| 彭建设,罗光兵,杨杰.卷积型GD半解析法及矩形薄板瞬态响应解[J].计算力学学报,2011,28(4):535~539,589 |
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| 卷积型GD半解析法及矩形薄板瞬态响应解 |
| A convolution type GD semi-analytic approach for the transient response analysis of rectangular plates |
| 投稿时间：2010-02-02 修订日期：2010-09-19 |
| DOI：10.7511/jslx201104008 |
| 中文关键词: 卷积 瞬态响应 GD法 半解析法 |
| 英文关键词:convolution transient response general differential method semi-analytic method |
| 基金项目:四川省科技厅应用基础项目;四川省教育厅重点科研资助项目. |
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| 中文摘要: |
| 卷积型的Gurtin变分原理是目前在数学上唯一能和动力学初值问题完全等价的变分原理,它完全反映了有关初值问题的全部特征。GD法(General Differential Method)是从泰勒展开式出发,推出的一种求解偏微分方程的数值方法,本文系统地介绍了GD法的基本原理,以及权系数的推导。本文通过卷积将矩形薄板原始控制方程构造成包含初始条件的新的具有完整初值问题特征的控制方程。对新的控制方程在时间域取解析函数,在空间域采用离散的GD法,从而构造了卷积型GD半解析法。该方法既可以达到和Gurtin变分原理相同的效果,又避开了Gurtin泛函的繁复。计算表明,该方法是一种精度好效率高的求解动力响应问题的计算方法。 |
| 英文摘要: |
| The Gurtin variation principles of convolution type is the only variation principles which can makes the initial values of dynamics equivalent completely in math, it contains all the characters of initial values. The GDM (General Differential Method) is a numerical method solving partial differential equations based on Taylor series. The principle and coefficients are reduced in this paper. The equations of motion of thin rectangular plates are blended with initial conditions by the method of convolution calculation and form new equations, whose solutions are then sought through the use of GDM approximation in space domain and an analytical series expansion in time domain. This approach obtains the same effects with Gurtin variation principles, at the same time, it avoids the complexity of Gurtin functional. The results of the examples show that the method has excellent accuracy and efficiency for the resolution of dynamic response analysis. |
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