Extension of higher-order infinitesimal bendings of a simply connected surface of positive curvature with boundary conditions

1990 ◽  
Vol 51 (5) ◽  
pp. 2528-2533
Author(s):  
S. B. Klimentov
Keyword(s):  
Boundary Conditions ◽  
Positive Curvature ◽  
Higher Order ◽  
Connected Surface ◽  
Simply Connected

Using the Multi-Parameter Fracture Mechanics for more Accurate Description of Stress/Displacement Crack Tip Fields

2013 ◽  
Vol 586 ◽  
pp. 237-240 ◽  
Author(s):  
Lucie Šestáková
Keyword(s):  
Stress Distribution ◽  
Fracture Mechanics ◽  
Boundary Conditions ◽  
Displacement Field ◽  
Singular Term ◽  
Crack Tip ◽  
Higher Order ◽  
Precise Description ◽  
Accurate Knowledge ◽  
Higher Order Terms

Most of fracture analyses often require an accurate knowledge of the stress/displacement field over the investigated body. However, this can be sometimes problematic when only one (singular) term of the Williams expansion is considered. Therefore, also other terms should be taken into account. Such an approach, referred to as multi-parameter fracture mechanics is used and investigated in this paper. Its importance for short/long cracks and the influence of different boundary conditions are studied. It has been found out that higher-order terms of the Williams expansion can contribute to more precise description of the stress distribution near the crack tip especially for long cracks. Unfortunately, the dependences obtained from the analyses presented are not unambiguous and it cannot be strictly derived how many of the higher-order terms are sufficient.

Stability of Thin Elastic Plates Covering an Arbitrary Simply Connected Region and Subject to any Admissible Boundary Conditions

1953 ◽  
Vol 20 (1) ◽  
pp. 23-29
Author(s):  
G. A. Zizicas
Keyword(s):  
Boundary Conditions ◽  
Direct Method ◽  
Elastic Plates ◽  
Simple Manner ◽  
Particular Solutions ◽  
Isotropic Plates ◽  
Simply Connected Region ◽  
Simply Connected ◽  
A Direct Method ◽  
Thin Elastic Plates

Abstract The Bergman method of solving boundary-value problems by means of particular solutions of the differential equation, which are constructed without reference to the boundary conditions, is applied to the problem of stability of thin elastic plates of an arbitrary simply connected shape and subject to any admissible boundary conditions. A direct method is presented for the construction of particular solutions that is applicable to both anisotropic and isotropic plates. Previous results of M. Z. Krzywoblocki for isotropic plates are obtained in a simple manner.

Free Vibration of Moderately Thick Conical Shells Using a Higher Order Shear Deformable Theory

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
R. D. Firouz-Abadi ◽  
M. Rahmanian ◽  
M. Amabili
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Higher Order ◽  
Arbitrary Boundary ◽  
Conical Shells ◽  
First Time ◽  
Circumferential Wave ◽  
Shear Deformable

The present study considers the free vibration analysis of moderately thick conical shells based on the Novozhilov theory. The higher order governing equations of motion and the associate boundary conditions are obtained for the first time. Using the Frobenius method, exact base solutions are obtained in the form of power series via general recursive relations which can be applied for any arbitrary boundary conditions. The obtained results are compared with the literature and very good agreement (up to 4%) is achieved. A comprehensive parametric study is performed to provide an insight into the variation of the natural frequencies with respect to thickness, semivertex angle, circumferential wave numbers for clamped (C), and simply supported (SS) boundary conditions.

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