is comprised of many layers of composite materials such as fiberglass or carbon fibers. There has been extensive research into D-spar cross-section while there is a lack of studies for C-spar cross-sections [1,3,4].

Experimental Studies Of Multilayer Glass Structures On Compression, Compression With Bending And Simple Bending

2019 ◽  
pp. 22-30
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Applied Load ◽  
Experimental Studies ◽  
Strength Properties ◽  
Research Topic ◽  
Normative Values ◽  
Laminated Glass ◽  
The Cross ◽  
Experimental Values

The work of multilayer glass structures for central and eccentric compression and bending are considered. The substantiation of the chosen research topic is made. The description and features of laminated glass for the structures investigated, their characteristics are presented. The analysis of the results obtained when testing for compression, compression with bending, simple bending of models of columns, beams, samples of laminated glass was made. Overview of the types and nature of destruction of the models are presented, diagrams of material operation are constructed, average values of the resistance of the cross-sections of samples are obtained, the table of destructive loads is generated. The need for development of a set of rules and guidelines for the design of glass structures, including laminated glass, for bearing elements, as well as standards for testing, rules for assessing the strength, stiffness, crack resistance and methods for determining the strength of control samples is emphasized. It is established that the strength properties of glass depend on the type of applied load and vary widely, and significantly lower than the corresponding normative values of the strength of heat-strengthened glass. The effect of the connecting polymeric material and manufacturing technology of laminated glass on the strength of the structure is also shown. The experimental values of the elastic modulus are different in different directions of the cross section and in the direction perpendicular to the glass layers are two times less than along the glass layers.

scholarly journals Total cross sections of eγ → $$ eX\overline{X} $$ processes with X = μ, γ, e via multiloop methods

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Roman N. Lee ◽  
Alexey A. Lyubyakin ◽  
Vyacheslav A. Stotsky
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Elliptic Integral ◽  
High Energy ◽  
Calculation Methods ◽  
Complete Elliptic Integral ◽  
Total Cross Sections ◽  
Multiloop Calculation ◽  
The Cross ◽  
Analytical Expressions

Abstract Using modern multiloop calculation methods, we derive the analytical expressions for the total cross sections of the processes e−γ →$$ {e}^{-}X\overline{X} $$ e − X X ¯ with X = μ, γ or e at arbitrary energies. For the first two processes our results are expressed via classical polylogarithms. The cross section of e−γ → e−e−e+ is represented as a one-fold integral of complete elliptic integral K and logarithms. Using our results, we calculate the threshold and high-energy asymptotics and compare them with available results.

scholarly journals Asymptotic Behavior of Stable Structures Made of Beams

2021 ◽  
Author(s):  
Georges Griso ◽  
Larysa Khilkova ◽  
Julia Orlik ◽  
Olena Sivak
Keyword(s):  
Asymptotic Behavior ◽  
Cross Section ◽  
Cross Sections ◽  
Linear Elasticity ◽  
Circular Cross Section ◽  
Linear Elasticity Theory ◽  
Linear Elastic ◽  
The Cross ◽  
Small Rotation ◽  
Stable Structures

AbstractIn this paper, we study the asymptotic behavior of an $\varepsilon $ ε -periodic 3D stable structure made of beams of circular cross-section of radius $r$ r when the periodicity parameter $\varepsilon $ ε and the ratio ${r/\varepsilon }$ r / ε simultaneously tend to 0. The analysis is performed within the frame of linear elasticity theory and it is based on the known decomposition of the beam displacements into a beam centerline displacement, a small rotation of the cross-sections and a warping (the deformation of the cross-sections). This decomposition allows to obtain Korn type inequalities. We introduce two unfolding operators, one for the homogenization of the set of beam centerlines and another for the dimension reduction of the beams. The limit homogenized problem is still a linear elastic, second order PDE.

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