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In this research, a new analytical solution is used for finding the buckling loads of rectangular plates with vertically and rotationally restrained edges. The solution method in this study is based on the development of a static solution for a plate. The solution is obtained in series form, and the coefficients are solved to match the edge conditions. The solution fits all the combinations of possible boundary conditions, of the deflection, slope, shear force and bending moment along the edges of the plate. In the case of springs, the edge force and moment boundary conditions are modified to include these effects. Any number of edges, from one to four, with both types of stiffening springs can be solved. Using this new method, the exact buckling loads and modes are found. The results are verified with published data, and many new cases are presented for uni-axially and bi-axially loaded isotropic, orthotropic, and composite plates.

A quasi-passive leg exoskeleton is presented for load-carrying augmentation during walking. The exoskeleton has no actuators, only ankle and hip springs and a knee variable-damper. Without a payload, the exoskeleton weighs 11.7 kg and requires only 2 Watts of electrical power during loaded walking. For a 36 kg payload, we demonstrate that the quasi-passive exoskeleton transfers on average 80% of the load to the ground during the single support phase of walking. By measuring the rate of oxygen consumption on a study participant walking at a self-selected speed, we find that the exoskeleton slightly increases the walking metabolic cost of transport (COT) as compared to a standard loaded backpack (10% increase). However, a similar exoskeleton without joint springs or damping control (zero-impedance exoskeleton) is found to increase COT by 23% compared to the loaded backpack, highlighting the benefits of passive and quasi-passive joint mechanisms in the design of efficient, low-mass leg exoskeletons.