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Unformatted text preview: Section 6.10 Solid Mechanics Part II Kelly 183 6.10 Limitations of Classical Plate Theory The validity of the classical plate theory depends on a number of factors: 1. the curvatures are small 2. the in-plane plate dimensions are large compared to the thickness 3. membrane strains can be neglected The second and third of these points are discussed briefly in what follows. 6.10.1 Moderately Thick Plates As with beam theory, and as mentioned already, it turns out that the solutions based on the classical theory agree well with the full elasticity solutions (away from the edges of the plate), provided the plate thickness is small relative to its other linear dimensions. When the plate is relatively thick, one is advised to use a more exact theory, for example one of the shear deformation theories: Shear deformation Theories The Mindlin plate theory ( or moderately thick plate theory or shear deformation theory ) was developed in the early-to-mid 1900s to allow for possible transverse shear strains. In this theory, there is the added complication that vertical line elements before deformation do not have to remain perpendicular to the mid-surface after deformation, although they do remain straight. Thus shear strains yz and zx are generated, constant through the thickness of the plate. The classical plate theory is inconsistent in the sense that elements are assumed to remain perpendicular to the mid-plane, yet equilibrium requires that stress components yz xz , still arise (which would cause these elements to deform). The theory of thick plates is more consistent, but it still makes the assumption that = zz . Note that both are approximations of the exact three-dimensional equations of elasticity....
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- Fall '11