Considered in this paper is the large deflection of a thin beam. One end of the beam is fixed (clamped) to a rigid wall, while the other end is placed on a flat surface of arbitrary orientation. It is shown that under certain conditions, the solution to the deflected shape of the plate is not unique. Conditions for the existence of multiple solutions are identified. Numerical methodologies are developed to obtain the multiple solutions. Experiments were conducted to verify the numerical predictions. Excellent agreements are found between the predicted deflection and the experimental measurements.

Considered in this paper is the large deflection of a thin beam. One end of the beam is fixed (clamped) to a rigid wall, while the other end is placed on a flat surface of arbitrary orientation. Under the assumption that the axial deformation of the neutral axis is negligible, a closed form analytical solution to the deflection curve is obtained in terms of elliptical functions. The analytical solution is shown to have certain scalability properties with respect to the beam length and cross-section. By using appropriate bending rigidity, the same solution can be used for a thin plate under large cylindrical bending. In addition, a finite element analysis using nonlinear shell elements is also conducted showing the axial strain of the neutral axis to be less than one percent of the overall deformation. Therefore, it is valid to assume that the axial strain is negligible.

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Considered in this paper is a special case relating to the large deflection of a thin beam. One end of the beam is fixed (i.e., clamped) to a rigid wall, whereas the other end is placed on a flat surface of arbitrary orientation. In previous studies, unique and non-unique solutions to the deflected shape were derived for cases in which the curvature of the beam experiences at least one change in sign. In this paper, a special case is examined in which the curvature of the beam does not change sign. Experimental results from photographs of deflected beams are presented to support the numerical predictions. An excellent agreement was found between the photographed and the predicted shapes.

The reliability of solder joints for surface mount components is closely related to the joint shape and "pedestal" (stand-off) height, i.e., the thickness of the fillet that separates the metallized surface of the component from the pad on the circuit board. In this paper, an analysis is presented to predict the profiles and pedestal heights of equilibrium solder joints that attach surface mount components to printed circuit boards. The common case of two-dimensional (2-D) joints with negligible solder density effects is considered. A criterion is also derived that represents the minimum critical volume of solder required to produce a "theoretically nonzero pedestal height," below which the model is inapplicable. The critical solder volume produces a convex joint. The criterion suggests that if a 2-D joint is concave and within the model simplifications, force equilibrium cannot exist on a component at a positive pedestal height. Extensions to cases in which solder density effects are significant are also discussed. The analysis results in a system of coupled nonlinear algebraic equations which are solved numerically. The sensitivity of joint shape and pedestal height to geometric and physical parameters is examined. Comparisons between the theory and experiment show good agreement.