Effects of Shear Deformation of Struts in Hexagonal Lattices on their Effective In-Plane Material Properties

2021 ◽  
Vol 1034 ◽  
pp. 193-198
Author(s):  
Pana Suttakul ◽  
Thongchai Fongsamootr ◽  
Duy Vo ◽  
Pruettha Nanakorn
Keyword(s):  
Shear Deformation ◽  
Material Properties ◽  
Strain Energy ◽  
Equivalent Strain ◽  
Homogenization Method ◽  
Two Dimensional ◽  
Engineering Applications ◽  
Large Numbers ◽  
Effective Material Properties ◽  
Unit Cells

Two-dimensional lattices are widely used in many engineering applications. If 2D lattices have large numbers of unit cells, they can be accurately modeled as 2D homogeneous solids having effective material properties. When the slenderness ratios of struts in these 2D lattices are low, the effects of shear deformation on the values of the effective material properties can be significant. This study aims to investigate the effects of shear deformation on the effective material properties of 2D lattices with hexagonal unit cells, by using the homogenization method based on equivalent strain energy. Several topologies of hexagonal unit cells and several slenderness ratios of struts are considered. The effects of struts’ shear deformation on the effective material properties are examined by comparing the results of the present study, in which shear deformation is neglected, with those from the literature, in which shear deformation is included.

scholarly journals Strong and Weak Formulations of a Mixed Higher-Order Shear Deformation Theory for the Static Analysis of Functionally Graded Beams under Thermo-Mechanical Loads

2020 ◽  
Vol 4 (4) ◽  
pp. 158 ◽  
Author(s):  
Chih-Ping Wu ◽  
Zhan-Rong Xu
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Static Analysis ◽  
Material Properties ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Mechanical Loads ◽  
Effective Material Properties ◽  
Fg Beam

The strong and weak formulations of a mixed layer-wise (LW) higher-order shear deformation theory (HSDT) are developed for the static analysis of functionally graded (FG) beams under various boundary conditions subjected to thermo-mechanical loads. The material properties of the FG beam are assumed to obey a power-law distribution of the volume fractions of the constituents through the thickness of the FG beam, for which the effective material properties are estimated using the rule of mixtures, or it is directly assumed that the effective material properties of the FG beam obey an exponential function distribution along the thickness direction of the FG beam. The results shown in the numerical examples indicate that the mixed LW HSDT solutions for elastic and thermal field variables are in excellent agreement with the accurate solutions available in the literature. A parametric study related to various effects on the coupled thermo-mechanical behavior of FG beams is carried out, including the aspect ratio, the material-property gradient index, and different boundary conditions.

Effective Material Properties of Damaged Elastic Solids

2006 ◽  
Vol 324-325 ◽  
pp. 1185-1188
Author(s):  
Usik Lee ◽  
Deokki Youn
Keyword(s):  
Elastic Properties ◽  
Material Properties ◽  
Equivalence Principle ◽  
Strain Energy ◽  
Damage Variable ◽  
Local Damage ◽  
Elastic Solids ◽  
Energy Equivalence ◽  
Effective Material Properties ◽  
Isotropic Solids

By using a continuum modeling approach based on the equivalent elliptical crack representation of a local damage and the strain energy equivalence principle, the effective elastic compliances and the effective engineering constants are derived in closed forms in terms of the virgin (undamaged) elastic properties and a scalar damage variable for damaged two- and threedimensional isotropic solids. It is shown that the effective Young’s modulus in the direction normal to the crack surfaces is always smaller than its intact value.

Design of Frame-Like Periodic Solids for Isotropic Symmetry by Member Sizing

2016 ◽  
Vol 33 (1) ◽  
pp. 41-54 ◽  
Author(s):  
K. Theerakittayakorn ◽  
P. Suttakul ◽  
P. Sam ◽  
P. Nanakorn
Keyword(s):  
Closed Form ◽  
Elastic Constants ◽  
Strain Energy ◽  
Equivalent Strain ◽  
Homogenization Method ◽  
Unit Cell ◽  
Cubic Symmetry ◽  
Effective Elastic Constants ◽  
Common Unit ◽  
2D And 3D

AbstractIn this study, a methodology to design frame-like periodic solids for isotropic symmetry by appropriate sizing of unit-cell struts is presented. The methodology utilizes the closed-form effective elastic constants of 2D frame-like periodic solids with square symmetry and 3D frame-like periodic solids with cubic symmetry, derived using the homogenization method based on equivalent strain energy. By using the closed-form effective elastic constants, an equation to enforce isotropic symmetry can be analytically constructed. Thereafter, the equation can be used to determine relative unit-cell strut sizes that are required for isotropic symmetry. The methodology is tested with 2D and 3D frame-like periodic solids with some common unit-cell topologies. Satisfactory results are observed.

Free Vibration Analysis of Nanocomposite Plates Reinforced by Graded Carbon Nanotubes Based on First-Order Shear Deformation Plate Theory

2013 ◽  
Vol 5 (1) ◽  
pp. 90-112 ◽  
Author(s):  
S. Jafari Mehrabadi ◽  
B. Sobhaniaragh ◽  
V. Pourdonya
Keyword(s):  
Carbon Nanotubes ◽  
Free Vibration ◽  
Shear Deformation ◽  
Material Properties ◽  
Volume Fraction ◽  
Plate Theory ◽  
Functionally Graded ◽  
First Order ◽  
Shear Deformation Plate Theory ◽  
Effective Material Properties

AbstractBased on the Mindlin’s first-order shear deformation plate theory this paper focuses on the free vibration behavior of functionally graded nanocomposite plates reinforced by aligned and straight single-walled carbon nanotubes (SWCNTs). The material properties of simply supported functionally graded carbon nanotube-reinforced (FGCNTR) plates are assumed to be graded in the thickness direction. The effective material properties at a point are estimated by either the Eshelby-Mori-Tanaka approach or the extended rule of mixture. Two types of symmetric carbon nanotubes (CNTs) volume fraction profiles are presented in this paper. The equations of motion and related boundary conditions are derived using the Hamilton’s principle. A semi-analytical solution composed of generalized differential quadrature (GDQ) method, as an efficient and accurate numerical method, and series solution is adopted to solve the equations of motions. The primary contribution of the present work is to provide a comparative study of the natural frequencies obtained by extended rule of mixture and Eshelby-Mori-Tanaka method. The detailed parametric studies are carried out to study the influences various types of the CNTs volume fraction profiles, geometrical parameters and CNTs volume fraction on the free vibration characteristics of FGCNTR plates. The results reveal that the prediction methods of effective material properties have an insignificant influence of the variation of the frequency parameters with the plate aspect ratio and the CNTs volume fraction.

Assessment of Computational Models for Multilayered Composite Shells

1990 ◽  
Vol 43 (4) ◽  
pp. 67-97 ◽  
Author(s):  
Ahmed K. Noor ◽  
W. Scott Burton
Keyword(s):  
Shear Deformation ◽  
Strain Energy ◽  
Computational Models ◽  
Three Dimensional ◽  
Linear Displacement ◽  
Two Dimensional ◽  
Composite Shells ◽  
Response Characteristics ◽  
Multilayered Composite ◽  
Shear Deformation Theories

A review is made of the different approaches used for modeling multilayered composite shells. Discussion focuses on different approaches for developing two-dimensional shear deformation theories; classification of two-dimensional theories based on introducing plausible displacement, strain and/or stress assumptions in the thickness direction; first-order shear deformation theories based on linear displacement assumptions in the thickness coordinate; and efficient computational strategies for anisotropic composite shells. Extensive numerical results are presented showing the effects of variation in the lamination and geometric parameters of simply supported composite cylinders on the accuracy of the static and vibrational responses predicted by eight different modeling approaches (based on two-dimensional shear deformation theories). The standard of comparison is taken to be the exact three-dimensional elasticity solutions. The quantities compared include both the gross response characteristics (eg, vibration frequencies and strain energy components); and detailed, through-the-thickness distributions of displacements, stresses, and strain energy densities. Some of the future directions for research on the modeling of multilayered composite shells are outlined.

Correlation averaging of two-dimensional crystals: basic strategy and refinements

1986 ◽  
Vol 44 ◽  
pp. 136-139
Author(s):  
W. Baumeister ◽  
R. Rachel ◽  
R. Guckenberger ◽  
R. Hegerl
Keyword(s):  
Low Dose ◽  
Signal To Noise Ratio ◽  
Real Space ◽  
Fourier Domain ◽  
Two Dimensional ◽  
Signal To Noise ◽  
Unit Cells ◽  
Lateral Displacements ◽  
Established Technique ◽  
Crystalline Array

IntroductionCorrelation averaging (CAV) is meanwhile an established technique in image processing of two-dimensional crystals /1,2/. The basic idea is to detect the real positions of unit cells in a crystalline array by means of correlation functions and to average them by real space superposition of the aligned motifs. The signal-to-noise ratio improves in proportion to the number of motifs included in the average. Unlike filtering in the Fourier domain, CAV corrects for lateral displacements of the unit cells; thus it avoids the loss of resolution entailed by these distortions in the conventional approach. Here we report on some variants of the method, aimed at retrieving a maximum of information from images with very low signal-to-noise ratios (low dose microscopy of unstained or lightly stained specimens) while keeping the procedure economical.

scholarly journals Broadband metamaterials and metasurfaces: a review from the perspectives of materials and devices

Nanophotonics ◽  
2020 ◽  
Vol 9 (10) ◽  
pp. 3165-3196 ◽  
Author(s):  
Joonkyo Jung ◽  
Hyeonjin Park ◽  
Junhyung Park ◽  
Taeyong Chang ◽  
Jonghwa Shin
Keyword(s):  
Material Properties ◽  
Frequency Bandwidth ◽  
Broad Bandwidth ◽  
Practical Applications ◽  
Effective Material Properties

AbstractMetamaterials can possess extraordinary properties not readily available in nature. While most of the early metamaterials had narrow frequency bandwidth of operation, many recent works have focused on how to implement exotic properties and functions over broad bandwidth for practical applications. Here, we provide two definitions of broadband operation in terms of effective material properties and device functionality, suitable for describing materials and devices, respectively, and overview existing broadband metamaterial designs in such two categories. Broadband metamaterials with nearly constant effective material properties are discussed in the materials part, and broadband absorbers, lens, and hologram devices based on metamaterials and metasurfaces are discussed in the devices part.

scholarly journals A methodology for hygrothermal modelling of imperfect masonry interfaces

2021 ◽  
pp. 174425912198938
Author(s):  
Michael Gutland ◽  
Scott Bucking ◽  
Mario Santana Quintero
Keyword(s):  
Boundary Conditions ◽  
Material Properties ◽  
Structural Integrity ◽  
Bulk Material ◽  
Weather Conditions ◽  
Masonry Wall ◽  
Two Dimensional ◽  
Liquid Transport ◽  
Imperfect Contact ◽  
Moisture Contents

Hygrothermal models are important tools for assessing the risk of moisture-related decay mechanisms which can compromise structural integrity, loss of architectural features and material. There are several sources of uncertainty when modelling masonry, related to material properties, boundary conditions, quality of construction and two-dimensional interactions between mortar and unit. This paper examines the uncertainty at the mortar-unit interface with imperfections such as hairline cracks or imperfect contact conditions. These imperfections will alter the rate of liquid transport into and out of the wall and impede the liquid transport between mortar and masonry unit. This means that the effective liquid transport of the wall system will be different then if only properties of the bulk material were modelled. A detailed methodology for modelling this interface as a fracture is presented including definition of material properties for the fracture. The modelling methodology considers the combined effect of both the interface resistance across the mortar-unit interface and increase liquid transport in parallel to the interface, and is generalisable to various combinations of materials, geometries and fracture apertures. Two-dimensional DELPHIN models of a clay brick/cement-mortar masonry wall were created to simulate this interaction. The models were exposed to different boundary conditions to simulate wetting, drying and natural cyclic weather conditions. The results of these simulations were compared to a baseline model where the fracture model was not included. The presence of fractures increased the rate of absorption in the wetting phase and an increased rate of desorption in the drying phase. Under cyclic conditions, the result was higher peak moisture contents after rain events compared to baseline and lower moisture contents after long periods of drying. This demonstrated that detailed modelling of imperfections at the mortar-unit interface can have a definitive influence on results and conclusions from hygrothermal simulations.

scholarly journals Buckling of regular, chiral and hierarchical honeycombs under a general macroscopic stress state

2014 ◽  
Vol 470 (2167) ◽  
pp. 20130856 ◽  
Author(s):  
Babak Haghpanah ◽  
Jim Papadopoulos ◽  
Davood Mousanezhad ◽  
Hamid Nayeb-Hashemi ◽  
Ashkan Vaziri
Keyword(s):  
Finite Element ◽  
Stress State ◽  
Closed Form ◽  
Plane Stress ◽  
Plane Stress State ◽  
Cellular Structures ◽  
Two Dimensional ◽  
Buckling Strength ◽  
Macroscopic Stress ◽  
Unit Cells

An approach to obtain analytical closed-form expressions for the macroscopic ‘buckling strength’ of various two-dimensional cellular structures is presented. The method is based on classical beam-column end-moment behaviour expressed in a matrix form. It is applied to sample honeycombs with square, triangular and hexagonal unit cells to determine their buckling strength under a general macroscopic in-plane stress state. The results were verified using finite-element Eigenvalue analysis.

Sign in / Sign up

Export Citation Format

Share Document