The method of the reciprocal theorem of forced vibration for the elastic thin rectangular plates (III)— Cantilever rectangular plates

1991 ◽  
Vol 12 (7) ◽  
pp. 663-680
Author(s):  
Fu Bao-lian ◽  
Li Nong
Keyword(s):  
Forced Vibration ◽  
Reciprocal Theorem ◽  
Rectangular Plates ◽  
The Reciprocal Theorem

Reciprocal theorem method for the forced vibration of elastic thick rectangular plates

1998 ◽  
Vol 19 (2) ◽  
pp. 191-205
Author(s):  
Li Huijian ◽  
Fu Baolian ◽  
Tan Wenfeng
Keyword(s):  
Forced Vibration ◽  
Reciprocal Theorem ◽  
Rectangular Plates ◽  
Reciprocal Theorem Method

The Reciprocal Theorem

1992 ◽  
pp. 281-289
Author(s):  
J. R. Barber
Keyword(s):  
Reciprocal Theorem ◽  
The Reciprocal Theorem

Nonlinear forced vibration of hybrid composite rectangular plates

2014 ◽  
Vol 2 (3) ◽  
pp. 209-228 ◽  
Author(s):  
Alireza Shooshtari ◽  
Soheil Razavi
Keyword(s):  
Forced Vibration ◽  
Hybrid Composite ◽  
Rectangular Plates ◽  
Nonlinear Forced Vibration

Boundary Conditions for Torsional Circular Shaft with Two-Dimensional Dodecagonal Quasicrystals

2012 ◽  
Vol 580 ◽  
pp. 411-414
Author(s):  
Bao Sheng Zhao ◽  
Di Wu
Keyword(s):  
Boundary Conditions ◽  
Necessary Conditions ◽  
Reciprocal Theorem ◽  
Interior Solution ◽  
Two Dimensional ◽  
Circular Shaft ◽  
Analysis Technique ◽  
State Boundary ◽  
The Reciprocal Theorem ◽  
Layer Solution

Through generalizing the method of a decay analysis technique determining the interior solution developed by Gregory and Wan, a set of necessary conditions on the end-data of torsional circular shaft in two-dimensional dodecagonal quasicrystals (2D dodecagonal QCs) for the existence of a rapidly decaying solution is established. By accurate solutions for auxiliary regular state, using the reciprocal theorem, these necessary conditions for the end-data to induce only a decaying elastostatic state (boundary layer solution) will be translated into appropriate boundary conditions for the torsional circular shaft in 2D dodecagonal QCs. The results of the present paper enable us to establish a set of boundary conditions.

Development of a Three-Dimensional Semi-Analytical Elastic-Plastic Contact Code

2002 ◽  
Vol 124 (4) ◽  
pp. 653-667 ◽  
Author(s):  
C. Jacq ◽  
D. Ne´lias ◽  
G. Lormand ◽  
D. Girodin
Keyword(s):  
Three Dimensional ◽  
Indentation Test ◽  
Closed Form Expression ◽  
Reciprocal Theorem ◽  
Plastic Strains ◽  
Surface Geometry ◽  
Fe Method ◽  
Elastic Plastic ◽  
Fine Mesh ◽  
The Reciprocal Theorem

A three-dimensional elastic-plastic contact code based on semi-analytical method is presented and validated. The contact is solved within a Hertz framework. The reciprocal theorem with initial strains is then introduced, to express the surface geometry as a function of contact pressure and plastic strains. The irreversible nature of plasticity leads to an incremental formulation of the elastic-plastic contact problem, and an algorithm to solve this problem is set up. Closed form expression, which give residual stresses and surface displacements from plastic strains, are obtained by integration of the reciprocal theorem. The resolution of the elastic-plastic contact using the finite element (FE) method is discussed, and the semi-analytical code presented in this paper is validated by comparing results with experimental data from the nano-indentation test. Finally, the resolution of the rolling elastic-plastic contact is presented for smooth and dented surfaces and for a vertical or rolling loading. The main advantage of this code over classical FE codes is that the calculation time makes the transient analysis of three-dimensional contact problems affordable, including when a fine mesh is required.

Sign in / Sign up

Export Citation Format

Share Document