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The subject of this paper is the buckling behavior of thin bar stiffeners attached to plates which are subjected to normal pressure loadings. The stiffeners are mathematically modeled by a nonlinear beam theory recently derived. An analytical solution is obtained to the beam buckling equations. The curvature of the centerline along the beam's base at the buckling load is expressed in terms of the beam's thickness, height, and rotational stiffness. Analytical results are compared with an experiment recently performed.
General sinusoidal stiffness matrices for buckling and vibration analyses of thin flat-walled structures
Abstract This paper is concerned with the derivation of stiffness matrices for the buckling or vibration analysis of any structure consisting of a series of long, thin, flat plates rigidly connected together at their longitudinal edges. Each plate is assumed to be subjected to a basic state of plane stress which is longitudinally invariant, and it is further assumed that the mode of buckling or vibration varies sinusoidally in the longitudinal direction. During buckling or vibration, the edges of any individual plate are subjected to additional systems of forces and moments which are sinusoidally distributed along the edges, and these give rise to sinusoidally varying edge displacements and rotations. Spatial phase differences between the forces and displacements are accounted for by defining them in terms of complex quantities. The sinusoidal edge forces and displacements are split into two uncoupled systems, corresponding to out-of-plane and in-plane displacements, and two stiffness matrices are defined. The out-of-plane stiffness matrix is shown to be in general complex, and Hermitian in form, but the inplane stiffness matrix is real and symmetrical. Explicit expressions are derived for the elements of the matrices, in which all the essential destabilizing effects of the basic stresses, as well as dynamic effects, are included. Finally, it is shown that buckling and vibration phenomena for any structure of this type are closely interrelated.
New approach to vision-based BGA package inspection
Ball grid array (BGA) techniques have developed very fast due to the advantages of more I/O ports, small size, and so on. In this paper, a vision-based algorithm for BGA package inspection is proposed to accurately estimate center and diameters of solder-balls of BGA packages, so that defects of BGA packages, such as missing or extra balls, oversize or undersize balls, over-height or under-height balls, and pitch can be detected for ensuring the quality of BGA packages.