scholarly journals Three-Dimensional Free Vibration Analyses of Preloaded Cracked Plates of Functionally Graded Materials via the MLS-Ritz Method

Materials ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 7712
Author(s):  
Chiung-Shiann Huang ◽  
Hao-Ting Lee ◽  
Pin-Yu Li ◽  
Ming-Ju Chang
Keyword(s):  
Ritz Method ◽  
Three Dimensional ◽  
Stress Singularity ◽  
Functionally Graded ◽  
Vibration Frequencies ◽  
Graded Materials ◽  
Plate Convergence ◽  
Cracked Plates ◽  
Graded Material ◽  
Admissible Functions

In this study, the moving least squares (MLS)-Ritz method, which involves combining the Ritz method with admissible functions established using the MLS approach, was used to predict the vibration frequencies of cracked functionally graded material (FGM) plates under static loading on the basis of the three-dimensional elasticity theory. Sets of crack functions are proposed to enrich a set of polynomial functions for constructing admissible functions that represent displacement and slope discontinuities across a crack and appropriate stress singularity behaviors near a crack front. These crack functions enhance the Ritz method in terms of its ability to identify a crack in a plate. Convergence studies of frequencies and comparisons with published results were conducted to demonstrate the correctness and accuracy of the proposed solutions. The proposed approach was also employed for accurately determining the frequencies of cantilevered and simply supported side-cracked rectangular FGM plates and cantilevered internally cracked skewed rhombic FGM plates under uniaxial normal traction. Moreover, the effects of the volume fractions of the FGM constituents, crack configurations, and traction magnitudes on the vibration frequencies of cracked FGM plates were investigated.

Three-dimensional buckling analyses of cracked functionally graded material plates via the MLS-Ritz method

2019 ◽  
Vol 134 ◽  
pp. 189-202 ◽  
Author(s):  
C.S. Huang ◽  
H.T. Lee ◽  
P.Y. Li ◽  
K.C. Hu ◽  
C.W. Lan ◽  
...  
Keyword(s):  
Functionally Graded Material ◽  
Ritz Method ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Graded Material

Natural vibration of imperfect sandwich plates considering the effects of transverse stretching

2021 ◽  
pp. 107754632110131
Author(s):  
YX Hao ◽  
MX Wang ◽  
W Zhang ◽  
LT Liu ◽  
SW Yang
Keyword(s):  
Functionally Graded Material ◽  
Natural Vibration ◽  
Sandwich Plate ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Three Dimensional ◽  
Core Layer ◽  
Functionally Graded ◽  
Three Dimensional Model ◽  
Graded Material

In this article, the natural vibration investigation of a functionally graded material sandwich plate with initial geometrical imperfection of the exponential function is conducted. Two face sheets of the sandwich plate are composited by functionally graded material. Their material coefficients are affected by temperature and vary in the direction of thickness following the power law. The core layer is only the metal. With the aid of Reddy’s displacement fields, a quasi-three-dimensional model is used, in which the effects of transverse stretching on natural vibration are considered. The natural frequencies and model shapes of the system are calculated on the basis of Rayleigh–Ritz method and Chebyshev polynomials. A comparison of these results with those of the existing three-dimensional theory results shows the validity and computability of present method. The influences of various parameters on the natural frequencies are researched in detail.

Three-Dimensional Dynamics Analysis of Rotating Functionally Gradient Beams Based on Timoshenko Beam Theory

2019 ◽  
Vol 11 (04) ◽  
pp. 1950040 ◽  
Author(s):  
Ding Zhou ◽  
Jianshi Fang ◽  
Hongwei Wang ◽  
Xiaopeng Zhang
Keyword(s):  
Timoshenko Beam ◽  
Chebyshev Polynomials ◽  
Slenderness Ratio ◽  
Ritz Method ◽  
Three Dimensional ◽  
Beam Theory ◽  
Functionally Graded ◽  
Timoshenko Beam Theory ◽  
Strengthening Effect ◽  
Graded Materials

Through the Timoshenko beam theory (TBT), the 3D dynamics of a rotary functional gradient (FG) cantilever beam are investigated. Material capabilities alter continuously throughout the thickness obeying the power law. It is assumed that the Poisson’s ratio does not change. Based on the von Kármán nonlinearity, the governing equation is determined through the Hamilton principle, which includes the Coriolis effects. The couplings among the axial, flapwise and chordwise deformations caused by the usage of the functionally graded materials (FGMs) are revealed. Chebyshev polynomials are utilized to construct trial functions of deformations in the Rayleigh–Ritz method. The centrifugal strengthening effect caused by the rotational motion is described through the nonlinear axial shortening deformations derived from transverse deformations. The influences of the dimensionless angular velocity, FG index and slenderness ratio on vibration characteristics are studied. It is proved that the FG index significantly affects the dynamic response of deformation. For high-frequency external excitation cases, selection of Chebyshev polynomials as trial functions is more stable and effective than other polynomials.

Thermal Stress in Discretely Layered Structures with Functional Graded Materials

2008 ◽  
Vol 24 (4) ◽  
pp. 297-300 ◽  
Author(s):  
S.-F. Hwang ◽  
W.-T. Liao
Keyword(s):  
Finite Element ◽  
Thermal Stress ◽  
Three Dimensional ◽  
Stress Singularity ◽  
Layered Structures ◽  
Two Dimensional ◽  
Element Analysis ◽  
Graded Materials ◽  
Dimensional Finite Element ◽  
Graded Material

AbstractFunctional graded materials are generally provided in discretely layered structures to reduce the abrupt mismatch and to improve failure performance. To investigate the thermal stress singularity occurring at the intersection of an interface and a free end, two-dimensional and three-dimensional finite element analyses are performed for titanium and aluminum layers with or without functional graded materials. The results indicate that once the functional graded material is added, the stress singularity around the intersection of an interface and a free end could be significantly relieved. If more FGM layers are used, the stress singularity could be further reduced to a very small value. If the longitudinal normal stresses and interlaminar shear stress are considered, two-dimensional finite element analysis may be enough, while three-dimensional analysis is necessary for the interlaminar normal stress. Otherwise, one may underestimate its stress singularity.

Free Vibrations of Thick, Complete Conical Shells of Revolution From a Three-Dimensional Theory

2005 ◽  
Vol 72 (5) ◽  
pp. 797-800 ◽  
Author(s):  
Jae-Hoon Kang ◽  
Arthur W. Leissa
Keyword(s):  
Ritz Method ◽  
Three Dimensional ◽  
Axial Direction ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Vibration Frequencies ◽  
Shells Of Revolution ◽  
Dimensional Theory ◽  
Conical Shells ◽  
Cylindrical Coordinate

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution in which the bottom edges are normal to the midsurface of the shells based upon the circular cylindrical coordinate system using the Ritz method. Comparisons are made between the frequencies and the corresponding mode shapes of the conical shells from the authors' former analysis with bottom edges parallel to the axial direction and the present analysis with the edges normal to shell midsurfaces.

The Elastic-Viscoelastic Correspondence Principle for Functionally Graded Materials, Revisited

2003 ◽  
Vol 70 (3) ◽  
pp. 359-363 ◽  
Author(s):  
S. Mukherjee ◽  
Glaucio H. Paulino
Keyword(s):  
Functionally Graded Materials ◽  
Functionally Graded Material ◽  
Correspondence Principle ◽  
Functionally Graded ◽  
Graded Materials ◽  
One Dimensional ◽  
Space And Time ◽  
Graded Material ◽  
Nonhomogeneous Materials ◽  
Exponentially Graded

Paulino and Jin [Paulino, G. H., and Jin, Z.-H., 2001, “Correspondence Principle in Viscoelastic Functionally Graded Materials,” ASME J. Appl. Mech., 68, pp. 129–132], have recently shown that the viscoelastic correspondence principle remains valid for a linearly isotropic viscoelastic functionally graded material with separable relaxation (or creep) functions in space and time. This paper revisits this issue by addressing some subtle points regarding this result and examines the reasons behind the success or failure of the correspondence principle for viscoelastic functionally graded materials. For the inseparable class of nonhomogeneous materials, the correspondence principle fails because of an inconsistency between the replacements of the moduli and of their derivatives. A simple but informative one-dimensional example, involving an exponentially graded material, is used to further clarify these reasons.

Incremental Melting and Solidification Process/Mechanical Characterization of Functionally Graded Al-Si Alloys

2008 ◽  
Vol 587-588 ◽  
pp. 400-404
Author(s):  
P. Pinto ◽  
L. Mazare ◽  
Delfim Soares ◽  
F.S. Silva
Keyword(s):  
Mechanical Properties ◽  
Functionally Graded Materials ◽  
Phase Distribution ◽  
Solidification Process ◽  
Functionally Graded ◽  
Graded Materials ◽  
Graded Material ◽  
Gradual Variation ◽  
Melting And Solidification

The Incremental Melting and Solidification Process (IMSP) is a relatively new field for material processing for the production of functionally graded materials. In this process a controlled liquid bath is maintained at the top of the component where new materials are added changing the components composition. Thus, a functionally graded material is obtained with a varying composition along one direction of the component. This paper deals with the influence of one of the process parameters, namely displacement rates between heating coil and mould, in order to evaluate its influence on both metallurgical and mechanical properties of different Al-Si alloys. Hardness and phase distribution, along the main castings axis, were measured. To better assess and characterize the process, two different Al-Si alloys with and without variation of chemical composition along the specimen were analysed. Results demonstrate that a gradual variation of metallurgical and mechanical properties along the component is obtained. It is also shown that Al-Si functionally graded materials can be produced by the incremental melting and solidification process. Results show that the displacement rate is very important on metallurgical and mechanical properties of the obtained alloy.

Задачи о дисперсии волн в неоднородных волноводах: методы решения (обзор). Часть I

2021 ◽  
Vol 27 (2) ◽  
pp. 227-260
Author(s):  
С. И. Жаворонок ◽  
Keyword(s):  
Functionally Graded Materials ◽  
Functionally Graded Material ◽  
Matrix Method ◽  
Degrees Of Freedom ◽  
Normal Wave ◽  
Wave Dispersion ◽  
Functionally Graded ◽  
Graded Materials ◽  
Generalized Fourier Series ◽  
Graded Material

A brief review of the modern state-of-the art and tendencies of further development of various methods of solution of wave dispersion problems in heterogeneous functionally graded elastic waveguides is presented. Main types of functionally graded materials and structures, including gradient thon-walled structures, and their main engineering applications is discussed. The main difficulties of modelling of the stress-strain state of functionally graded shells and plates are pointed, as well as the possible ways to overcome such difficulties. The main theoretical bases of definition of effective constitutive constants of functionally graded materials and their possible estimates used in the practice are considered. Main dependencies of the effective constitutive constants of a functionally graded material on coordinates used for the mathematical modelling of the dynamics are also shown. The statement of the dynamics problem for a functionally graded waveguide and the appropriate statement of the normal wave dispersion problem are pointed. The presented Part I of the review consider some analytical methods of solution of dispersion problems, mainly the matrix ones based on the formulation of the steady dynamics problem in the image space as a first-order ordinary differential equations system. The state vectors corresponding to the useful Cauchy and Stroh formalisms are introduced, and the appropriate governing equations and the boundary conditions on waveguide’s faces are presented. Classical methods for solving the steady dynamics problem for a laminated waveguide are briefly described, which could be a basis for the further approximation of a functionally graded material by a system of layers with constant properties, i.e. the transfer matrix method, its main modifications developed to ensure the stability of calculations, and the global matrix method. Then, the intensively developed last 15 years reverberation matrix method, stiffness matrix method, and the Peano series method are discussed. Some key solutions of the wave dispersion problems for heterogeneous layers are presented; such solutions improve the efficiency of approximation of a functionally graded structure by a laminated one. The implicit solution of the general problem of steady dynamics for a waveguide with arbitrary gradation law is shown. The key features of the discussed matrix methods are pointed briefly as well as their main drawbacks. In the Part II, the main attention will be paid to methods of semi-analytical solution of dispersion problems based on the approximation of a waveguide by an equivalent system with a finite number of degrees of freedom: power series, generalized Fourier series, semi-analytical finite elements. spectral elements, as well as methods based on various theories of plates and shells.

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