【作者】 秦桐；

【导师】 秦洪德；

【作者基本信息】 哈尔滨工程大学 ， 船舶与海洋结构物设计制造， 2011， 硕士

【摘要】 无网格法是一门新兴的数值计算方法,和有限元方法相比,它在对系统进行分析时可以消除或者部分消除单元网格的约束,从而在处理如高速碰撞,大变形,裂纹扩展等类型的问题时显示出了其优越性。在动力学问题中,常常伴随着上面所述的各种问题,因此采用无网格法对动力学问题进行分析显然是适合的。本文介绍了无网格方法的基本理论,并着重对无网格伽辽金法(Element-Free Galerkin Method,以下简称EFG法)的流程体系和影响因素进行了分析和讨论；然后,基于EFG法的理论推导了采用无网格法离散动力学问题系统方程的过程,给出了振动问题无网格系统方程的形式和求解方法；最后,将无网格法应用于动力学中的另一个重要领域——接触碰撞问题,详细介绍了碰撞问题的无网格分析方法,并提出了采用无网格与有限元结合的方法分析大型船舶碰撞问题的观点,为大型船舶碰撞问题的研究提出了新的思路。本文编制了无伽辽金法的计算机程序,应用程序对一些算例进行了分析,算例的类型涵盖了静力学问题,振动问题以及接触碰撞问题。计算结果与影响因素分析充分证明无网格算法的可靠性和所编制程序的正确性,在理论上和应用上都具有一定的价值。通过本文的论述,证明了将无网格法应用于振动问题和碰撞问题是完全可行的,无网格法在动力学领域中具有广泛的应用前景。更多还原

【Abstract】 Meshless method is a newly arisen kind of numerical method. Compare with Finite Element Method (FEM), it can eliminate or partly eliminate the bond lead by element mesh during the process of analyzing. For which it shows the advantage in dealing with issues such as high-speed impact, large deformation, dynamic crack growth, etc. Problems likes above usually come about in dynamics area so that it seems obviously adapted to make analysis of dynamics by using meshless method.This paper firstly makes a summarization in meshless method and process system and influencing factors of Element-Free Galerkin Method (EFG) are analyzed and discussed based on the meshless method theories; And then from the same way,meshless-form function and its solving processes of vibration problem are derived; At last this paper makes application of meshless method into another important area of dynamics-contact impact problems, and detailedly introduces the analyzing process of contact impact problems by using meshless method. Furthermore a new thoughts is given that it is a good way to combine the meshless and FE methods to solving large-scale ship collision problems.In this paper, some examples containing statics, vibration, and contact impact problems are analyzed by the EFG program. The analysis results sufficiently proof both reliability of the method and correctness of the program. So it is completely feasible to make use of meshless method in analysis of vibration and contact impact problems and the prospect is broad.更多还原