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.

Assessment of Shear Deformation Theories for Multilayered Composite Plates

1989 ◽  
Vol 42 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Ahmed K. Noor ◽  
W. Scott Burton
Keyword(s):  
Shear Deformation ◽  
Three Dimensional ◽  
Composite Plates ◽  
Linear Displacement ◽  
Two Dimensional ◽  
Multilayered Composite ◽  
Standard Of Comparison ◽  
Elasticity Solutions ◽  
Shear Deformation Theories ◽  
Three Dimensional Elasticity

A review is made of the different approaches used for modeling multilayered composite plates. 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; and first-order shear deformation theories based on linear displacement assumptions in the thickness coordinate. Extensive numerical results are presented showing the effects of variation in the lamination and geometric parameters of simply supported composite plates on the accuracy of the static and vibrational responses predicted by six different modeling approaches (based on two-dimensional shear deformation theories). The standard of comparison is taken to be the exact three-dimensional elasticity solutions. Some of the future directions for research on the modeling of multilayered composite plates are outlined.

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 Experience of employment of computational models for water quality modelling

2019 ◽  
Vol 97 ◽  
pp. 05030 ◽  
Author(s):  
Anatoly Krutov ◽  
Dilshod Bazarov ◽  
Begzod Norkulov ◽  
Bakhtiyar Obidov ◽  
Bobur Nazarov
Keyword(s):  
Computational Models ◽  
Numerical Models ◽  
Qualitative Difference ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Aral Sea ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Two Dimensional Model ◽  
Wind Currents

The purpose of the article is to develop the required and sufficient conditions under which numerical methods can be used for engineering calculations and for scientific research of hydrodynamic processes in solving practical problems related to predicting the spread of pollutants in water bodies and streams. The conducted studies consisted in comparing the results of laboratory experiments and mathematical modelling, in particular the distribution of heat in a stream with different temperature in water layers was studied. To check the adequacy of the proposed numerical models, calculations were performed and comparisons were made with the results of experimental data. The obtained results allowed to determine the boundaries of the qualitative difference in the flow behaviour for different numbers of Froude and Reynolds. The accuracy of the method was also studied. A number of additional requirements for numerical models were proposed in addition to approcsimation and stability, such as requirements of conservativeness (divergence), existence of trivial solutions on grids, possibility to calculate highly unsteady, quasi-stable, pulsating and stationary flows, requirement of invariance of linearized equations, as well as the requirement of a one-dimensional scheme to be a consequence of a two-dimensional scheme. Distribution of velocities of wind currents using a three-dimensional and two-dimensional model was studied for a real object. A shallow-water bay of the Aral Sea was chosen as the object for the research. Comparison of the calculation results for both models showed that the flow velocity fields, as well as the distribution of pollutants in shallow waters, can be performed using a two-dimensional model.

Growth and Decay of Germanium Islands on Silicon Studied by High Temperature Stm

1999 ◽  
Vol 583 ◽  
Author(s):  
M. Kästner ◽  
B. Voigtländer
Keyword(s):  
High Temperature ◽  
Molecular Beam Epitaxy ◽  
Epitaxial Growth ◽  
Scanning Tunneling Microscope ◽  
Strain Energy ◽  
Molecular Beam ◽  
Three Dimensional ◽  
Scanning Tunneling ◽  
Two Dimensional ◽  
Tunneling Microscope

AbstractWe use a scanning tunneling microscope (STM) capable of imaging the growing layer at high temperature during molecular beam epitaxy (MBE) to study the epitaxial growth of Germanium on Silicon and the decay of Ge islands. The periodicity of the (2×N) reconstruction of two-dimensional Ge layers on Si(001) is measured as function of the Ge coverage. Strain energy drives the formation of the (2×N) reconstruction and Si/Ge intermixing. A comparison to total energy calculations predicting the periodicity of the (2×N) reconstruction is used to estimate the amount of Si-Ge intermixing near the surface. The evolution of the size and shape of individual “hut clusters” is measured and explained by kinetically self-limiting growth. The relaxation of kinetically a determined morphology towards equilibrium is followed for a Ge layer on Si(111). Strained two-dimensional as well as partially relaxed three-dimensional islands dissolve and are soaked up by larger three-dimensional islands which are dislocated and therefore fully relaxed.

Reflections on the Theory of Elastic Plates

1985 ◽  
Vol 38 (11) ◽  
pp. 1453-1464 ◽  
Author(s):  
Eric Reissner
Keyword(s):  
Shear Deformation ◽  
Fourth Order ◽  
Transverse Shear ◽  
Three Dimensional ◽  
Order Theory ◽  
Sixth Order ◽  
Interior Solution ◽  
Transverse Shear Deformation ◽  
Two Dimensional ◽  
Elastic Plates

We depart from a three-dimensional statement of the problem of small bending of elastic plates, for a survey of approximate two-dimensional theories, beginning with Kirchhoff’s fourth-order formulation. After discussing various variational statements of the three-dimensional problem, we describe the development of two-dimensional sixth-order theories by Bolle´, Hencky, Mindlin, and Reissner which take account of the effect of transverse shear deformation. Additionally, we report on an early analysis by Le´vy, on a direct two-dimensional formulation of sixth-order theory, on constitutive coupling of bending and stretching of laminated plates, on higher than sixth-order theories, and on an asymptotic analysis of sixth-order theory which leads to a fourth-order interior solution contribution with first-order transverse shear deformation effects included, as well as to a sequentially determined second-order edge zone solution contribution.

Kinematic Design of Deployable Structures With Low Actuation Requirements Based on Pop-Up Folding

2021 ◽  
Author(s):  
Eduardo E. Montano ◽  
Edwin A. Peraza Hernandez
Keyword(s):  
Strain Energy ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Kinematic Modeling ◽  
Deployable Structures ◽  
Design Algorithm ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Area And Volume

Abstract This paper presents the kinematic modeling and design of deployable structures inspired by pop-up books. These pop-up structures can exhibit large changes in area and volume through deployment motion that resembles opening the pages of a book. The pop-up structures have a modular topology and are formed by multiple parallelepiped units, here termed as pop-up units. The analysis of the kinematics of single pop-up units and assemblies of these that form larger structures is presented. An algorithm that integrates multiple pop-up units to form structures that approximate two-dimensional and three-dimensional target shapes when deployed is subsequently devised. The algorithm ensures that the structures formed by the assemblies of multiple pop-up units retain the single degree of freedom of a pop-up unit. The stored strain energy of these structures, which can provide the means to deploy them in practice, is also analyzed. Finally, various examples showing the applicability of the design algorithm in the synthesis of pop-up structures that approximate a diverse set of two-dimensional and three-dimensional target shapes are provided. The pop-up structures can be applied to a large spectrum of applications that need extensive deployment from small volumes while requiring a low number of degrees of freedom. These applications may include aerospace structures and MEMS.

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