A Reissner’s Mixed Variational Theorem Applied to Vibration Analysis of Multilayered Shell

1999 ◽  
Vol 66 (1) ◽  
pp. 69-78 ◽  
Author(s):  
E. Carrera
Keyword(s):  
Normal Stress ◽  
Structural Model ◽  
Dynamic Equilibrium ◽  
A Priori ◽  
Three Dimensional ◽  
Single Layer ◽  
Transverse Normal Stress ◽  
Variational Theorem ◽  
Reissner’S Mixed Variational Theorem ◽  
Static Conditions

A comprehensive model of anisotropic multilayered double curved shells fulfilling a priori the interlaminar continuity requirements for the transverse shear and transverse normal stress as well as the static conditions on the bounding surfaces of the shell is developed in this paper. To this end, Reissner’s mixed variational theorem is employed to derive the equations governing the dynamic equilibrium and compatibility of each layer, while the interlaminar continuity conditions are used to drive the equations at the multilayered level. No assumptions have been made concerning the terms of type thickness to radii shell ratio h/R. Classical displacement formulations and related equivalent single layer equations have been derived for comparison purposes. Comparison of frequency predictions based upon the presented structural model with a number of results spread throughout the specialized literature and obtained via other models reveals that this advanced model provides results in excellent agreement with the ones based on three-dimensional elasticity theory, and better as compared to the ones violating the interlaminar stress continuity requirements and/or transverse normal stress and related effects.

Layer-Wise Mixed Models for Accurate Vibrations Analysis of Multilayered Plates

1998 ◽  
Vol 65 (4) ◽  
pp. 820-828 ◽  
Author(s):  
E. Carrera
Keyword(s):  
Mixed Models ◽  
Dynamic Equilibrium ◽  
Variational Equation ◽  
A Priori ◽  
Three Dimensional ◽  
Single Layer ◽  
Multilayered Plates ◽  
Three Dimensional Elasticity ◽  
Free Vibration Response ◽  
Principle Of Virtual Displacements

This paper presents the dynamic analysis of multilayered plates using layer-wise mixed theories. With respect to existing two-dimensional theories at the displacement formulated, the proposed models a priori fulfill the continuity of transverse shear and normal stress components at each interface between two adjacent layers. A Reissner’s mixed variational equation is employed to derive the differential equations, in terms of the introduced stress and displacement variables, that govern the dynamic equilibrium and compatibility of each layer. The continuity conditions at the interfaces are used to write corresponding equations at multilayered level. Related standard displacement formulations, based on the principle of virtual displacements, are given for comparison purposes. Numerical results are presented for the free-vibration response (fundamental and higher order frequencies are calculated) of symmetrically and unsymmetrically laminated cross-ply plates. Several comparisons to three-dimensional elasticity analysis and to some available results, related to both layer-wise and equivalent single-layer theories, have shown that the presented mixed models: (1) match the exact three-dimensional results very well and (2) lead to a better description in comparison to results related to other available analysis.

Asymptotic Construction of a Generalized Reissner-Mindlin Model for Multilayer Piezoelectric Plates

2007 ◽  
Author(s):  
Lin Liao ◽  
Wenbin Yu
Keyword(s):  
A Priori ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Single Layer ◽  
Plate And Shell ◽  
Shell Analysis ◽  
Variational Asymptotic ◽  
Variational Asymptotic Method ◽  
Plate Analysis ◽  
Piezoelectric Plates

The variational asymptotic method is used to construct a generalized Reissner-Mindlin model for multilayer piezoelectric plates with faces surfaces or other surfaces parallel to the reference surface coated with electrodes. Without invoking a priori kinematic assumptions, we asymptotically split the original three-dimensional electromechanical problem into a one-dimensional through-the-thickness analysis and a two-dimensional plate analysis. The through-the-thickness analysis is implemented using the finite element method into the computer program VAPAS (Variational Asymptotic Plate and Shell Analysis). The resulting model is as simple as an equivalent single-layer, first-order shear deformation theory with accuracy comparable to higher-order layerwise theories. Numerical results of cylindrical bending problems for piezoelectric plates have been compared with 3D exact solutions to validate the present model.

scholarly journals FOX: A friendly tool to solve nonmolecular structures from powder diffraction

2005 ◽  
Vol 20 (4) ◽  
pp. 359-365 ◽  
Author(s):  
Radovan Černý ◽  
Vincent Favre-Nicolin
Keyword(s):  
Powder Diffraction ◽  
Structural Model ◽  
A Priori ◽  
Three Dimensional ◽  
Building Blocks ◽  
Global Optimization Algorithm ◽  
Structural Units ◽  
Coordination Polyhedra ◽  
Extended Solids ◽  
Framework Compounds

Structural characterization from powder diffraction of compounds not containing isolated molecules but three-dimensional infinite structure (alloys, intermetallics, framework compounds, extended solids) by direct space methods has been largely improved in the last 15 years. The success of the method depends very much on a proper modeling of the structure from building blocks. The modeling from larger building blocks improves the convergence of the global optimization algorithm by a factor of up to 10. However, care must be taken about the correctness of the building block, like its rigidity, deformation, bonding distances, and ligand identity. Dynamical occupancy correction implemented in the direct space program FOX has shown to be useful when merging excess atoms, and even larger building blocks like coordination polyhedra. It also allows joining smaller blocks into larger ones in the case when the connectivity was not a priori evident from the structural model. We will show in several examples of nonmolecular structures the effect of the modeling by correct structural units.

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.

scholarly journals Mastering of NIL Stamps with Undercut T-Shaped Features from Single Layer to Multilayer Stamps

Nanomaterials ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 956
Author(s):  
Philipp Taus ◽  
Adrian Prinz ◽  
Heinz D. Wanzenboeck ◽  
Patrick Schuller ◽  
Anton Tsenov ◽  
...  
Keyword(s):  
Electron Beam Lithography ◽  
Nanoimprint Lithography ◽  
Silicon Oxide ◽  
Three Dimensional ◽  
Single Layer ◽  
Fabrication Technology ◽  
Large Area ◽  
Structural Colors ◽  
Biomimetic Structures ◽  
Morpho Butterfly

Biomimetic structures such as structural colors demand a fabrication technology of complex three-dimensional nanostructures on large areas. Nanoimprint lithography (NIL) is capable of large area replication of three-dimensional structures, but the master stamp fabrication is often a bottleneck. We have demonstrated different approaches allowing for the generation of sophisticated undercut T-shaped masters for NIL replication. With a layer-stack of phase transition material (PTM) on poly-Si, we have demonstrated the successful fabrication of a single layer undercut T-shaped structure. With a multilayer-stack of silicon oxide on silicon, we have shown the successful fabrication of a multilayer undercut T-shaped structures. For patterning optical lithography, electron beam lithography and nanoimprint lithography have been compared and have yielded structures from 10 µm down to 300 nm. The multilayer undercut T-shaped structures closely resemble the geometry of the surface of a Morpho butterfly, and may be used in future to replicate structural colors on artificial surfaces.

scholarly journals Homogeneous 2D and 3D alignment of cardiomyocyte in dilated cardiomyopathy revealed by intravital heart imaging

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Kiyoshi Masuyama ◽  
Tomoaki Higo ◽  
Jong-Kook Lee ◽  
Ryohei Matsuura ◽  
Ian Jones ◽  
...  
Keyword(s):  
Heart Failure ◽  
Dilated Cardiomyopathy ◽  
Cardiac Dysfunction ◽  
Three Dimensional ◽  
Single Layer ◽  
Specific Pattern ◽  
Two Dimensional ◽  
Heart Imaging ◽  
Novel Method ◽  
2D And 3D

AbstractIn contrast to hypertrophic cardiomyopathy, there has been reported no specific pattern of cardiomyocyte array in dilated cardiomyopathy (DCM), partially because lack of alignment assessment in a three-dimensional (3D) manner. Here we have established a novel method to evaluate cardiomyocyte alignment in 3D using intravital heart imaging and demonstrated homogeneous alignment in DCM mice. Whilst cardiomyocytes of control mice changed their alignment by every layer in 3D and position twistedly even in a single layer, termed myocyte twist, cardiomyocytes of DCM mice aligned homogeneously both in two-dimensional (2D) and in 3D and lost myocyte twist. Manipulation of cultured cardiomyocyte toward homogeneously aligned increased their contractility, suggesting that homogeneous alignment in DCM mice is due to a sort of alignment remodelling as a way to compensate cardiac dysfunction. Our findings provide the first intravital evidence of cardiomyocyte alignment and will bring new insights into understanding the mechanism of heart failure.

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