【摘要】：本文給出了一個(gè)建立在半測地坐標(biāo)系下的非線性彈性殼體的維數(shù)分裂方法,它把一個(gè)非線性彈性算子,在這個(gè)坐標(biāo)系下,分裂為一個(gè)稱為膜彈性算子和彎曲彈性算子之和.假設(shè)非線性彈性殼體的解可以展開為關(guān)于貫裁變量的Taylor級(jí)數(shù),那么本文建立了關(guān)于首項(xiàng)的2D-3C非線性偏微分方程組,證明其解的存在性,同時(shí)給出了兩個(gè)關(guān)于一階項(xiàng)和二階項(xiàng)對于首項(xiàng)的函數(shù),從而無需求解偏微分方程即可得到一階項(xiàng)和二階項(xiàng).
[Abstract]:In this paper, a dimension splitting method for nonlinear elastic shells based on semi-geodesic coordinate system is presented. It divides a nonlinear elastic operator into a sum of membrane elastic operator and bending elastic operator in this coordinate system. Assuming that the solution of a nonlinear elastic shell can be expanded into a Taylor series of intersecting variables, a 2D-3C nonlinear partial differential equation system for the first term is established, and the existence of the solution is proved. At the same time, two functions about the first order term and the second order term for the first term are given, so that the first order term and the second order term can be obtained without solving the partial differential equation.
【作者單位】： 西安交通大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院;燕山大學(xué)理學(xué)院;
【基金】：國家自然科學(xué)基金(91330115;11371289;11371288)~~
【分類號(hào)】：O343.5

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