横观各向同性板的分解理论

THE DECOMPOSED THEOREM OF THE TRANSVERSELY ISOTROPIC ELASTIC PLATE

将分解理论从各向同性板推广至横观各向同性板,得到横观各向同性板的分解理论,即横观各向同性板 内应力状态可以分解成内应力状态、剪切应力状态和超越应力状态,并给出严格的数学证明.

In 1992, Gregory gave a rigorous proof about the decomposed form when stress is anti-symmetrical about the mid-plane. His proof is dependent on his previous work, i.e., the Papkovich-Fadle eigenfunction expansion of bi-orthogonal functions. In this paper, we generalize isotropic elastic plate to transversely isotropic elastic plate. And give the decomposed theorem of the transversely isotropic elastic plate, ie. the general state of stress in the plate can be decomposed three parts: the interior state, the shear state and the transcendental state. Our proof is concise and direct and independent of the Papkovich-Fadle eigenfunction expansion of bi-orthogonal functions.