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

The Hadamard and SJT product of matrices are two types of special matrix product. The latter was first defined by Chen. In this study, they are applied to the differential quadrature (DQ) solution of geometrically nonlinear bending of isotropic and orthotropic rectangular plates. By using the Hadamard product, the nonlinear formulations are greatly simplified, while the SJT product approach minimizes the effort to evaluate the Jacobian derivative matrix in the Newton-Raphson method for solving the resultant nonlinear formulations. In addition, the coupled nonlinear formulations for the present problems can easily be decoupled by means of the Hadamard and SJT product. Therefore, the size of the simultaneous nonlinear algebraic equations is reduced by two-thirds and the computing effort and storage requirements are alleviated greatly. Two recent approaches applying the multiple boundary conditions are employed in the present DQ nonlinear computations. The solution accuracies are improved obviously in comparison to the previously given by Bert et al. The numerical results and detailed solution procedures are provided to demonstrate the superb efficiency, accuracy and simplicity of the new approaches in applying DQ method for nonlinear computations.

• Publication year

  1999

• Venue

  arXiv.org

• Publication date

  1999-06-09

• Fields of study

  Mathematics, Computer Science, Engineering

• Identifiers
  arXiv cs/9906012
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• The Study on the Nonlinear Computations of the DQ and DC Methods

  1999influential reference
• A comparative study of differential quadrature and cubature methods vis-à-vis some conventional techniques in context of convection-diffusion-reaction problems

  1995cited by this paper
• The method of differential quadrature and its application to the approximate solution of ocean engineering problems

  1994cited by this paper
• A NEW APPROACH IN APPLYING DIFFERENTIAL QUADRATURE TO STATIC AND FREE VIBRATIONAL ANALYSES OF BEAMS AND PLATES

  1993influential reference
• A comparison of differential quadrature methods for the solution of partial differential equations

  1993cited by this paper
• Differential quadrature analysis of deflection, buckling, and free vibration of beams and rectangular plates

  1993cited by this paper
• Differential quadrature for static and free vibration analyses of anisotropic plates

  1993cited by this paper
• Application of the quadrature method to flexural vibration analysis of a geometrically nonlinear beam

  1992cited by this paper
• Parallel simulation of incompressible viscous flows by generalized differential quadrature

  1992cited by this paper
• Nonlinear bending analysis of orthotropic rectangular plates by the method of differential quadrature

  1989influential reference
• New insights in solving distributed system equations by the quadrature method—II. Numerical experiments

  1989cited by this paper
• New insights in solving distributed system equations by the quadrature method—I. Analysis

  1989cited by this paper
• Nonlinear bending analysis of thin circular plates by differential quadrature

  1988influential reference
• Differential quadrature and partial differential equations: Some numerical results

  1984cited by this paper
• Solution of stiff ordinary differential equations by decomposition and orthogonal collocation

  1982cited by this paper
• The method of differential quadrature for transient nonlinear diffusion

  1977cited by this paper
• DIFFERENTIAL QUADRATURE: A TECHNIQUE FOR THE RAPID SOLUTION OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

  1972cited by this paper
• Finite displacement plate flexure by the use of matrix incremental approach

  1972cited by this paper
• DIFFERENTIAL QUADRATURE AND LONG-TERM INTEGRATION

  1971influential reference
• Bending of Rectangular Plates With Large Deflections

  1942cited by this paper
• Square plate with clamped edges under normal pressure producing large deflections

  1942cited by this paper

• Stability of cold-formed steel stud walls subjected to vertical compression

  2024cites this paper
• Accurate non-linear bending analytical solutions setting new benchmarks for rectangular thin plates with four simply supported edges

  2024cites this paper
• Radial basis function-differential quadrature-based physics-informed neural network for steady incompressible flows

  2023cites this paper
• High-Accurate Numerical Schemes for Black–Scholes Models with Sensitivity Analysis

  2022cites this paper
• Deflection Analysis of a Nonlocal Euler-Bernoulli Nanobeam Model Resting on Two Elastic Foundations: A Generalized Differential Quadrature Approach

  2022cites this paper
• Nonlocal elasticity analysis of moderately thick porous functionally graded plates in a hygro-thermal environment

  2021cites this paper
• Thermal post-buckling analyses of magneto-electro-elastic laminated beams via generalized differential quadrature method

  2021cites this paper
• Bending analysis of functionally graded nanoplates based on a higher-order shear deformation theory using dynamic relaxation method

  2021cites this paper
• Ritz method for large deflection of orthotropic thin plates with mixed boundary conditions

  2020cites this paper
• FCAA special issue – In memory of late professor Wen Chen (FCAA–Volume 22–6–2019)

  2019cites this paper
• Static and dynamic analysis of the postbuckling of bi-directional functionally graded material microbeams

  2019cites this paper
• Differential Quadrature Element Method for Free Vibration of Strain Gradient Beams with Elastic Boundary Conditions

  2019cites this paper
• Surface Energy Effects on the Nonlinear Free Vibration of Functionally Graded Timoshenko Nanobeams Based on Modified Couple Stress Theory

  2019cites this paper
• A decomposition method for nonlinear bending of anisotropic thin plates

  2019cites this paper
• Size-dependent pull-in analysis of a composite laminated micro-beam actuated by electrostatic and piezoelectric forces: Generalized differential quadrature method

  2018cites this paper
• Large deflection of thermo-mechanical loaded bilayer orthotropic graphene sheet in/on polymer matrix based on nonlocal elasticity theory

  2018cites this paper
• The Nonlinear Dynamic Behaviors of Electrostatic Micro-Tweezers

  2018influential citation
• Bending and buckling formulation of graphene sheets based on nonlocal simple first-order shear deformation theory

  2018cites this paper
• The effect of small scale and intermolecular forces on the nonlinear Pull-in instability behavior of nano-switches using differential quadrature method

  2017cites this paper
• Effect of temperature on pull-in voltage and nonlinear vibration behavior of nanoplate-based NEMS under hydrostatic and electrostatic actuations

  2017cites this paper
• An Investigation into the Application of Generalized Differential Quadrature Method to Bending Analysis of Composite Sandwich Plates

  2017cites this paper
• Using DQM method on residual vibration analysis of an electrostatically actuated microswitch structure

  2016cites this paper
• Using DQM method on residual vibration analysis of an electrostatically actuated microswitch structure

  2016cites this paper
• Nonlinear electroelastic vibration analysis of NEMS consisting of double-viscoelastic nanoplates

  2016cites this paper
• Differential Quadrature Analysis of Moving Load Problems

  2016cites this paper
• A Differential Quadrature based procedure for parameter identification

  2016cites this paper
• Nonlinear thermo-elastic bending behavior of graphene sheets embedded in an elastic medium based on nonlocal elasticity theory

  2016cites this paper
• Nonlinear electroelastic vibration analysis of NEMS consisting of double-viscoelastic nanoplates

  2016cites this paper
• Nonlinear bending analysis of bilayer orthotropic graphene sheets resting on Winkler–Pasternak elastic foundation based on non-local continuum mechanics

  2016cites this paper
• Buckling and postbuckling of variable angle tow composite plates under in-plane shear loading

  2015influential citation
• Strong Formulation Finite Element Method Based on Differential Quadrature: A Survey

  2015cites this paper
• Wavelet solution for large deflection bending problems of thin rectangular plates

  2015cites this paper
• Kronecker Solutions for the Matrix Differantial Equations

  2015cites this paper
• Wavelet solution for large deflection bending problems of thin rectangular plates

  2014cites this paper
• Steady-State Responses of Pulley-Belt Systems With a One-Way Clutch and Belt Bending Stiffness

  2014cites this paper
• Non-axisymmetric bending of thin annular plates due to circumferentially distributed moments

  2014influential citation
• A theoretical model for investigating the effect of vacuum fluctuations on the electromechanical stability of nanotweezers

  2014cites this paper
• Surface effects on the nonlinear forced vibration response of third-order shear deformable nanobeams

  2014cites this paper
• Nonlinear bending based on nonlocal m

  2014cites this paper
• Barycentric Interpolation Newton-Raphson Iterative Method for Solving Nonlinear Beam Equations

  2014influential citation
• Nonlinear bending analysis of orthotropic nanoscale plates in an elastic matrix based on nonlocal continuum mechanics

  2014cites this paper
• Novel weak form quadrature element method with expanded Chebyshev nodes

  2014cites this paper
• 2D-Magnetic Field and Biaxiall In-Plane Pre-Load Effects on the Vibration of Double Bonded Orthotropic Graphene Sheets

  2013cites this paper
• Postbuckling analysis of variable angle tow plates using differential quadrature method

  2013cites this paper
• Postbuckling analysis of variable angle tow composite plates under shear load

  2013cites this paper
• Elastic foundation effect on nonlinear thermo-vibration of embedded double-layered orthotropic graphene sheets using differential quadrature method

  2013cites this paper
• Postbuckling response of variable angle tow composite plates under shear load

  2013cites this paper
• Large deflection elasto-plastic analysis of frames using the weak-form quadrature element method

  2012cites this paper
• Nonlinear Vibration and Instability Analysis of a PVDF Cylindrical Shell Reinforced with BNNTs Conveying Viscose Fluid Using HDQ Method

  2012cites this paper
• DQ Based Methods: Theory and Application to Engineering and Physical Sciences

  2012cites this paper
• A Lie-group adaptive differential quadrature method to identify an unknown force in an Euler–Bernoulli beam equation

  2012cites this paper
• Semi-Analytical Solution for Functionally Graded Solid Circular and Annular Plates Resting on Elastic Foundations Subjected to Axisymmetric Transverse Loading

  2012cites this paper
• Bending analysis of thin functionally graded plates using generalized differential quadrature method

  2011cites this paper
• Elastoplastic buckling analysis of thick rectangular plates by using the differential quadrature method

  2011influential citation
• Direct Expansion Method of Boundary Condition for solving 3D elliptic equations with small parameters in the irregular domain

  2011cites this paper
• Differential quadrature method for analyzing nonlinear dynamic characteristics of viscoelastic plates with shear effects

  2010cites this paper
• Identification of neutral biochemical network models from time series data

  2009cites this paper
• Large Amplitude Free Vibration Analysis of Composite Plates with Rotationally Restrained Edges using DQM

  2008cites this paper
• NONLINEAR FREE VIBRATION OF TAPERED MINDLIN PLATES WITH EDGES ELASTICALLY RESTRAINED AGAINST ROTATION USING DQM

  2008cites this paper
• Differential quadrature large amplitude free vibration analysis of laminated skew plates based on FSDT

  2008cites this paper
• Differential quadrature analysis of the buckling of thin rectangular plates with cosine-distributed compressive loads on two opposite sides

  2008cites this paper
• Large deformation analysis of orthotropic skew plates with nonlinear rotationally restrained edges using DQM

  2007cites this paper
• Modellazione e soluzione di strutture a guscio in materiale anisotropo

  2007cites this paper
• A direct matrix method for computing analytical Jacobians of discretized nonlinear integro-differential equations

  2007cites this paper
• A DQ large deformation analysis of composite plates on nonlinear elastic foundations

  2007cites this paper
• Nonlinear stability analysis of thin doubly curved orthotropic shallow shells by the differential quadrature method

  2007cites this paper
• A DQ nonlinear bending analysis of skew composite thin plates

  2007cites this paper
• Large deformation analysis of moderately thick laminated plates on nonlinear elastic foundations by DQM

  2007cites this paper
• A differential quadrature nonlinear free vibration analysis of laminated composite skew thin plates

  2007cites this paper
• Application of the Generalized Differential Quadrature Method to the Study of Pull-In Phenomena of MEMS Switches

  2007cites this paper
• Differential quadrature method based on the highest derivative and its applications

  2007cites this paper
• A collocation method based on one-dimensional RBF interpolation scheme for solving PDEs

  2007influential citation
• Electromechanical Behavior of Microbeams with Piezoelectric and Electrostatic Actuation

  2006cites this paper
• Mechanical analysis of non-uniform beams resting on nonlinear elastic foundation by the differential quadrature method

  2006cites this paper
• Differential quadrature nonlinear analysis of skew composite plates based on FSDT

  2006cites this paper
• Differential quadrature method for nonlinear vibration of orthotropic plates with finite deformation and transverse shear effect

  2005cites this paper
• The nonlinear electrostatic behavior for shaped electrode actuators

  2005cites this paper
• Dynamic characteristics of shaped micro-actuators solved using the differential quadrature method

  2004influential citation
• Differential quadrature method for bending of orthotropic plates with finite deformation and transverse shear effects

  2004cites this paper
• Dynamic characteristics of shaped micro-actuators solved using the differential quadrature method

  2004influential citation
• Localized triangular differential quadrature

  2003cites this paper
• Nonlinear Vibration Analysis of Timoshenko Beams Using the Differential Quadrature Method

  2003cites this paper
• Differential quadrature method for pricing American options

  2002cites this paper
• Relationship Theorem between Nonlinear Polynomial Equations and the Corresponding Jacobian Matrix

  2000cites this paper
• A novel methodology of weighted residual for nonlinear computations

  1999influential citation
• Relationship formula between nonlinear polynomial equations and the corresponding Jacobian matrix

  1999cites this paper
• Hadamard product nonlinear formulation of Galerkin and finite element methods

  1999cites this paper