粘弹性薄板准静态分析中一种时域算法

基金项目: 国家自然科学基金资助项目(19772027);上海市教育发展基金资助项目(99A01);上海市博士后基金资助项目(1999年度)

A Time Domain Method for Quasi-Static Analysis of Viscoelastic Thin Plates

Shanghai Institute of Applied Mathematics and Mechanics; Department of Mechanics, Shanghai University, Shanghai 200072, P R China

摘要: 基于线性粘弹性材料的Boltzmann叠加原理和大挠度薄板的von Kûrmûn假设,给出了粘弹性薄板准静态问题的数学模型。在空域上采用Galerkin方法可将原积分-偏微分系统化为积分系统,而在时域上利用本文所提出的新方法可将该积分系统化为微分系统。计算结果表明,新算法与常用的有限差分法相比操作简单,具有无存贮和计算快等优点。
- 粘弹性薄板 /
- von Kûrmûn假设 /
- Galerkin方法 /
- 准静态响应 /
- 直接法 /
- 积分-微分方程
Abstract: Based on the Boltzmann's superposition principles of linear viscoelastic materials and the von Kûrmûn's hypotheses of thin plates with large deflections,a mathematical model for quasi-static problems of viscoelastic thin plates was given.By the Galerkin method in spatial domain,the original integro-partial-differential system could be transformed into an integral system.The latter further was reduced to a differential system by using the new method for temporal domain presented in this paper.Numerical results show that compared with the ordinary finite difference method,the new method in this paper is simpler to operate and has some advantages,such as,no storage and quicker computational speed etc.
- viscoelastic thin plate /
- von Kûrmûn’s hypothesis /
- Galerkin method /
- quasi-static response /
- direct method /
- integro-differential equation

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