Interval Finite Element Method and Its Application on Anti-Slide Stability Analysis
-
摘要: 通过区间值函数和实值函数的关系探讨了区间相关性导致的区间扩张的问题，给出了保证区间计算获得足够精度的计算方法；提出了基于单元的子区间摄动有限元计算方法，并给出了提高计算效率的一些方法和获得较好计算精度时的子区间数目的近似计算公式．结合工程实例，基于单元的子区间有限元方法和抗滑稳定性分析方法给出了稳定性的区间范围，为更合理地估计和评价结构的抗滑稳定性提供一定的依据．Abstract: The problem of interval correlation results in interval extension is discussed by the relationship of interva-lvalued functions and real-valued functions. The methods of reducing interval extension are given. Based on the ideas of the paper, the formulas of sub-interval perturbed finite element method based on the elements were given. The sub-interval amount is discussed and the approximate computation formula was given. At the same time, the computational precision was discussed and some measures of improving computational efficiency were given. Finally, based on sub-interval perturbed finite element method and anti-slide stability analysis method, the formula for computing the bounds of stability factor was given. Which will provide a basis for estimating and evaluating reasonably anti-slide stability of structures.
-
[1] Rao S S，Berke L. Analysis of uncertain structural systems using interval analysis[J].AIAA J，1997，35(4)：725-735. [2] QIU Zhi-ping，Elishakoff I. Anti-optimization of structures with large uncertain but non-random parameters via interval analysis[J].Computer Methods in Applied Mechanics and Engineering，1998，152(3/4)：361-372. doi: 10.1016/S0045-7825(96)01211-X [3] 邱志平，顾元宪. 有界不确定参数结构位移范围的区间摄动法[J]. 应用力学学报，1999，16(1)：1-10. [4] Mcwilliam S. Anti-optimization of uncertain structures using interval analysis[J].Computers and Structures，2001，79(4)：421-430. doi: 10.1016/S0045-7949(00)00143-7 [5] CHEN Su-huan,LIAN Hua-dong,YANG Xiao-wei.Interval static displacement analysis for structures with interval parameters[J].International Journal for Numerical Methods in Engineering，2002，53(2)：393-407. doi: 10.1002/nme.281 [6] 杨晓伟，陈塑寰，滕绍勇. 基于单元的静力区间有限元法[J]. 计算力学学报，2002，19(2)：179-183. [7] QIU Zhi-ping.Comparison of static response of structures using convex models and interval analysis method[J].International Journal for Numerical Methods in Engineering，2003，56(12)：1735-1753. doi: 10.1002/nme.636 [8] 邱志平，陈塑寰，刘中生.区间参数结构振动问题的矩阵摄动法[J].应用数学和力学，1994，15(6)：519-527. [9] 邱志平，顾元宪，王寿梅. 有界参数结构特征值的上下界定理[J]. 力学学报，1999，31(4)：466-474. [10] QIU Zhi-ping，WANG Xia-jun. Comparison of dynamic response of structures with uncertain-but-bounded parameters using non-probabilistic interval analysis method and probabilistic approach[J].International Journal of Solids and Structures，2003，40(20)：5423-5439. doi: 10.1016/S0020-7683(03)00282-8 [11] 吴杰，陈塑寰. 区间参数振动系统的动力优化[J]. 力学学报，2003，35(3)：373-376. [12] Ben-Haim Y. A non-probabilistic concept of reliability[J].Structure Safety，1994，14(4):227-245. doi: 10.1016/0167-4730(94)90013-2 [13] 郭书祥. 非随机不确定结构的可靠性方法和优化设计研究[D]. 西安：西北工业大学，2002. [14] Nakagiri S，Suzuki K. Finite element interval analysis of external loads identified by displacement input with uncertainty[J].Computers Methods in Applied Mechanics and Engineering，1999，168(1)：63-72. doi: 10.1016/S0045-7825(98)00134-0 [15] 王登刚，刘迎曦，李守巨，等. 巷道围岩初始应力场和弹性模量的区间反演方法[J]. 岩石力学与工程学报，2002，21(3)：305-308. [16] 王登刚，刘迎曦，李守巨.混凝土坝振动参数区间逆分析[J].大连理工大学学报,2002,42(5)：522-526. [17] 刘世君，徐卫亚，王红春，等. 岩石力学参数的区间参数摄动反分析方法[J].岩土工程学报，2002，24(6)：760-763. [18] 仝凌云，杨钊. 区间数和泛灰数在区间分析中的比较[J]. 河北工业大学学报，2001，30(4)：93-96. -
计量
- 文章访问数: 2613
- HTML全文浏览量: 144
- PDF下载量: 583
- 被引次数: 0
下载:
渝公网安备50010802005915号