Macroapproach Closed-Form Series Solution for Orthotropic Plates

In this article, a new analytical technique called Improved Parker-Sochacki Method (IPSM) for solving nonlinear Michaelis-Menten enzyme catalyzed reaction model is proposed. The global form of the solution for the concentrations of the substrate, enzyme and the enyzme-free product are obtained. Employing the Laplace-Pade resummation as a post processing technique on the computed series solution, the domain of convergence of the solution is greatly extended. The solution is therefore devoid of limited convergence interval that is typical of series solution of nonlinear differential equations. The proposed method showed a significant improvement over the conventional Parker-Sochacki Method (PSM). Furthermore, comparison of the results with numerically computed solutions elucidated the simplicity and accuracy of the proposed method.

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On the Shear Buckling of Clamped Narrow Rectangular Orthotropic Plates

Mathematical Problems in Engineering ◽

10.1155/2015/569356 ◽

2015 ◽

Vol 2015 ◽

pp. 1-11 ◽

Cited By ~ 1

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.

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The Flexural Vibration of Rectangular Orthotropic Plates

Journal of Applied Mechanics ◽

10.1115/1.3564566 ◽

1969 ◽

Vol 36 (1) ◽

pp. 101-106 ◽

Cited By ~ 35

Author(s):

S. M. Dickinson

Keyword(s):

Free Vibration ◽

Series Solution ◽

Flexural Vibration ◽

Numerical Results ◽

Sine Series ◽

Orthotropic Plates ◽

Isotropic Plates ◽

Support Conditions

A sine series solution previously used for the study of the flexural vibration of rectangular isotropic plates is extended to apply to the free vibration of orthotropic plates. Application to three particular plates with different support conditions is given and numerical results are presented for two of these examples. Where possible, the numerical results presented are compared with values given by other writers.

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Closed Form Solutions for Vibration and Sound Radiation of Orthotropic Plates under Thermal Environment

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455418500980 ◽

2018 ◽

Vol 18 (07) ◽

pp. 1850098 ◽

Cited By ~ 9

Author(s):

Kai Zhou ◽

Jinpeng Su ◽

Hongxing Hua

Keyword(s):

Closed Form ◽

Orthotropic Plate ◽

Acoustic Analysis ◽

Thermal Environment ◽

Separation Of Variables ◽

Closed Form Solution ◽

Form Solution ◽

Thermal Loads ◽

Orthotropic Plates ◽

Heated Plates

This paper presents a closed form solution for the vibration and acoustic problem of orthotropic plates under a thermal environment. Hamilton’s principle is utilized to derive the governing equation of motion for the orthotropic plate with thermal loads, which is then solved by the method of separation of variables. The frequency equations and mode functions obtained for the orthotropic heated plates with at least two adjacent edges clamped are much simpler than those by the conventional methods. Several numerical examples are carried out for the modal, dynamic and acoustic analysis of orthotropic heated plates with different combinations of thermal loads and boundary conditions. The results of the parametric study for the orthotropic plate with different thermal loads are discussed in detail. The validity of the present formulation is confirmed by comparing the results obtained with the numerical ones. Due to its accuracy, efficiency and versatility, the present method offers an efficient tool for the structural and acoustic analysis of the orthotropic plate under the thermal environment.

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