Abstract
In 1992, Gregory [1] gave a rigorous proof about the decomposed form when stress is anti-symmetrical about the mid-plane. His proof is dependent on his previous works [3], [4], i.e., the Papkovich-Fadle eigenfunction expansion of bi-harmonic functions. In this paper, we give a new proof concisely and directly, which is independent of the Papkovich-Fadle expansion, when stress is anti-symmetrical about the mid-plane. The general state of stress in the plate can be decomposed into three parts: the interior state, the shear state and the Papkovich-Fadle state.
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