| 高光藩,丁信伟.拱形金属薄膜非线性力学行为数学建模及其计算[J].计算力学学报,2004,21(5):625~629 |
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| 拱形金属薄膜非线性力学行为数学建模及其计算 |
| Mathematical modeling and simulation for nonlinear mechanical behavior of vaulted metallic membrane |
| 修订日期：2002-11-22 |
| DOI：10.7511/jslx20045111 |
| 中文关键词: 大变形 金属膜 数学模型 数值计算 |
| 英文关键词:large deformation,metallic membrane,mathematical models,numerical solution |
| 基金项目: |
| 高光藩 丁信伟 |
| 大连理工大学化工装备特种技术研究所,辽宁大连116012 |
| 摘要点击次数: 1144 |
| 全文下载次数: 8 |
| 中文摘要: |
| 对大变形金属薄膜结构塑性应力应交关系、几何关系和静力平衡关系进行整理和适当交换，将其转化成由3个微分方程和1个代数约束方程组成的初值问题的1阶微分代数方程。采用可变步长和交阶的Klopfenstein-Shampine数值微分方法和Newton-Raphson求解方法，可求得膜片任何位置在任意时刻的应力、应交和变形等力学参量，还可以估算出膜片的极限荷载。最后对一个实例作了数值分析，其计算结果与实验数据得到了较好的符合。 |
| 英文摘要: |
| A method for plastic large deformation analysis of circular metallic membrane subjected to lateral pressure was presented. Stress-strain relationships of plasticity, geometrical equations, and static equilibrium conditions were acquired. Then these expressions were transformed to initial-value problems in differential algebraic equations of index 1. Which consists of three ordinary differential equations and one algebraic constraint equation. Numerical solutions were carried out using the Newton-Raphson root-locating method and Klopfenstein-Shampine numerical differentiation formulas with varying step size and variable order. The stresses, strains, deformations of metallic membrane at specific times could be obtained and the ultimate pressure could also be estimated. Finally, numerical analysis for an example was completed. The comparison shows fairly close agreement between numerical and experimental results. |
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