scholarly journals Deleterious localized stress fields: the effects of boundaries and stiffness tailoring in anisotropic laminated plates

2016 ◽  
Vol 472 (2194) ◽  
pp. 20160391 ◽  
Author(s):  
R. M. J. Groh ◽  
P. M. Weaver
Keyword(s):  
Boundary Layer ◽  
Composite Laminates ◽  
Three Dimensional ◽  
Single Layer ◽  
Variable Stiffness ◽  
Laminated Plates ◽  
Stress Fields ◽  
Relative Significance ◽  
Shear Moduli ◽  
Constant Stiffness

The safe design of primary load-bearing structures requires accurate prediction of stresses, especially in the vicinity of geometric discontinuities where deleterious three-dimensional stress fields can be induced. Even for thin-walled structures significant through-thickness stresses arise at edges and boundaries, and this is especially precarious for laminates of advanced fibre-reinforced composites because through-thickness stresses are the predominant drivers in delamination failure. Here, we use a higher-order equivalent single-layer model derived from the Hellinger–Reissner mixed variational principle to examine boundary layer effects in laminated plates comprising constant-stiffness and variable-stiffness laminae and deforming statically in cylindrical bending. The results show that zigzag deformations, which arise due to layerwise differences in the transverse shear moduli, drive boundary layers towards clamped edges and are therefore critically important in quantifying localized stress gradients. The relative significance of the boundary layer scales with the degree of layerwise anisotropy and the thickness to characteristic length ratio. Finally, we demonstrate that the phenomenon of alternating positive and negative transverse shearing deformation through the thickness of composite laminates, previously only observed at clamped boundaries, can also occur at other locations as a result of smoothly varying the material properties over the in-plane dimensions of the laminate.

Multiterm Extended Kantorovich Method for Three-Dimensional Elasticity Solution of Laminated Plates

2012 ◽  
Vol 79 (6) ◽  
Author(s):  
Santosh Kapuria ◽  
Poonam Kumari
Keyword(s):  
Stress Field ◽  
Composite Laminates ◽  
Three Dimensional ◽  
Laminated Plates ◽  
Elasticity Solution ◽  
Kantorovich Method ◽  
Extended Kantorovich Method ◽  
Single Term ◽  
3D Elasticity ◽  
Laminated Structures

In an article recently published in this journal, the powerful single-term extended Kantorovich method (EKM) originally proposed by Kerr in 1968 for two-dimensional (2D) elasticity problems was further extended by the authors to the three-dimensional (3D) elasticity solution for laminated plates. The single-term solution, however, failed to predict accurately the stress field near the boundaries; thus limiting its applicability. In this work, the method is generalized to the multiterm solution. The solution is developed using the Reissner-type mixed variational principle that ensures the same order of accuracy for displacements and stresses. An n-term solution generates a set of 8n algebraic-ordinary differential equations in the in-plane direction and a similar set in the thickness direction for each lamina, which are solved in close form. The problem of large eigenvalues associated with higher order terms is addressed. In addition to the composite laminates considered in the previous article, results are also presented for sandwich laminates, for which the inaccuracy in the single-term solution is even more prominent. It is shown that considering just one or two additional terms in the solution (n = 2 or 3) leads to a very accurate prediction and drastic improvement over the single-term solution (n = 1) for all entities including the stress field near the boundaries. This work will facilitate development of near-exact solutions of many important unresolved problems involving 3D elasticity, such as the free edge stresses in laminated structures under bending, tension and torsion.

A Layer-Wise Laminate Theory Rationally Deduced From the Three-Dimenstonal Elasticity

1997 ◽  
Vol 64 (3) ◽  
pp. 538-545 ◽  
Author(s):  
P. Bisegna ◽  
E. Sacco
Keyword(s):  
Lagrange Multipliers ◽  
Three Dimensional ◽  
Laminated Plates ◽  
Stress Fields ◽  
Simultaneous Presence ◽  
Numerical Application ◽  
Piecewise Constant ◽  
Laminate Theory ◽  
The Difference ◽  
Three Dimensional Elasticity

A layer-wise theory of laminated plates, which accounts for piecewise constant shear strain in the thickness, is derived from the three-dimensional elasticity theory by imposing suitable constraints on the strain and stress fields. At this aim, the functional of the three-dimensional elasticity is modified according to the Lagrange multipliers theory. In fact, a nonstandard application of the Lagrange theory is presented, because of the simultaneous presence of constraints on dual spaces. The imposed constraints make reactive strain and stress fields arise. Thus, it is necessary to distinguish between elastic and total strain and stress fields. The difference between them is emphasized in a numerical application.

FAILURE PERFORMANCE OF BEND-FREE VARIABLE STIFFNESS COMPOSITE PRESSURE VESSELS

2021 ◽  
Author(s):  
SHAHRZAD DAGHIGHI ◽  
PAUL M. WEAVER
Keyword(s):  
Failure Load ◽  
Three Dimensional ◽  
Variable Stiffness ◽  
Failure Criteria ◽  
Free Variable ◽  
Pressure Vessels ◽  
Design Factor ◽  
Constant Stiffness ◽  
Bending Stresses ◽  
Composite Pressure Vessels

Pressure vessels are designed to store liquids and gases and have various applications spanning from chemical plants to automotive and aerospace industries. Currently, lightweight composite pressure vessels are desirable, especially in transportation industry applications because of their subsequent benefits in fuel consumption, cost and environmental issues. Using composite materials for pressure vessels along with advanced manufacturing technologies such as automated fiber placement provides excellent scope to tailor stiffness through the structural surface using fiber steering to achieve desirable structural performance. Recently, variable angle tow (VAT) technology has been used to suppress bending in super ellipsoids of revolution composite pressure vessels, resulting in minimizing the inefficient bending stresses and deformations and increasing their load-carrying capacity. It is worth noting that such geometries can provide excellent packing efficiency. These advantages make the bend-free super ellipsoids of revolution composite pressure vessels potential candidates for the next generation of pressure vessels. Therefore, their failure performance as the most important design factor should be studied carefully due to safety reasons. In this study, the maximum allowable internal pressure for VAT bend-free ellipsoidal pressure vessels, using the first-ply failure based on both Tsai-Wu and three-dimensional invariant-based failure criteria is determined. Subsequently, VAT bend-free pressure vessels’ failure performance is compared against that obtained for conventional constant stiffness composite vessels. Among structures considered, the VAT bend-free composite vessel has the best failure performance. Moreover, the predicted failure load using the three-dimensional invariant-based failure criterion for the VAT bend-free design is 34% lower than the failure load predicted by the Tsai- Wu. Finally, the effect of various material properties on the difference in predicted failure load using these criteria is assessed. Results provide physical insight useful for designers in materials selection.

Exact solutions for the macro-, meso- and micro-scale analysis of composite laminates and sandwich structures

2018 ◽  
Vol 52 (22) ◽  
pp. 3109-3124 ◽  
Author(s):  
Yang Yan ◽  
Alfonso Pagani ◽  
Erasmo Carrera ◽  
Qingwen Ren
Keyword(s):  
Composite Laminates ◽  
Computational Cost ◽  
Three Dimensional ◽  
Sandwich Beam ◽  
Closed Form Solution ◽  
Single Layer ◽  
Transversely Isotropic ◽  
Global Scale ◽  
Form Solution ◽  
Lagrange Polynomials

The present work proposes a closed-form solution based on refined beam theories for the static analysis of fiber-reinforced composite and sandwich beams under simply supported boundary conditions. The higher-order beam models are developed by employing Carrera Unified Formulation, which uses Lagrange-polynomials expansions to approximate the kinematic field over the cross section. The proposed methodology allows to carry out analysis of composite structure analysis through a single formulation in global-local sense, i.e. homogenized laminates at a global scale and fiber-matrix constituents at a local scale, leading to component-wise analysis. Therefore, three-dimensional stress/displacement fields at different scales can be successfully detected by increasing the order of Lagrange polynomials opportunely. The governing equations are derived in a strong-form and solved in a Navier-type sense. Three benchmark numerical assessments are carried out on a single-layer transversely isotropic beam, a cross-ply laminate [Formula: see text] beam and a sandwich beam. The results show that accurate displacement and stress values can be obtained in different parts of the structure with lower computational cost in comparison with traditional, enhanced as well as three-dimensional finite element methods. Besides, this study may serve as benchmarks for future assessments in this field.

Buckling and vibration analyses of composite laminates with weak interfaces by a coupled meshfree and finite element method

2016 ◽  
Vol 23 (1) ◽  
pp. 93-105
Author(s):  
Jie Chen ◽  
Hai Wang ◽  
Jie Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Composite Laminates ◽  
Interpolation Method ◽  
Three Dimensional ◽  
Hamiltonian Function ◽  
Laminated Plates ◽  
Hamilton System ◽  
Point Interpolation Method ◽  
Element Method

AbstractBuckling and free vibration analyses for composite laminates with weak interfaces were performed based on a three-dimensional hybrid semianalytical model. The model was established by coupling the radial point interpolation method and finite element method (FEM) in a Hamilton system. A direct coupling approach was developed based on the FEM background cell algorithm, and a modified Hamiltonian function for buckling analysis of rectangular laminated plates was given. The governing equations were deduced with the transfer matrix technique and a general linear spring layer model based on the modified Hellinger-Reissner variational principle. Several numerical examples are also presented to validate the efficiency and accuracy of the present method.

scholarly journals Extended Kantorovich method for coupled piezoelasticity solution of piezolaminated plates showing edge effects

2013 ◽  
Vol 469 (2151) ◽  
pp. 20120565 ◽  
Author(s):  
Santosh Kapuria ◽  
Poonam Kumari
Keyword(s):  
Edge Effects ◽  
Electric Potential ◽  
Three Dimensional ◽  
Single Layer ◽  
Free Edge ◽  
Laminated Plates ◽  
Kantorovich Method ◽  
Extended Kantorovich Method ◽  
Hybrid Laminates ◽  
Laminated Panels

The powerful extended Kantorovich method (EKM) originally proposed by Kerr in 1968 is generalized to obtain a three-dimensional coupled piezoelasticity solution of smart piezoelectric laminated plates in cylindrical bending. Such solutions are needed to accurately predict the edge effects in these laminates under electromechanical loading. The Reissner-type mixed variational principle extended to piezoelasticity is used to develop the governing equations in terms of displacements, electric potential as well as stresses and electric displacements. It allows for exact satisfaction of the boundary conditions, including the non-homogeneous ones at all points. An n -term solution generates a set of 11 n algebraic ordinary differential equations in the inplane direction and a similar set in the thickness direction for each lamina, which are solved in closed form. The multi-term EKM is shown to predict the coupled electromechanical response, including the edge effects, of single-layer piezoelectric sensors as well as hybrid laminated panels accurately, for both pressure and electric potential loadings. This work will facilitate development of accurate semi-analytical solutions of many other unresolved problems in three-dimensional piezoelasticity, such as the free-edge stresses in hybrid laminates under bending, tension and twisting.

Generalized Free-Edge Stress Analysis Using Mechanics of Structure Genome

2016 ◽  
Vol 83 (10) ◽  
Author(s):  
Bo Peng ◽  
Johnathan Goodsell ◽  
R. Byron Pipes ◽  
Wenbin Yu
Keyword(s):  
Stress Analysis ◽  
Composite Laminates ◽  
Three Dimensional ◽  
Free Edge ◽  
Stress Fields ◽  
Element Analysis ◽  
Cross Sectional ◽  
Edge Stress ◽  
Out Of Plane ◽  
Sectional Analysis

This work reveals the potential of mechanics of structure genome (MSG) for the free-edge stress analysis of composite laminates. First, the cross-sectional analysis specialized from MSG is formulated for solving a generalized free-edge problem of composite laminates. Then, MSG and the companion code SwiftComp™ are applied to the free-edge stress analysis of several composite laminates with arbitrary layups and general loads including extension, torsion, in-plane and out-of-plane bending, and their combinations. The results of MSG are compared with various existing solutions for symmetric angle-ply laminates. New results are presented for the free-edge stress fields in general laminates for combined mechanical loads and compared with three-dimensional (3D) finite element analysis (FEA) results, which agree very well.

scholarly journals Measurement report: Vehicle-based multi-lidar observational study of the effect of meteorological elements on the three-dimensional distribution of particles in the western Guangdong–Hong Kong–Macao Greater Bay Area

2022 ◽  
Vol 22 (1) ◽  
pp. 139-153
Author(s):  
Xinqi Xu ◽  
Jielan Xie ◽  
Yuman Li ◽  
Shengjie Miao ◽  
Shaojia Fan
Keyword(s):  
Boundary Layer ◽  
Hong Kong ◽  
Particulate Matter ◽  
Vertical Distribution ◽  
Three Dimensional ◽  
Single Layer ◽  
Bay Area ◽  
Dimensional Distribution ◽  
Meteorological Elements ◽  
Horizontal And Vertical Distribution

Abstract. The distribution of meteorological elements has always been an important factor in determining the horizontal and vertical distribution of particles in the atmosphere. To study the effect of meteorological elements on the three-dimensional distribution structure of particles, mobile vehicle lidar and fixed-location observations were collected in the western Guangdong–Hong Kong–Macao Greater Bay Area of China during September and October in 2019 and 2020. Vertical aerosol extinction coefficient, depolarization ratio, and wind and temperature profiles were measured using a micro pulse lidar, a Raman scattering lidar, and a Doppler wind profile lidar installed on a mobile monitoring vehicle. The mechanism of how wind and temperature in the boundary layer affects the horizontal and vertical distribution of particles was analysed. The results show that particles were mostly distributed in downstream areas on days with moderate wind speed in the boundary layer, whereas they were distributed homogeneously on days with weaker wind. There are three typical types of vertical distribution of particles in the western Guangdong–Hong Kong–Macao Greater Bay Area (GBA): surface single layer, elevated single layer, and double layer. Analysis of wind profiles and Hybrid Single-Particle Lagrangian Integrated Trajectory Model (HYSPLIT) backward trajectory reveals different sources of particles for the three types. Particles concentrating near the temperature inversion and multiple inversions could cause more than one peak in the extinction coefficient profile. There were two mechanisms affecting the distribution of particulate matter in the upper and lower boundary layers. Based on this observational study, a general model of meteorological elements affecting the vertical distribution of urban particulate matter is proposed.

scholarly journals Measurement report: Vehicle-based and In Situ Multi-lidar Observational Study on the Effect of Meteorological Elements on the Three-dimensional Distribution of Particles in the Western Guangdong–Hong Kong–Macao Greater Bay Area

2021 ◽  
Author(s):  
Xinqi Xu ◽  
Jielan Xie ◽  
Yuman Li ◽  
Shengjie Miao ◽  
Shaojia Fan
Keyword(s):  
Boundary Layer ◽  
Hong Kong ◽  
Vertical Distribution ◽  
Three Dimensional ◽  
Single Layer ◽  
Bay Area ◽  
Dimensional Distribution ◽  
Meteorological Elements ◽  
Horizontal And Vertical Distribution

Abstract. The distribution of meteorological elements has always been an important factor in determining the horizontal and vertical distribution of particles in the atmosphere. To study the effect of meteorological elements on the three-dimensional distribution structure of particles, mobile vehicle lidar observations, and in situ observations were presented in the western Guangdong–Hong Kong–Macao Greater Bay Area of China during September and October of 2019 and 2020. Vertical aerosol extinction coefficient, depolarization ratio, wind and temperature profiles were measured by using a micro pulse lidar, a Raman scattering lidar, and a Doppler wind profile lidar installed on a mobile monitoring vehicle. The mechanism of how wind and temperature in the boundary layer affects the horizontal and vertical distribution of particles was analyzed. The result showed that particles were mostly distributed in downstream areas on days with moderate wind speed in the boundary layer, while they presented homogeneously on days with weaker wind. There are three typical types of vertical distribution of particles in the western Guangdong–Hong Kong–Macao Greater Bay Area (GBA): surface single layer, elevated single layer, and double layer. Analysis of wind profiles and Hybrid Single-Particle Lagrangian Integrated Trajectory Model (HYSPLIT) backward trajectory revealed different sources of particles for the three types. Particles concentrated near the temperature inversion and multiple inversions could cause more than one peak in the extinction coefficient profile. There are two mechanisms that affected the distribution of particulate matter in the upper and lower boundary layers. Based on observational study, a general model of meteorological elements affecting the vertical distribution of urban particulate matter was made.

Characterization of a monolayer graphitic structure

1994 ◽  
Vol 52 ◽  
pp. 760-761
Author(s):  
X. Lin ◽  
X. K. Wang ◽  
V. P. Dravid ◽  
J. B. Ketterson ◽  
R. P. H. Chang
Keyword(s):  
Three Dimensional ◽  
Single Layer ◽  
Synthesis Process ◽  
Graphitic Structure ◽  
Positive Gaussian Curvature ◽  
Graphitic Sheet ◽  
Structural And Electronic Properties ◽  
New Material ◽  
Hexagonal Network

For small curvatures of a graphitic sheet, carbon atoms can maintain their preferred sp2 bonding while allowing the sheet to have various three-dimensional geometries, which may have exotic structural and electronic properties. In addition the fivefold rings will lead to a positive Gaussian curvature in the hexagonal network, and the sevenfold rings cause a negative one. By combining these sevenfold and fivefold rings with sixfold rings, it is possible to construct complicated carbon sp2 networks. Because it is much easier to introduce pentagons and heptagons into the single-layer hexagonal network than into the multilayer network, the complicated morphologies would be more common in the single-layer graphite structures. In this contribution, we report the observation and characterization of a new material of monolayer graphitic structure by electron diffraction, HREM, EELS.The synthesis process used in this study is reported early. We utilized a composite anode of graphite and copper for arc evaporation in helium.

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