共查询到18条相似文献,搜索用时 125 毫秒
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为克服传统的有限元耦合无限元方法中的单元匹配问题,研究了径向基点插值法和无限元法的耦合规律,提出了一种预报无限域结构振动噪声的径向基点插值无网格与可变阶无限声波包络单元耦合方法,推导了预报声压的计算公式。为提高声场预报精度和满足声波在无限域的自由衰减,结构外部无限声场分为使用无网格表示的近场和可变阶声波包络单元离散的远场。在该耦合方法中,通过在近场与远场之间的交界面上配置虚拟网格来构造具有连续性的声压形函数,确保了声压的连续与一致性。采用数值仿真和试验对该耦合方法进行了验证,结果表明该耦合方法拥有无网格法的高精度和可变阶声波包络单元法满足声波自由衰减的特点,具有良好的精度和收敛性,可用于实际噪声预报。 相似文献
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轴对称动力学问题的无网格自然邻接点Petrov-Galerkin法 总被引:2,自引:0,他引:2
基于无网格自然邻接点Petrov-Galerkin法,提出了复杂轴对称动力学问题求解的一条新途径。几何形状和边界条件的轴对称特点,将原来的空间问题转化为平面问题求解。计算时仅仅需要横截面上离散节点的信息,无论积分还是插值都不需要网格。自然邻接点插值构造的试函数具有Kronecker delta函数性质,因此能够直接准确地施加本质边界条件。有限元三节点三角形单元的形函数作为权函数,可以减少域积分中被积函数的阶次,提高了计算效率。数值算例结果表明,本文提出的方法对求解轴对称动力学问题是行之有效的。 相似文献
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本文针对传统无单元Galerkin方法不能直接施加本质边界条件的缺点,提出了基于多边形支持域的无单元Galerkin方法.该方法将计算点的支持域由矩形或圆形扩展为多边形,使得移动最小二乘形函数满足Kronecker函数性质,进而使无单元Galerkin方法可以直接施加本质边界条件.此外,该方法将积分背景网格与多边形支持域关联,可以避免重复的节点搜索,提高了无单元Galerkin方法的计算效率.数值结果表明,基于多边形支持域的无单元Galerkin方法不但具有较高的计算效率,且与稳定化方案耦合,可以成功克服对流占优引起的数值不稳定问题. 相似文献
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自然单元法主要是基于给定结点的Voronoi图,利用自然相邻插值进行形函数的构造,其形函数满足Kronecker delta性质,便于施加本质边界条件,这使得自然单元法同时兼有有限单元法和无网格法的优点。在材料非线性本构关系的基础上,推导了考虑材料非线性问题的自然单元法模型。算例表明:该模型在处理材料非线性问题时,具有一定的合理性和可行性,是一种有效的数值方法。 相似文献
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扩展有限元法利用了非网格重剖分技术,但需要基于裂尖解析解构造复杂的插值基函数,计算精度受网格疏密和插值基函数等因素影响。比例边界有限元法则在求解无限域和裂尖奇异性问题优势明显,两者衔接于有限元法理论内,可建立一种结合二者优势的断裂耦合数值模型。该文从虚功原理出发,利用位移协调与力平衡机制,提出了一种断裂计算的新方法X-SBFEM,达到了扩展有限元模拟裂纹主体、比例边界有限元模拟裂尖的目的。在数值算例中,通过边裂纹和混合型裂纹的应力强度因子计算,并与理论解对比,验证了该方法的准确性和有效性。 相似文献
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The natural element method (NEM) is a meshless method. The trial and test functions of the NEM are constructed using natural neighbor interpolations which are based on the Voronoi tessellation of a set of nodes. The NEM interpolation is linear between adjacent nodes on the boundary of the convex hull, which makes imposition of essential boundary conditions easy to implement. We investigate the performance of the NEM combined with the Newmark method for problems of elastodynamics in this article. Applications are considered for a cantilever beam with different initial load conditions. The NEM numerical results are compared with the finite element method. NEM shows promise for these applications. 相似文献
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有限元极限分析法发展及其在岩土工程中的应用 总被引:37,自引:0,他引:37
有限元极限分析法兼有数值分析法与经典极限分析法两者的优点,特别适用于岩土工程的分析与设计。20世纪初,国内岩土工程界应用国际上通用程序,大力发展有限元极限分析法并拓宽其在岩土工程中的应用。在基本理论研究、提高计算精度、拓宽应用范围及工程实际应用等方面取得了很大成绩。重点介绍作者及其合作者的一些研究成果。主要包括岩土工程安全系数定义、方法原理、整体失稳判据、强度准则的推导、选用及提高计算精度等方面的研究。应用范围从二维扩大到三维,从均质土坡、土基扩大到有节理的岩质边坡与岩基,从稳定渗流扩大到不稳定渗流、从边坡与地基工程扩大到隧道、还用于寻找边(滑)坡中的多个潜在滑面,进行岩土与结构共同作用的支挡结构设计,计算机仿真地基承载板载荷试验等应用项目,以逐渐达到革新岩土工程设计方法的目的。 相似文献
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B. Calvo M. A. Martinez M. Doblar 《International journal for numerical methods in engineering》2005,62(2):159-185
In this paper, an extension of the natural element method (NEM) is presented to solve finite deformation problems. Since NEM is a meshless method, its implementation does not require an explicit connectivity definition. Consequently, it is quite adequate to simulate large strain problems with important mesh distortions, reducing the need for remeshing and projection of results (extremely important in three‐dimensional problems). NEM has important advantages over other meshless methods, such as the interpolant character of its shape functions and the ability of exactly reproducing essential boundary conditions along convex boundaries. The α‐NEM extension generalizes this behaviour to non‐convex boundaries. A total Lagrangian formulation has been employed to solve different problems with large strains, considering hyperelastic behaviour. Several examples are presented in two and three dimensions, comparing the results with the ones of the finite element method. NEM performs better showing its important capabilities in this kind of applications. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
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The natural element method (NEM) is a special meshless method. Its shape functions are constructed using natural neighbor node interpolations based on the concepts of Voronoi tessellation. The NEM interpolation is linear between adjacent nodes on the boundary of the convex hull, which facilitates imposition of essential boundary conditions. However, for a three-dimensional problem, the computation of shape function derivative of NEM is still very complicated even with the non-Sibson interpolation function, which makes the NEM an unpopular numerical method. In this paper, we adopt the direct mathematical derivative technique, and after some rigorous deduction, finally obtain the shape function derivative expression of three-dimensional NEM. Compared with the Lasserre algorithm, this algorithm is more intuitionistic and can be conveniently programmed. The NEM numerical results for cantilever beams verify the correctness of the shape function derivative expression of NEM derived in this paper. 相似文献
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某矿Ⅱ号矿体7-9线-55m中段采区稳定性研究 总被引:1,自引:1,他引:0
采用工程地质力学方法、岩土工程实验技术和有限元数值分析计算方法,综合研究了某矿Ⅱ号矿体7-9线-55m中段以上采区系统的稳定性和采场结构;改进和优化了采场结构参数,确定了合理的回采顺序和回采方案,从而保障了在该矿采掘过程中的安全性和可靠性. 相似文献
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Hyun‐Gyu Kim 《International journal for numerical methods in engineering》2003,56(15):2279-2312
A new method is proposed to place local meshes in a global mesh with the aid of the interface‐element method (IEM). The interface‐elements use moving least‐square (MLS)‐based shape functions to join partitioned finite‐element domains with non‐matching interfaces. The supports of nodes are defined to satisfy the continuity condition on the interfaces by introducing pseudonodes on the boundaries of interface regions. Particularly, the weight functions of nodes on the boundaries of interface regions span only neighbouring nodes, ensuring that the resulting shape functions are identical to those of adjoining finite‐elements. The completeness of the shape functions of the interface‐elements up to the order of basis provides a reasonable transfer of strain fields through the non‐matching interfaces between partitioned domains. Taking these great advantages of the IEM, local meshes can be easily inserted at arbitrary places in a global mesh. Several numerical examples show the effectiveness of this technique for modelling of local regions in a global domain. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
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单位分解增强自然单元法计算应力强度因子 总被引:2,自引:2,他引:0
自然单元法是一种新兴的无网格数值计算方法,但应用于裂纹问题计算时,其近似函数并不能准确反映裂纹尖端附近应力场的奇异性,需要在缝尖附近增大结点布置密度以获得一定的计算精度。在单位分解框架下将缝尖渐近位移场函数嵌入到自然单元法近似函数中,应用伽辽金过程获得平衡方程的离散线性方程,用相互作用能量积分方法计算了混合模式裂纹的应力强度因子。算例分析表明:单位分解增强自然单元法可以方便地处理裂纹问题,在不增加结点布置密度的情况下可有效提高应力强度因子的计算精度。 相似文献
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Thomas Most 《International journal for numerical methods in engineering》2007,71(2):224-252
The element-free Galerkin method (EFG) and the natural element method (NEM) are two well known and widely used meshless methods. Whereas the EFG method can represent moving boundaries like cracks only by modifying the weighting functions the NEM requires an adaptation of the nodal set-up. But on the other hand the NEM is computationally more efficient than EFG. In this paper a new concept for the automatic adjustment of nodal influence domains in the EFG method is presented in order to obtain an efficiency similar to the NEM. This concept is based on the definition of natural neighbours for each meshless node which can be determined from a Voronoi diagram of the nodal set-up. In this approach adapted nodal influence domains are obtained by interpolating the distances to the natural neighbours depending on the direction. In the paper we show that this concept leads, especially for problems with grading node density, to a reduced number of influencing nodes at the interpolation points and consequently a significant reduction of the numerical effort. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献