On the anticlastic curvature in free edges and the corner transverse shear in soft simply-supported edges in anisotropic rectangular thick plates

2017 ◽  
Author(s):  
Tales de Vargas Lisbôa ◽  
Rogério José Marczak
Keyword(s):  
Transverse Shear ◽  
Thick Plates ◽  
Simply Supported ◽  
Anticlastic Curvature ◽  
Free Edges

The Bending of a Long Strip Reinforced by Transverse Ribs

1965 ◽  
Vol 69 (650) ◽  
pp. 131-133
Author(s):  
G. G. Pope
Keyword(s):  
Middle Surface ◽  
Elastic Strip ◽  
Finite Deflection ◽  
Engineering Applications ◽  
Surface Stresses ◽  
Small Deflection ◽  
Cylindrical Form ◽  
Deflection Analysis ◽  
Anticlastic Curvature ◽  
Free Edges

When a long unreinforced flat elastic strip with free edges is bent to a uniform curvature about transverse axes in its own plane, anticlastic curvature is produced due to the influence of Poisson's ratio. Provided that the applied curvature is sufficiently small, the anticlastic curvature is constant across the strip and is proportional to the applied curvature. A finite deflection analysis shows, however, that the anticlastic deformation is reduced by the action of middle surface stresses, and the deformed strip approaches asymptotically a cylindrical form as the applied curvature is increased. Nevertheless, in some engineering applications it is necessary to limit the anticlastic deformation when the applied curvature is small, and for this purpose transverse ribs can be attached to the strip. In this note a small deflection analysis is given of the effect of uniformly spaced rigid ribs on the deformation of such a strip.

scholarly journals Frequency Equations and Modes of Free Vibrations of Rectangular Plates with Various Edge Conditions

1994 ◽  
Vol 208 (5) ◽  
pp. 307-319 ◽  
Author(s):  
C W Bert ◽  
M Malik
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Free Vibrations ◽  
Edge Condition ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Edge Conditions ◽  
Classical Boundary ◽  
Free Edges

This paper considers linear free vibrations of thin isotropic rectangular plates with combinations of the classical boundary conditions of simply supported, clamped and free edges and the mathematically possible condition of guided edges. The total number of plate configurations with the classical boundary conditions are known to be twenty-one. The inclusion of the guided edge condition gives rise to an additional thirty-four plate configurations. Of these additional cases, twenty-one cases have exact solutions for which frequency equations in explicit or transcendental form may be obtained. The frequency equations of these cases are given and, for each case, results of the first nine mode frequencies are tabulated for a range of the plate aspect ratios.

End Effects in Laminated Anisotropic Beams — Part I

1995 ◽  
Vol 117 (4) ◽  
pp. 279-284
Author(s):  
J. A. Ackermann ◽  
T. J. Kozik
Keyword(s):  
Stress Field ◽  
Normal Stress ◽  
Transverse Shear ◽  
Analytical Method ◽  
Normal Load ◽  
End Effects ◽  
Laminated Beam ◽  
Simply Supported ◽  
Combination Of Material

The derivation of an analytical method to examine the stress field near the end of a simply supported, laminated beam is presented. Specific effort has been directed to accurately calculate the transverse-shear and normal stress by incorporating the exact displacement relations derived, by Kozik (1970). The method accommodates any combination of material lay-up and any type of normal load on the upper and lower surfaces. The reactions at the ends of the beam may be distributed over the surface edges in a fashion most accurately characterizing the physical supports. The solution and application of the method is presented in Part II of this paper.

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