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Solutions are obtained using Ritz minimization techniques with constant curvature shape functions.
The curvature shape of each modal sensor/actuator fiber can be determined by solving a differential equation.
The influence of initial curvature shape and size variability of the member axis on the variability of load-carrying capacity is investigated.
For thoroughness, various types of local 3D shape indicators have been considered, such as mean curvature, Gaussian curvature, shape index and curvedness, as well as their fusion.
One characteristic that has proved suitable for damage identification and location is the operational curvature shape which exhibits changing features at locations of stiffness change.
Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time.
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A method that finds theses features, SIDER, employs an algorithm that operates on broadband operational curvature shapes.
The analytical expressions derived for mode shapes, curvature shapes, natural frequencies and an improved strain energy based damage measure, are verified using experiments.
The procedure is a two-dimensional generalization of a previously published one-dimensional gapped smoothing method, whereby local features in vibration curvature shapes are extracted using a localized curve fit (i.e., smoothing).
Frequency response functions are individually measured between each excitation point and the reference accelerometers, and the required operating curvature shapes are determined from the resulting array of frequency response functions.
Remarkably, the constant-curvature shape, indeed the most used, provokes shear stress concentrations in the interlayer with consequent risks of delamination.
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