ISOGEOMETRIC SIMULATION FOR BUCKLING, FREE AND FORCED VIBRATION OF ORTHOTROPIC PLATES

2013 ◽  
Vol 05 (02) ◽  
pp. 1350017 ◽  
Author(s):  
N. VALIZADEH ◽  
T. Q. BUI ◽  
V. T. VU ◽  
H. T. THAI ◽  
M. N. NGUYEN
Keyword(s):  
Boundary Conditions ◽  
Forced Vibration ◽  
Isogeometric Analysis ◽  
Plate Theory ◽  
Present Formulation ◽  
Orthotropic Plates ◽  
Classical Plate Theory ◽  
Numerical Examples ◽  
Nurbs Basis Function ◽  
Plate Deflection

Buckling, free and forced vibration analyses of orthotropic plates are studied numerically using Isogeometric analysis. The present formulation is based on the classical plate theory (CPT) while the NURBS basis function is employed for both the parametrization of the geometry and the approximation of plate deflection. An efficient and easy-to-implement technique is used for imposing the essential boundary conditions. Numerical examples for free and forced vibration and buckling of orthotropic plates with different boundary conditions and configurations are considered. The numerical results are compared with other existing solutions to show the efficiency and accuracy of the proposed approach for such problems.

Response of a Plate Supported by a Fluid Half Space to a Moving Pressure

1970 ◽  
Vol 37 (4) ◽  
pp. 1050-1054 ◽  
Author(s):  
D. H. Y. Yen ◽  
C. C. Chou
Keyword(s):  
Half Space ◽  
Elastic Plate ◽  
Plate Theory ◽  
Fluid Pressure ◽  
Integral Transforms ◽  
Classical Plate Theory ◽  
Plate Deflection

The response of an elastic plate supported by a fluid half space to a steadily moving pressure is studied. The Timoshenko plate theory is used in the study. By the method of integral transforms, solutions for both the plate deflection and the interaction fluid pressure are obtained. The results are then compared in detail with those obtained previously using the classical plate theory.

Free Bending Vibrations of Adhesively Bonded Orthotropic Plates With a Single Lap Joint

1996 ◽  
Vol 118 (1) ◽  
pp. 122-134 ◽  
Author(s):  
U. Yuceoglu ◽  
F. Toghi ◽  
O. Tekinalp
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Lap Joint ◽  
Orthotropic Plates ◽  
Adhesively Bonded ◽  
Bending Vibrations ◽  
Free Bending

This study is concerned with the free bending vibrations of two rectangular, orthotropic plates connected by an adhesively bonded lap joint. The influence of shear deformation and rotatory inertia in plates are taken into account in the equations according to the Mindlin plate theory. The effects of both thickness and shear deformations in the thin adhesive layer are included in the formulation. Plates are assumed to have simply supported boundary conditions at two opposite edges. However, any boundary conditions can be prescribed at the other two edges. First, equations of motion at the overlap region are derived. Then, a Levy-type solution for displacements and stress resultants are used to formulate the problem in terms of a system of first order ordinary differential equations. A revised version of the Transfer Matrix Method together with the boundary and continuity conditions are used to obtain the frequency equation of the system. The natural frequencies and corresponding mode shapes are obtained for identical and dissimilar adherends with different boundary conditions. The effects of some parameters on the natural frequencies are studied and plotted.

Vibration analysis of a nano-turbine blade based on Eringen nonlocal elasticity applying the differential quadrature method

2016 ◽  
Vol 23 (19) ◽  
pp. 3247-3265 ◽  
Author(s):  
Majid Ghadiri ◽  
Navvab Shafiei
Keyword(s):  
Boundary Conditions ◽  
Nonlocal Elasticity ◽  
Plate Theory ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Small Scale ◽  
Quadrature Method ◽  
Bending Vibrations ◽  
Classical Plate Theory ◽  
Axial Forces

This study investigates the small-scale effect on the flapwise bending vibrations of a rotating nanoplate that can be the basis of nano-turbine design. The nanoplate is modeled as classical plate theory (CPT) with boundary conditions as the cantilever and propped cantilever. The axial forces are also included in the model as the true spatial variation due to the rotation. Hamilton’s principle is used to derive the governing equation and boundary conditions for the classic plate based on Eringen’s nonlocal elasticity theory and the differential quadrature method is employed to solve the governing equations. The effect of the small-scale parameter, nondimensional angular velocity, nondimensional hub radius, setting angle and different boundary conditions in the first four nondimensional frequencies is discussed. Due to considering rotating effects, results of this study are applicable in nanomachines such as nanomotors and nano-turbines and other nanostructures.

scholarly journals Multiparametric Analytical Solution for the Eigenvalue Problem of FGM Porous Circular Plates

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 429 ◽  
Author(s):  
Krzysztof Żur ◽  
Piotr Jankowski
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Special Functions ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Circular Plates ◽  
Classical Plate Theory ◽  
Coupled Equations

Free vibration analysis of the porous functionally graded circular plates has been presented on the basis of classical plate theory. The three defined coupled equations of motion of the porous functionally graded circular/annular plate were decoupled to one differential equation of free transverse vibrations of plate. The one universal general solution was obtained as a linear combination of the multiparametric special functions for the functionally graded circular and annular plates with even and uneven porosity distributions. The multiparametric frequency equations of functionally graded porous circular plate with diverse boundary conditions were obtained in the exact closed-form. The influences of the even and uneven distributions of porosity, power-law index, diverse boundary conditions and the neglected effect of the coupling in-plane and transverse displacements on the dimensionless frequencies of the circular plate were comprehensively studied for the first time. The formulated boundary value problem, the exact method of solution and the numerical results for the perfect and imperfect functionally graded circular plates have not yet been reported.

Isogeometric Analysis of Functionally-Graded Graphene Platelets Reinforced Porous Nanocomposite Plates Using a Refined Plate Theory

2020 ◽  
Vol 20 (07) ◽  
pp. 2050076
Author(s):  
Duc-Huynh Phan
Keyword(s):  
Forced Vibration ◽  
Isogeometric Analysis ◽  
Plate Theory ◽  
Mass Density ◽  
Weight Fraction ◽  
Functionally Graded ◽  
Integration Scheme ◽  
Dispersion Pattern ◽  
Refined Plate Theory ◽  
Graphene Platelets

In this study, we propose a novel and effective computational approach for free and forced vibration analyses of functionally graded (FG) porous plates with graphene platelets (GPLs) reinforcement under various loads. To this end, the outstanding features of isogeometric analysis (IGA) are first combined with the four-variable refined plate theory (RPT). The non-uniform rational B-splines (NURBS) are adopted to obtain the [Formula: see text]-continuity essential to the RPT model. The various distributions of internal pores as well as GPLs with uniform or non-uniform properties along the plate’s thickness are investigated. The effective elastic properties of the material models are obtained by the Halpin–Tsai micromechanics model for Young’s modulus, the rule of mixture for Poisson’s ratio and mass density. The Newmark’s time integration scheme is implemented to obtain the solutions of the forced vibration problems. Numerical examples are carried out to investigate the effects of various key parameters such as porosity coefficient, GPL weight fraction, porosity distribution, as well as GPL dispersion pattern, on the behaviors of the plate structure.

Elasticity Solutions for Annular Plates of Functionally Graded Materials Subjected to a Uniform Load

2011 ◽  
Vol 261-263 ◽  
pp. 853-857
Author(s):  
Bo Yang ◽  
Xin Zhang ◽  
Han Yu Yu
Keyword(s):  
Boundary Conditions ◽  
Complex Variable ◽  
Plate Theory ◽  
Theory Of Elasticity ◽  
Functionally Graded ◽  
Transverse Load ◽  
Functionally Graded Plates ◽  
Uniform Load ◽  
Classical Plate Theory ◽  
Elasticity Solutions

England (2006) proposed a novel theory to study the bending problem of isotropic functionally graded plates subjected to transverse biharmonic loads. His theory is extended here to functionally graded plates of transversely isotropic materials. Using the complex variable method, the governing equations of three plate displacements appearing in the expansions of the displacement field are formulated based on the three-dimensional theory of elasticity for a transverse load satisfying the biharmonic equation. The solutions may be expressed in terms of four analytic functions of the complex variable, in which the unknown constants can be determined from the boundary conditions similar to that in the classical plate theory(CPT). The elasticity solutions of an FGM annular plate under a uniform load are derived. A comparison of the present results for a uniform load with existing solutions is made and good agreement is observed. The influence of boundary conditions, material inhomogeneity and radius-to-radius ratio on the plate deflection and stresses are studied numerically.

scholarly journals On the Shear Buckling of Clamped Narrow Rectangular Orthotropic Plates

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Seyed Rasoul Atashipour ◽  
Ulf Arne Girhammar
Keyword(s):  
Closed Form ◽  
Plate Theory ◽  
Exact Analytical Solution ◽  
Differential Quadrature Method ◽  
Thin Plates ◽  
Orthotropic Plates ◽  
Classical Plate Theory ◽  
Aspect Ratios ◽  
Wide Range ◽  
Shear Buckling

This paper deals with stability analysis of clamped rectangular orthotropic thin plates subjected to uniformly distributed shear load around the edges. Due to the nature of this problem, it is impossible to present mathematically exact analytical solution for the governing differential equations. Consequently, all existing studies in the literature have been performed by means of different numerical approaches. Here, a closed-form approach is presented for simple and fast prediction of the critical buckling load of clamped narrow rectangular orthotropic thin plates. Next, a practical modification factor is proposed to extend the validity of the obtained results for a wide range of plate aspect ratios. To demonstrate the efficiency and reliability of the proposed closed-form formulas, an accurate computational code is developed based on the classical plate theory (CPT) by means of differential quadrature method (DQM) for comparison purposes. Moreover, several finite element (FE) simulations are performed via ANSYS software. It is shown that simplicity, high accuracy, and rapid prediction of the critical load for different values of the plate aspect ratio and for a wide range of effective geometric and mechanical parameters are the main advantages of the proposed closed-form formulas over other existing studies in the literature for the same problem.

Dynamic Instability of Stiffened Plates with Cutout Subjected to In-Plane Uniform Edge Loadings

2003 ◽  
Vol 03 (03) ◽  
pp. 391-403 ◽  
Author(s):  
A. K. L. Srivastava ◽  
P. K. Datta ◽  
A. H. Sheikh
Keyword(s):  
Boundary Conditions ◽  
Dynamic Stability ◽  
Dynamic Instability ◽  
Plate Theory ◽  
Stiffened Plates ◽  
Numerical Examples ◽  
Different Boundary Conditions ◽  
Reissner Plate ◽  
Aspect Ratios ◽  
Instability Regions

This paper is concerned with the dynamic stability of stiffened plates with cutout subjected to harmonic in-plane edge loadings. The plate is modelled using the Mindlin–Reissner plate theory and the method of Hill's infinite determinants is applied to analyze the dynamic instability regions. Stiffened plates with cutout possessing different boundary conditions, aspect ratios, and cutout sizes considering and neglecting in-plane displacements have been analyzed for dynamic instability. The boundaries of the instability regions, including those of the principal one, are computed and presented graphically. These results are given in a non-dimensional form and illustrated by means of numerical examples.

Flexure of Polygonal Plates with Circular Holes

1985 ◽  
Vol 29 (03) ◽  
pp. 209-211
Author(s):  
Thein Wah
Keyword(s):  
Boundary Conditions ◽  
Circular Hole ◽  
Plate Theory ◽  
Numerical Results ◽  
Classical Plate Theory ◽  
Circular Holes ◽  
Polygonal Plate

A procedure is developed for determining the stresses in a polygonal plate with a circular hole. Classical plate theory is assumed. The boundary conditions are satisfied exactly term by term. Numerical results are given.

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