无单元法在结构动力计算中的应用及与有限元精度的比较
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摘要
本文论述无单元法在结构动力计算应用中的一些关键技术问题,并对无单元法和有限元法进行了比较,特别是通过实际算例对二者的计算精度进行了比较。结果表明:无单元解的精度始终和理论解保持高度一致,而有限元解(例如ANSYS软件)对简单轴力杆件和欧拉梁在高阶振型上有一定的误差。当二者同时应用于某一实际工程时,由于可以只采用低阶振型,因而相差较小,从而证实了无单元法在结构动力计算中更加简便、精确和实用。
This paper introduces the problems of critical technique in structural dynamic computation with element-free Galerkin method(EFGM),and EFGM is compared with finite element method(FEM),especially the comparison of computation precision bewteen EFGM and FEM.The result shows that the precision based on EFGM is approximate to the theoretical solution greatly all the time,but the solution based on FEM(taking ANSYS for example) exists with a certain error in higher vibration of simple pole and Euler beam.When both EFGM and FEM are applied to a practical engineering at the same time,the distinction between the two methods is smaller. It shows that EFGM applied to structural dynamic computation is more easy and convenient,more accurate and practical.
This paper introduces the problems of critical technique in structural dynamic computation with element-free Galerkin method(EFGM),and EFGM is compared with finite element method(FEM),especially the comparison of computation precision bewteen EFGM and FEM.The result shows that the precision based on EFGM is approximate to the theoretical solution greatly all the time,but the solution based on FEM(taking ANSYS for example) exists with a certain error in higher vibration of simple pole and Euler beam.When both EFGM and FEM are applied to a practical engineering at the same time,the distinction between the two methods is smaller. It shows that EFGM applied to structural dynamic computation is more easy and convenient,more accurate and practical.
引文
[1]Lu Y Y,Belytschko T,Gu L.A new implementation of the element free Galerkin method[J].Computer Methods in Applied Mechanics andEngineering,1994,113:397~414.
[2]Nagashima Toshio.Node-by-node meshless approach and its applications to structural analysis[J].International Journal for NumericalMethods in Engineering,1995,38:1655~1679.
[3]李卧东,陈胜宏.结构振动分析中的无网格方法[J].计算力学学报.2003,20(6):756~762.LI Wodong,CHEN Shenghong.Meshless method in analysis of structure vibration[J].Journal of Computational Mechanics,2003,20(6):756~762.(in Chinese)
[4]周瑞忠,吴琛,周小平.求解结构动力响应的小波分解法[J].地震工程与工程振动,2005,25(6):43~48.ZHOU Ruizhong,WU Chen,ZHOU Xiaoping.Wavelet decomposition method for solution of structural dynamic response[J].EarthquakeEngineering and Engineering Vibrations,2005,25(6):43~48.(in Chinese)
[5]周瑞忠,周小平,缪圆冰.具有自适应影响半径的无单元法[J].工程力学.2001,18(6):94~100ZHOU Ruizhong,ZHOU Xiaoping,MIAO Yuanbing.Element-free Galerkin method with adaption influential radius[J].EngineeringMechanics,2001,18(6):94~100.(in Chinese)
[2]Nagashima Toshio.Node-by-node meshless approach and its applications to structural analysis[J].International Journal for NumericalMethods in Engineering,1995,38:1655~1679.
[3]李卧东,陈胜宏.结构振动分析中的无网格方法[J].计算力学学报.2003,20(6):756~762.LI Wodong,CHEN Shenghong.Meshless method in analysis of structure vibration[J].Journal of Computational Mechanics,2003,20(6):756~762.(in Chinese)
[4]周瑞忠,吴琛,周小平.求解结构动力响应的小波分解法[J].地震工程与工程振动,2005,25(6):43~48.ZHOU Ruizhong,WU Chen,ZHOU Xiaoping.Wavelet decomposition method for solution of structural dynamic response[J].EarthquakeEngineering and Engineering Vibrations,2005,25(6):43~48.(in Chinese)
[5]周瑞忠,周小平,缪圆冰.具有自适应影响半径的无单元法[J].工程力学.2001,18(6):94~100ZHOU Ruizhong,ZHOU Xiaoping,MIAO Yuanbing.Element-free Galerkin method with adaption influential radius[J].EngineeringMechanics,2001,18(6):94~100.(in Chinese)
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