Effect of Assumed Tow Architecture on Predicted Moduli and Stresses in Plain Weave Composites

1995 ◽  
Vol 29 (16) ◽  
pp. 2134-2159 ◽  
Author(s):  
Clinton Chapman ◽  
John Whitcomb
Keyword(s):  
Finite Elements ◽  
Cross Section ◽  
Transverse Shear ◽  
Material Properties ◽  
Three Dimensional ◽  
Textile Composites ◽  
Unit Cell ◽  
Accurate Prediction ◽  
Constant Cross Section ◽  
Plain Weave

This paper examines the effect of assumed tow architecture on the predicted moduli and stresses in plain weave textile composites. In particular, the effect of how a constant cross-section is assumed to sweep-out the volume of a tow is explored. Two architectures are examined which have a sinusoidal tow path and a lenticular cross-section. Three-dimensional finite elements are employed to model a T300/Epoxy plain weave composite with symmetrically stacked mats. Macroscopically homogeneous in-plane extension and shear and transverse shear loadings were considered. Symmetries are exploited which permitted modeling of only 1/32nd of the unit cell. Accounting for the variation of material properties throughout each element is determined to be necessary for accurate prediction of stresses in the composite. For low waviness, the two tow architectures examined are very similar. At high waviness, the stress predictions are much more sensitive to the assumed tow geometry.

scholarly journals Hierarchical Beam Finite Elements Based Upon a Variables Separation Method

2016 ◽  
Vol 08 (02) ◽  
pp. 1650026 ◽  
Author(s):  
Gaetano Giunta ◽  
Salim Belouettar ◽  
Olivier Polit ◽  
Laurent Gallimard ◽  
Philippe Vidal ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Cross Section ◽  
Three Dimensional ◽  
Finite Element Solution ◽  
Stress Fields ◽  
Element Solution ◽  
One Dimensional ◽  
Kinematic Approximation ◽  
The Cross

A family of hierarchical one-dimensional beam finite elements developed within a variables separation framework is presented. A Proper Generalized Decomposition (PGD) is used to divide the global three-dimensional problem into two coupled ones: one defined on the cross-section space (beam modeling kinematic approximation) and one belonging to the axis space (finite element solution). The displacements over the cross-section are approximated via a Unified Formulation (UF). A Lagrangian approximation is used along the beam axis. The resulting problems size is smaller than that of the classical equivalent finite element solution. The approach is, then, particularly attractive for higher-order beam models and refined axial meshes. The numerical investigations show that the proposed method yields accurate yet computationally affordable three-dimensional displacement and stress fields solutions.

Formulation of a unit cell of a reduced size for plain weave textile composites

2011 ◽  
Vol 50 (5) ◽  
pp. 1770-1780 ◽  
Author(s):  
S. Li ◽  
C. Zhou ◽  
H. Yu ◽  
L. Li
Keyword(s):  
Textile Composites ◽  
Unit Cell ◽  
Plain Weave

Mechanics and Finite Elements of Shells

1989 ◽  
Vol 42 (5) ◽  
pp. 129-142 ◽  
Author(s):  
Gerald Wempner
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
General Theory ◽  
Transverse Shear ◽  
Three Dimensional ◽  
Discrete Models ◽  
Thick Shell ◽  
Dimensional Approximation ◽  
Transverse Strains

This article begins with a brief review of the foundations: The classical theory of Love is described with attention to the underlying hypothesis and consequent limitations. A more general theory is described which removes the constraints of Love; the inclusion of transverse strains admits simpler finite elements, accommodates the thick shell via layers and even a transition to the three-dimensional approximation. The concept of the finite element is reviewed in the context of the discrete approximation of shells. Specific attention is given to those problems which are peculiar to shells: The predominant roles of flexural and extensional deformations, the lesser role of transverse shear, can lead to excessive stiffness (“locking”). Origins and procedures are described to circumvent these problems. The review is intended to bridge some chasms between the mechanics of the continua and the discrete models of finite elements. As such, the emphasis is upon those mechanical attributes of shells and elements which play key roles in forming practical models. Since the limitations of space, time and the author’s knowledge, preclude a full expose, the review includes only commentaries on some topics, such as inelasticity, nonlinearity and instability. Citations include original sources and some recent works which provide entree to contemporary developments.

Topology Synthesis of Extrusion-Based Nonlinear Transient Designs

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Neal M. Patel ◽  
Charles L. Penninger ◽  
John E. Renaud
Keyword(s):  
Cross Section ◽  
Three Dimensional ◽  
Optimization Methods ◽  
Constant Cross Section ◽  
Cross Sectional ◽  
Design Concepts ◽  
Nonlinear Transient ◽  
Cross Sectional Profile ◽  
Sectional Profile ◽  
Finishing Processes

Many practical structural designs require that the structure is easily manufactured. Design concepts synthesized using conventional topology optimization methods are typically not easily manufactured, in that multiple finishing processes are required to construct the component. A manufacturing technique that requires only minimal effort is extrusion. Extrusion is a manufacturing process used to create objects of a fixed cross-sectional profile. The result of using this process is lower costs for the manufacture of the final product. In this paper, a hybrid cellular automaton algorithm is developed to synthesize constant cross section structures that are subjected to nonlinear transient loading. The novelty of the proposed method is the ability to generate constant cross section topologies for plastic-dynamic problems since the issue of complex gradients can be avoided. This methodology is applied to extrusions with a curved sweep along the direction of extrusion as well. Three-dimensional examples are presented to demonstrate the efficiency of the proposed methodology in synthesizing these structures. Both static and dynamic loading cases are studied.

Statistics of low-density microcellular materials

1994 ◽  
Vol 9 (2) ◽  
pp. 515-522 ◽  
Author(s):  
David A. Noever
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Material Properties ◽  
Three Dimensional ◽  
Low Density ◽  
Topological Relations ◽  
Packing Effects

The statistics of random cellular patterns are analyzed in cross sections of low-density microcellular materials. Agreement is found with a variety of topological relations previously found for other networks, namely Lewis's law and Aboav's law. To investigate three-dimensional packing effects, experiments are performed on compressed polystyrene shot material, the resulting networks of which are subsequently analyzed in cross section. Implications for material properties and stability are discussed.

Nonconformal mesh-based finite element strategy for 3D textile composites

2016 ◽  
Vol 51 (16) ◽  
pp. 2315-2330 ◽  
Author(s):  
B Wucher ◽  
S Hallström ◽  
D Dumas ◽  
T Pardoen ◽  
C Bailly ◽  
...  
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Material Properties ◽  
Three Dimensional ◽  
Textile Composites ◽  
Thermoelastic Properties ◽  
Material Interfaces ◽  
Local Correction ◽  
Finite Element Procedure ◽  
Woven Reinforcement

A finite element procedure is developed for the computation of the thermoelastic properties of textile composites with complex and compact two- and three-dimensional woven reinforcement architectures. The purpose of the method is to provide estimates of the properties of the composite with minimum geometrical modeling effort. The software TexGen is used to model simplified representations of complex textiles. This results in severe yarn penetrations, which prevent conventional meshing. A non-conformal meshing strategy is adopted, where the mesh is refined at material interfaces. Penetrations are mitigated by using an original local correction of the material properties of the yarns to account for the true fiber content. The method is compared to more sophisticated textile modeling approaches and successfully assessed towards experimental data selected from the literature.

Studies on chitan (β-(1 → 4)-linked 2-acetamido-2-deoxy-D-glucan) fibers of the diatom Thalassiosira fluviatilis, Hustedt. III. The structure of chitan from x-ray diffraction and electron microscope observations

1968 ◽  
Vol 46 (9) ◽  
pp. 1513-1521 ◽  
Author(s):  
N. E. Dweltz ◽  
J. Ross Colvin ◽  
A. G. McInnes
Keyword(s):  
Electron Microscope ◽  
Cross Section ◽  
Three Dimensional ◽  
Unit Cell ◽  
Dimensional Structure ◽  
Polymeric Chain ◽  
X Ray Diffraction ◽  
Screw Axis ◽  
X Ray ◽  
Good Agreement

The form and crystal structure of the fibers attached to the diatom Thalassiosira fluviatilis were studied by the electron microscope and x-ray diffraction.These fibers, which were shown previously to be pure, highly crystalline β-(1 → 4) linked poly-N-acetyl-D-glucosamine (chitan), are strap-like in cross section, 1000–2000 Å in width at their widest point close to the base, from which they taper uniformly to a very small tip at their outer extremity. Three connected filaments or microfibrils form the fiber at its widest point.The unit cell of chitan is monoclinic with the space group P21. The parameters of the unit cell are a = 4.80, b = 10.32, c = 9.83 Å, and β = 112°. The density of the chitan fibers is 1.495 g/cm3. There is only one polymeric chain per unit cell with a two-fold screw axis and therefore the chains are parallel to each other. A three-dimensional structure is proposed for chitan which is reasonable from stereochemical considerations and which is in good agreement with all observed x-ray diffraction data.

Analysis of Three-Dimensional Piezo-Electric Beams via a Unified Formulation

2013 ◽  
Vol 745 ◽  
pp. 101-118 ◽  
Author(s):  
Gaetano Giunta ◽  
Yao Koutsawa ◽  
Salim Belouettar
Keyword(s):  
Finite Elements ◽  
Cross Section ◽  
Electrical Potential ◽  
Three Dimensional ◽  
Higher Order ◽  
Computational Costs ◽  
Generic Term ◽  
Mass Matrices ◽  
Out Of Plane ◽  
Piezo Electric

A Unified Formulation for deriving several higher-order theories and related finite elements for beams is presented within this paper.Three-dimensional structures with piezo-electric layers are considered.Static and free vibration analyses are carried out.Models' main unknowns are the displacements and the electric potential.They are approximated above the beam cross-section via Lagrange's polynomials in a layer-wise sense.Finite elements stiffness and mass matrices are derived in a nucleal form using d'Alembert's Principle.This nucleal form is representative of the generic term in the approximating expansion of the displacements and electric potential over the cross-section.It is, therefore, invariant versus the theory expansion order and the element nodes' number.In such a manner, higher-order displacements-based theories that account for non-classical effectssuch as transverse shear deformations and cross-section in- and out-of-plane warping are straightforwardly formulated.Results are given in terms of displacements, electrical potential and stresses.Comparison with three-dimensional finite elements models are provided, showing thataccurate results can be obtained with reduced computational costs.

Microstructure Analysis of in-Plane Quasi-Isotropic Composites Reinforced by Multi-Direction and Multi-Layer Three Dimensional Fabric

2011 ◽  
Vol 415-417 ◽  
pp. 210-213
Author(s):  
Lan Ying Liu ◽  
Ya Nan Jiao
Keyword(s):  
Cross Section ◽  
Volume Content ◽  
Three Dimensional ◽  
Unit Cell ◽  
Experimental Results ◽  
The Other ◽  
Cell Models ◽  
Mathematical Relationship ◽  
Fiber Volume ◽  
Relationship Of

In this paper, a new multi-direction three-dimensional fabric, called in-plane quasi-isotropic fabric, including warps 0, wefts 90o, a set of bias yarns ±45o, and a vertical yarns Z fastening the other yarns together is designed. Unit cell models are established on the basis of the rule of yarn movement and on the basis of optimizing the yarn cross section on the method of braiding-solidify-cutting-polishing-viewing. Mathematical relationship of the parameters with geometry parameters is founded and the fiber volume content is calculated, the valid relationship is proved by experimental results.

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