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The application of special matrix product to differential quadrature solution of geometrically nonlinear bending of orthotropic rectangular plates [article]

W. Chen, C. Shu, W. He
1999 arXiv   pre-print
In this study, they are applied to the differential quadrature (DQ) solution of geometrically nonlinear bending of isotropic and orthotropic rectangular plates.  ...  The Hadamard and SJT product of matrices are two types of special matrix product. The latter was first defined by Chen.  ...  Bert et al. [9] employed the DQ method to solve the static von Karman equations in analyzing geometrically nonlinear bending of isotropic and orthotropic rectangular plates.  ... 
arXiv:cs/9906012v1 fatcat:lslkqvy54bba3ozjszmpxocfxy

The application of special matrix product to differential quadrature solution of geometrically nonlinear bending of orthotropic rectangular plates

W. Chen, C. Shu, W. He, T. Zhong
2000 Computers & structures  
In this study, they are applied to the dierential quadrature (DQ) solution of geometrically nonlinear bending of isotropic and orthotropic rectangular plates.  ...  The Hadamard and SJT product of matrices are two types of special matrix product. The latter was ®rst de®ned by Chen.  ...  [9] employed the DQ method to solve the static von Karman equations in analyzing geometrically nonlinear bending of isotropic and orthotropic rectangular plates.  ... 
doi:10.1016/s0045-7949(98)00320-4 fatcat:myrggbiw2nb7fcgsf2ws6lzgxq

Nonlocal elasticity theory for graphene modeling and simulation: prospects and challenges

K. M. Liew, Yang Zhang, L. W. Zhang
2017 Journal of Modeling in Mechanics and Materials  
A systematic introduction to the application of nonlocal elasticity on linear modeling and nonlinear modeling for single-layer graphene sheets (SLGSs) and multilayered graphene sheets (MLGSs) is also provided  ...  This work is intended to review the development of GSs, give an introduction to the research studies on nonlocal elasticity theory in the modeling of GSs, and provide recommendations for future research  ...  , the nonlinear factor of the polymer matrix and geometric properties on the nonlinear vibrational behavior of a DLGS were discussed in detail.  ... 
doi:10.1515/jmmm-2016-0159 fatcat:smpx6idquzcrtby4vroxgojuoi

Static analysis of an isotropic rectangular plate using finite element analysis (FEA)

Vanam B. C. L
2012 Journal of Mechanical Engineering Research  
This research work aims to analyze the static analysis of an isotropic rectangular plate with various boundary conditions and various types of load applications.  ...  During this analysis, the optimal thickness of the plate has been obtained when the plate is subjected to different loading and boundary conditions.  ...  Liew et al. (2001) developed the differential quadrature method and harmonic differential quadrature method for static analysis of three dimensional rectangular plates.  ... 
doi:10.5897/jmer11.088 fatcat:j5f22yazzfccdhazyp2eyip2f4

Large deflection elastic-plastic analysis of plate structures by the finite strip method

S. B. S. Abayakoon, M. D. Olson, D. L. Anderson
1989 International Journal for Numerical Methods in Engineering  
Special emphasis is given to the particular problem of rectangular plates with stiffeners running in a direction parallel to one side of the plate.  ...  method is presented herein, for the analysis of plate systems exhibiting geometric and material non-linearities.  ...  An elastic small deflection analysis of a rectangular orthotropic plate yields the following differential equation to be solved for the lateral diaplacement w. of the non-linear terms in the first equation  ... 
doi:10.1002/nme.1620280207 fatcat:7iuun236xjh7bl3z3bl25atk6a

Hybrid Sandwich Panels: A Review

S.H. Sandeep, C.V. Srinivasa
2020 International Journal of Applied Mechanics and Engineering  
AbstractA high specific stiffness, high specific strength, and tailoring the properties for specific application have attracted the attention of the researchers to work in the field of laminated composites  ...  In this article, a review on free vibration analysis of shear deformable isotropic beams, plates, shells, laminated composites and sandwich structures based on various theories and the exact solution is  ...  Large deflection theory of thin plates has been used to consider the geometric nonlinearity effects.  ... 
doi:10.2478/ijame-2020-0035 fatcat:rqucxlwzpzfo5dmdhwk5uexqgu

Mechanical Analysis of Woven Fabrics:The State of the Art [chapter]

Savvas Vassiliadis, Argyro Kallivretaki, Dimitra Domvoglou, Christofer Provatidis
2011 Advances in Modern Woven Fabrics Technology  
drapeability of the fabric reinforcement offers the advantage of bending around doublecurvature mould producing complex shaped composite parts.  ...  Bäcklund transformations were chosen for the solution of the nonlinear partial differential equations of the dynamic system.  ...  Geometric nonlinearity and linear elastic orthotropic material properties of the fabric were considered in the formulation.  ... 
doi:10.5772/25255 fatcat:34h4leiz3re3zceyhsmmqtmqpy

Advances in modelling and analysis of nano structures: a review

Vikram Singh Chandel, Guannan Wang, Mohammad Talha
2020 Nanotechnology Reviews  
be helpful for appropriate design and analysis of nanodevices for the application in the various fields of nanotechnology.  ...  The focus has been made, to present the structural analysis of nanostructures under thermo-magneto-electro-mechanical loadings under various boundary and environmental conditions.  ...  Civalek and Demir [130] formulated a nonlocal EBT for bending analysis of microtubules using the differential quadrature method (DQM).  ... 
doi:10.1515/ntrev-2020-0020 fatcat:sxggxo77qjhmlblbmlczepmkby

Modeling and Analysis of Functionally Graded Materials and Structures [chapter]

Victor Birman
2014 Encyclopedia of Thermal Stresses  
Diverse areas relevant to various aspects of theory and applications of FGM are reflected in this paper.  ...  The critical areas where further research is needed for a successful implementation of FGM in design are outlined in the conclusions.  ...  The paper of Cheng ͓67͔ contains the solution for nonlinear bending of transversely isotropic symmetric shear-deformable FGM plates.  ... 
doi:10.1007/978-94-007-2739-7_574 fatcat:s6ssbispkjg37lvkmc7gv5dala

英文版2009年第3期"机械科学专辑"摘要

2010 Scientia Sinica Technologica  
This paper studies the bending of simple-supported rectangular plate on point supports, line supports and elastic foundation.  ...  Three-dimensional elasticity solution of simple-supported rectangular plate on point supports, line supports and elastic foundation.  ...  Liu and Wang [2] analyzed the bending problem of anisotropic rectangular plates with four free edges on an elastic foundation.  ... 
doi:10.1360/ze2010-40-3-320 fatcat:ewz7ocjff5h65ixvudgapxw43m

Computational approaches to vibration analysis of shells under different boundary conditions – a literature review

Fazl e Ahad, Dongyan Shi, Zarnab Hina
2017 Journal of Vibroengineering  
A huge amount of research efforts has been devoted to vibration analysis and dynamic behaviors of the shells.  ...  For different cases different computational approaches have been used in literature to study the vibration characteristics of shells.  ...  Acknowledgements The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (No.  ... 
doi:10.21595/jve.2016.16884 fatcat:gs7bc64z4fbhlhvfjtjz4wlbeq

Thin Plates and Shells [chapter]

Phillip L. Gould
2012 Introduction to Linear Elasticity  
Part I (Chapters 1-9) presents plate bending theory and its application and Part II (Chapters 10-20) covers the theory, analysis, and principles of shell structures.  ...  Our third goal was to apply the theories and methods developed in the book to the analysis and design of thin plate-shell structures in engineering.  ...  In the former Soviet Union the works of Volmir [29] and Panov [30] were devoted mostly to solution of nonlinear plate bending problems.  ... 
doi:10.1007/978-1-4614-4833-4_8 fatcat:lcgj45efsvdmtnkyauluavskai

Computational analysis of the nonlinear vibrational behavior of perforated plates with initial imperfection using NURBS-based isogeometric approach

Abdollah VeisiAra, Hamid Mohammad-Sedighi, Arash Reza
2021 Journal of Computational Design and Engineering  
The results of linear vibrations, geometrically nonlinear vibrations, and nonlinear vibrations of imperfect plates are separately validated by considering the previously reported findings, which shows  ...  In this article, an isogeometric analysis through NURBS basis functions is presented to study the nonlinear vibrational behavior of perforated plates with initial imperfection.  ...  Foremost, it should be also mentioned that the closed-form solutions for free vibration analysis of Mindlin plate are complicated and restricted to special cases because of the number of governing equations  ... 
doi:10.1093/jcde/qwab043 fatcat:jkjpv36igbfynoqc7t7n5sa47q

Free vibration analysis of laminated composite plates based on FSDT using one-dimensional IRBFN method

D. Ngo-Cong, N. Mai-Duy, W. Karunasena, T. Tran-Cong
2011 Computers & structures  
The plates, which can be rectangular or non-rectangular, are simply discretised by means of Cartesian grids.  ...  Results obtained are compared with the exact solutions and numerical results by other techniques in the literature to investigate the performance of the proposed method.  ...  This research is supported by the University of Southern Queensland, Australia through a USQ Postgraduate Research Scholarship awarded to D. Ngo-Cong.  ... 
doi:10.1016/j.compstruc.2010.07.012 fatcat:nsokv5y5hnaonntd5rxmjqtzse

Large amplitude free vibration analysis of cross-ply composite and sandwich laminates with a refined theory and finite elements

T. Kant, J.R. Kommineni
1994 Computers & structures  
A special mass matrix diagonalization scheme is employed which conserves the total mass of the element and includes the effects due to rotary inertia terms.  ...  The validity and efficiency of the present development is then established by obtaining the solutions to a wide range of problems and comparing them with the available two-and three-dimensional closed-form  ...  The element mass matrix is evaluated using a 3 x 3 Gauss quadrature rule.  ... 
doi:10.1016/0045-7949(94)90443-x fatcat:herljmyshzgapbpvo6r5vgykdq
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