开孔粘弹性薄板的非线性数学模型

THE NONLINEAR MATHEMATICAL MODELS OF PERFORATED VISCOELASTIC THIN PLATES

应力函数的多值性和位移单值性要求,是开孔薄板大挠度问题中必须注意的两个方面。本文利用线粘弹性力学中的Boltzmann蠕变律,把开孔弹性薄板大挠度问题的一般数学理论推广到开孔粘弹性薄板。在考察应力函数的多值性和位移单值性条件的基础上,提出了开孔粘弹性薄板的控制方程和初、边值条件,系统地建立了开孔粘弹性薄板非线性分析的三类初一边值问题。

The multivaluedness of the stress function and the single-valuedness conditions of the displacements in the midle-plane have to be paid more attention to in the analysis for perforated thin plates with large deflections. In this paper, the general mathematical theory of perforated elastic thin plates with large deflections - has been generalized to the nonlinear analysis for perforated viscoelastic thin plates by means of the Boltzmann's creep law in linear viscoelasticity. The governing equations, initial conditions and boundary conditions of the nonlinear analysis of perforated viscoelastic thin plates have been given on the basis of the analysis for the multivaluedness of the stress function and the single-valuedness conditions of the displacements. The three kinds of single-valued initial-boundary value problems of the nonlinear analysis for perforated viscoelastic thin plates have been established systematically.