Determination op the geometric characteristics of shells of revolution satisfying finite strain compatibility conditions

1978 ◽  
Vol 42 (2) ◽  
pp. 341-346
Author(s):  
B.A Gorlach
Keyword(s):  
Finite Strain ◽  
Shells Of Revolution ◽  
Compatibility Conditions ◽  
Strain Compatibility ◽  
Geometric Characteristics

Thermal Stress Analysis of a Multi-Layered Structure

2011 ◽  
Vol 467-469 ◽  
pp. 275-278
Author(s):  
Shiuh Chuan Her ◽  
Chin Hsien Lin
Keyword(s):  
Analytical Model ◽  
Layered Structure ◽  
Thermal Stresses ◽  
Closed Form Solution ◽  
Beam Theory ◽  
Form Solution ◽  
Bernoulli Beam ◽  
Compatibility Conditions ◽  
Strain Compatibility ◽  
Good Agreement

Analytical model based on the Bernoulli beam theory and strain compatibility conditions at the interfaces between the two layers have been developed to predict the distribution of thermal stresses within the multi-layered structure due to the mismatch of thermal expansion. The closed-form solution of thermal stresses related to the material properties and geometry were obtained. It is useful to provide a simple and efficient analytical model, so that the stress level in the layers can be accurately estimated. The analytical results are compared with finite element results. Good agreement demonstrates that the proposed approach is able to provide an efficient way for the calculation of the thermal stresses.

Diffusion of incremental loads in prestrained bars

1992 ◽  
Vol 439 (1907) ◽  
pp. 583-600 ◽  
Keyword(s):  
Finite Strain ◽  
Integration Method ◽  
Broad Class ◽  
Large Strains ◽  
Infinite Strip ◽  
Compatibility Equation ◽  
Axial Diffusion ◽  
Strain Compatibility ◽  
Linear Elastic ◽  
Finite Strain Theory

Axial diffusion of perturbed fields generated by concentrated traction rates applied to the surface of a prestrained bar are examined within the framework of finite strain theory. The analysis centres on a plane-strain compatibility equation for a stress rate potential. This formulation covers a broad class of elastic and elastoplastic solids at large strains. A family of elemental rate boundary-value problems for concentrated incremental loads are solved exactly in terms of Fourier integrals. This is done in the spirit of earlier studies by Filon and von Kármán for linear elastic materials. Numerical examples for the Blatz–Ko constitutive relation reveal that the rate of axial diffusion has a strong sensitivity to the level of prestrain. Of special interest here is the surprising redistribution of the perturbed transversely symmetric stress rates for axial strains near necking. This behaviour is accompanied by considerable reduction in the rate of axial diffusion. A similar pattern is displayed by antisymmetric disturbances near the stress free configuration. These findings are supported by an asymptotic expansion based on the residue integration method. At a distance from the applied loads, axial diffusion is dominated by the exponential decay of the first self-equilibrating eigenfunction of the associated end problem for a semi-infinite strip.

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