Application of the R-function method to nonlinear vibrations of thin plates of arbitrary shape

2005 ◽  
Vol 284 (1-2) ◽  
pp. 379-392 ◽  
Author(s):  
Lidia Kurpa ◽  
Galina Pilgun ◽  
Eduard Ventsel
Keyword(s):  
Arbitrary Shape ◽  
Function Method ◽  
Nonlinear Vibrations ◽  
Thin Plates

Nonlinear vibrations of rectangular laminated thin plates

AIAA Journal ◽  
1992 ◽  
Vol 30 (1) ◽  
pp. 180-188 ◽  
Author(s):  
Jongsik Woo ◽  
Sudhakar Nair
Keyword(s):  
Nonlinear Vibrations ◽  
Thin Plates

scholarly journals Calculation of Stress Intensity Factors for Elliptical Cracks in Finite Bodies by Using the Boundary Weight Function Method

1999 ◽  
Vol 121 (2) ◽  
pp. 181-187 ◽  
Author(s):  
C.-C. Ma ◽  
I-K. Shen
Keyword(s):  
Stress Intensity ◽  
Weight Function ◽  
Stress Intensity Factors ◽  
Arbitrary Shape ◽  
Function Method ◽  
Weight Functions ◽  
Mode I ◽  
Intensity Factors ◽  
Weight Function Method ◽  
Arbitrary Loading

In this study, mode I stress intensity factors for a three-dimensional finite cracked body with arbitrary shape and subjected to arbitrary loading is presented by using the boundary weight function method. The weight function is a universal function for a given cracked body and can be obtained from any arbitrary loading system. A numerical finite element method for the determination of weight function relevant to cracked bodies with finite dimensions is used. Explicit boundary weight functions are successfully demonstrated by using the least-squares fitting procedure for elliptical quarter-corner crack and embedded elliptical crack in parallelepipedic finite bodies. If the stress distribution of a cut-out parallelepipedic cracked body from any arbitrary shape of cracked body subjected to arbitrary loading is determined, the mode I stress intensity factors for the cracked body can be obtained from the predetermined boundary weight functions by a simple surface integration. Comparison of the calculated results with some available solutions in the published literature confirms the efficiency and accuracy of the proposed boundary weight function method.

Nonlinear Vibrations of Beams, Strings, Plates, and Membranes Without Initial Tension

2004 ◽  
Vol 71 (4) ◽  
pp. 551-559 ◽  
Author(s):  
Zhongping Bao ◽  
Subrata Mukherjee ◽  
Max Roman ◽  
Nadine Aubry
Keyword(s):  
Boundary Conditions ◽  
Young’S Modulus ◽  
Cross Sections ◽  
Nonlinear Vibrations ◽  
Young's Modulus ◽  
Thin Plates ◽  
Radius Of Gyration ◽  
Initial Tension ◽  
Various Boundary Conditions ◽  
Analytical Expressions

The subject of this paper is nonlinear vibrations of beams, strings (defined as beams with very thin uniform cross sections), plates and membranes (defined as very thin plates) without initial tension. Such problems are of great current interest in minute structures with some dimensions in the range of nanometers (nm) to micrometers (μm). A general discussion of these problems is followed by finite element method (FEM) analyses of beams and square plates with different boundary conditions. It is shown that the common practice of neglecting the bending stiffness of strings and membranes, while permissible in the presence of significant initial tension, is not appropriate in the case of nonlinear vibrations of such objects, with no initial tension, and with moderately large amplitude (of the order of the diameter of a string or the thickness of a plate). Approximate, but accurate analytical expressions are presented in this paper for the ratio of the nonlinear to the linear natural fundamental frequency of beams and plates, as functions of the ratio of amplitude to radius of gyration for beams, or the ratio of amplitude to thickness for square plates, for various boundary conditions. These expressions are independent of system parameters—the Young’s modulus, density, length, and radius of gyration for beams; the Young’s modulus, density, length of side, and thickness for square plates. (The plate formula exhibits explicit dependence on the Poisson’s ratio.) It is expected that these results will prove to be useful for the design of macro as well as micro and nano structures.

scholarly journals Green's Function Method for an Axisymmetric Void Between Parallel Walls

2007 ◽  
Vol 5 (2) ◽  
Author(s):  
Gautam Sudhir Chandekar ◽  
Joseph D. Richardson ◽  
Yuri A. Melnikov ◽  
Sally J. Pardue
Keyword(s):  
Finite Element ◽  
Green’S Function ◽  
Green's Function ◽  
Arbitrary Shape ◽  
Function Method ◽  
Numerical Solutions ◽  
Numerical Implementation ◽  
Finite Element Code ◽  
Present Formulation ◽  
Function Formulation

The Green's function for potential theory is developed for an axisymmetric void of arbitrary shape located between two parallel walls. Numerical results are given to demonstrate the accuracy in the Green's function formulation by comparison with numerical solutions obtained using a commercial finite element code. The present formulation is attractive since numerical implementation only involves unknowns on the surface of the void.

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