Discussion: “A Semi-Analytical Investigation of Fatigue Stresses in a Bolted Headplate by Finite Elements and Classical Plate Theory” (McPhate, A.-J., Gipson, G. S., and Ortiz, J. C., ASME J. Vibr. Acoust. Stress Rel. Des., 1987, 109, pp. 302–308)

1988 ◽  
Vol 110 (3) ◽  
pp. 423-424
Author(s):  
Rual Guerguerian
Keyword(s):  
Finite Elements ◽  
Plate Theory ◽  
Analytical Investigation ◽  
Classical Plate Theory

A Semi-Analytical Investigation of Fatigue Stresses in a Bolted Headplate by Finite Elements and Classical Plate Theory

1987 ◽  
Vol 109 (3) ◽  
pp. 302-308
Author(s):  
A. J. McPhate ◽  
G. Steven Gipson ◽  
J. C. Ortiz
Keyword(s):  
Stress State ◽  
Finite Elements ◽  
Ball Mill ◽  
Plate Theory ◽  
Analytical Investigation ◽  
Hybrid Analysis ◽  
Early Failure ◽  
Classical Plate Theory ◽  
Analysis Techniques ◽  
Manufacturing Errors

A semi-analytical analysis involving finite elements in conjunction with classical plate theory is used to determine the stress state in a concentrated region of the headplate on an industrial ball mill. The study illustrates the practical benefits of combining analysis techniques. With this procedure, manufacturing errors in the mill design and construction are confirmed to be a facing cut and a series of nonstructural welds on a wrapper plate between the headplate and its bearing bell mounting. The early failure of the ball mill is shown to arise from the combined detrimental effects of the residual stresses formed in the welds and groupings of broken bolts in the headplate assembly. The result, confirmed by actual site examinations, is an emphatic positive verification of the merits of hybrid analysis methods, when applied in a rational manner.

scholarly journals Analytical Solutions To Boundary Value Problem Of Free Vibration Of Sandwich Thin Circular Plates With Discrete Elements

2015 ◽  
Vol 20 (3) ◽  
pp. 617-627
Author(s):  
K.K. Żur ◽  
J. Jaroszewicz ◽  
Ł. Dragun
Keyword(s):  
Circular Plate ◽  
Plate Theory ◽  
Analytical Investigation ◽  
Axisymmetric Vibration ◽  
Circular Plates ◽  
Discrete Elements ◽  
Classical Plate Theory ◽  
Influence Matrix ◽  
The Core ◽  
Variable Distribution

Abstract In the paper the influence function and the method of partial discretization in free axisymmetric vibration analysis of multilayered circular plates of constant and linearly variable thickness were presented. The effects of shear deformation and rotary inertia for the core as well as the facings were neglected. An analytical investigation based on the classical plate theory was made for the multilayered plate which satisfies Sokołowski’s condition. Discretization of mass and replacing stiffness of a fixed circular plate were presented. Formulas of influence matrix and Bernstein-Kieropian’s estimators for different steps of discretization were defined. The influence of variable distribution of parameters on the value of double estimators of natural basic and higher frequency of a sandwich circular plate was investigated.

Characterization of the vibration, stability and static responses of graphene-reinforced sandwich plates under mechanical and thermal loadings using the refined shear deformation plate theory

2021 ◽  
pp. 109963622199386
Author(s):  
Hessameddin Yaghoobi ◽  
Farid Taheri
Keyword(s):  
Shear Deformation ◽  
Volume Fraction ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Sheet Thickness ◽  
Analytical Investigation ◽  
Sandwich Plates ◽  
Simply Supported ◽  
Vibration Stability ◽  
Shear Deformation Plate Theory

An analytical investigation was carried out to assess the free vibration, buckling and deformation responses of simply-supported sandwich plates. The plates constructed with graphene-reinforced polymer composite (GRPC) face sheets and are subjected to mechanical and thermal loadings while being simply-supported or resting on different types of elastic foundation. The temperature-dependent material properties of the face sheets are estimated by employing the modified Halpin-Tsai micromechanical model. The governing differential equations of the system are established based on the refined shear deformation plate theory and solved analytically using the Navier method. The validation of the formulation is carried out through comparisons of the calculated natural frequencies, thermal buckling capacities and maximum deflections of the sandwich plates with those evaluated by the available solutions in the literature. Numerical case studies are considered to examine the influences of the core to face sheet thickness ratio, temperature variation, Winkler- and Pasternak-types foundation, as well as the volume fraction of graphene on the response of the plates. It will be explicitly demonstrated that the vibration, stability and deflection responses of the sandwich plates become significantly affected by the aforementioned parameters.

Dynamical Behaviors of Sinusoidal Nanocomposite Plates Subjected to Thermomechanical Loads

2021 ◽  
Author(s):  
Vu Ngoc Viet Hoang ◽  
Dinh Gia Ninh
Keyword(s):  
Thermal Environment ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Rectangular Plates ◽  
Sine Function ◽  
Classical Plate Theory ◽  
Wolfram Mathematica ◽  
Number Of Cycles

In this paper, a new plate structure has been found with the change of profile according to the sine function which we temporarily call as the sinusoidal plate. The classical plate theory and Galerkin’s technique have been utilized in estimating the nonlinear vibration behavior of the new non-rectangular plates reinforced by functionally graded (FG) graphene nanoplatelets (GNPs) resting on the Kerr foundation. The FG-GNP plates were assumed to have two horizontal variable edges according to the sine function. Four different configurations of the FG-GNP plates based on the number of cycles of sine function were analyzed. The material characteristics of the GNPs were evaluated in terms of two models called the Halpin–Tsai micromechanical model and the rule of mixtures. First, to verify this method, the natural frequencies of new non-rectangular plates made of metal were compared with those obtained by the Finite Element Method (FEM). Then, the numerical outcomes are validated by comparing with the previous papers for rectangular FGM/GNP plates — a special case of this structure. Furthermore, the impacts of the thermal environment, geometrical parameters, and the elastic foundation on the dynamical responses are scrutinized by the 2D/3D graphical results and coded in Wolfram-Mathematica. The results of this work proved that the introduced approach has the advantages of being fast, having high accuracy, and involving uncomplicated calculation.

scholarly journals Nonlinear Dynamic Analysis for Rectangular FGM Plates with Variable Thickness Subjected to Mechanical Load

2019 ◽  
Vol 35 (3) ◽  
Author(s):  
Khuc Van Phu ◽  
Le Xuan Doan ◽  
Nguyen Van Thanh
Keyword(s):  
Variable Thickness ◽  
Nonlinear Dynamic ◽  
Volume Fraction ◽  
Mechanical Load ◽  
Plate Theory ◽  
Geometrical Nonlinearity ◽  
Nonlinear Dynamic Analysis ◽  
Dynamic Responses ◽  
Rectangular Plates ◽  
Classical Plate Theory

 In this paper, the governing equations of rectangular plates with variable thickness subjected to mechanical load are established by using the classical plate theory, the geometrical nonlinearity in von Karman-Donnell sense. Solutions of the problem are derived according to Galerkin method. Nonlinear dynamic responses, critical dynamic loads are obtained by using Runge-Kutta method and the Budiansky–Roth criterion. Effect of volume-fraction index k and some geometric factors are considered and presented in numerical results.

A Study on Adhesively Bonded Aluminum Plates Under Shock-Wave Loading

2017 ◽  
Author(s):  
Salih Yildiz ◽  
Yiannis Andreopoulos ◽  
Robert E. Jensen ◽  
Daniel Shaffren ◽  
Doug Jahnke ◽  
...  
Keyword(s):  
Shock Wave ◽  
Plate Theory ◽  
Dissimilar Materials ◽  
Laminated Plates ◽  
Shock Wave Loading ◽  
Wave Loading ◽  
Classical Plate Theory ◽  
Film Adhesive ◽  
Aluminum Plates ◽  
Application Fields

Adhesive joint technology has been developed gradually, and the application fields of this type of joints have been expanded increasingly since they reduce the weight of the applications, provide uniform stress distribution across the joints, allow to bond similar, and dissimilar materials, and contribute to dampen the shock, and vibration. However, the performance of the adhesive joints under high loading rate such as blast or ballistic loading has been studied by few researchers. In this study, fully laminated plates consisting of 6061 aluminum plates (15” in diameter and 1/16” thick) and FM300K epoxy film adhesive were tested under shock wave loading. Full displacement field over the testing plates were obtained by TRC-SDIC technique, and the strain on the plates were computed by classical plate theory for large deflections. FEM model was analyzed and the results were compared with experimental results.

Determination of vibration of single-layered graphene sheets using nonlocal modified couple stress theory

2021 ◽  
pp. 2250011
Author(s):  
F. Attar ◽  
R. Khordad ◽  
A. Zarifi
Keyword(s):  
Couple Stress ◽  
Plate Theory ◽  
Couple Stress Theory ◽  
Nonlocal Parameter ◽  
Modified Couple Stress Theory ◽  
Length Scale ◽  
Vibration Modes ◽  
Classical Plate Theory ◽  
Stress Theory ◽  
Modified Couple Stress

The free vibration of single-layered graphene sheet (SLGS) has been studied by nonlocal modified couple stress theory (NMCS), analytically. Governing equation of motion for SLGS is obtained via thin plate theory in conjunction with Hamilton’s principle for two cases: (1) using nonlocal parameter only for stress tensor, (2) using nonlocal parameter for both stress and couple stress tensors. Navier’s approach has been used to solve the governing equations for simply supported boundary conditions. It is found that the frequency ratios decrease with increasing nonlocal parameter and also with enhancing vibration modes, but increase with raising length scale parameter. The nonlocal and length scale parameters are more prominent in higher vibration modes. The obtained results have been compared with the previous studies obtained by using classical plate theory, the modified couple stress theory and nonlocal elasticity theory, separately.

A Non-Classical Analytical Approach for Vibration Analysis of Isotropic and Fgm Plate Containing a Star Shaped Crack

2020 ◽  
Vol 36 (4) ◽  
pp. 465-484
Author(s):  
Ankur Gupta ◽  
Shashank Soni ◽  
N. K. Jain
Keyword(s):  
Governing Equation ◽  
Vibration Analysis ◽  
Plate Theory ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Multiple Cracks ◽  
Arbitrary Orientation ◽  
Response Curves ◽  
Classical Plate Theory ◽  
Orientation Gradient

ABSTRACTA non-classical analytical model for vibration analysis of thin isotropic and FGM plate containing multiple part-through cracks (star shaped) of arbitrary orientation is proposed. A plate containing four concentric cracks of arbitrary orientation in the form of continuous line is considered for analysis. The proposed governing equation is derived based on classical plate theory and modified couple stress theory. Line spring model is modified to accommodate all the crack terms. The application of Berger’s formulation introduces nonlinearities in the governing equation and then the Galerkin’s method is applied for solving final governing equation. Results for fundamental frequencies for different values of crack length, crack orientation, gradient index and material length scale parameters are presented for two different boundary conditions. Furthermore, to study the phenomenon of bending hardening/softening in a cracked plate, the frequency response curves are plotted for the parameters stated above. Based on the outcomes of this study, it can be concluded that stiffness of the plate is severely affected by the presence of multiple cracks and the stiffness goes on decreasing with increase in number of cracks thereby affecting the fundamental frequency.

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