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1.
This paper presents a general method for dynamic particle refinement in smoothed particle hydrodynamics (SPH). Candidate particles are split into several ‘daughter’ particles according to a given refinement pattern centred about the original particle. Through the solution of a non‐linear minimization problem the optimal mass distribution of the daughter particles is obtained so as to reduce the errors introduced to the underlying density field. This procedure necessarily conserves the mass of the system. Conservation of energy and momentum results are also discussed. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
2.
Antonio Huerta Sonia Fernndez‐Mndez 《International journal for numerical methods in engineering》2000,48(11):1615-1636
A mixed hierarchical approximation based on finite elements and meshless methods is presented. Two cases are considered. The first one couples regions where finite elements or meshless methods are used to interpolate: continuity and consistency is preserved. The second one enriches a finite element mesh with particles. Thus, there is no need to remesh in adaptive refinement processes. In both cases the same formulation is used, convergence is studied and examples are shown. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
3.
F. B. Barros S. P. B. Proena C. S. de Barcellos 《International journal for numerical methods in engineering》2004,60(14):2373-2398
This paper addresses the issue of a p‐adaptive version of the generalized finite element method (GFEM). The technique adopted here is the equilibrated element residual method, but presented under the GFEM approach, i.e., by taking into account the typical nodal enrichment scheme of the method. Such scheme consists of multiplying the partition of unity functions by a set of enrichment functions. These functions, in the case of the element residual method are monomials, and can be used to build the polynomial space, one degree higher than the one of the solution, in which the error functions is approximated. Global and local measures are defined and used as error estimator and indicators, respectively. The error indicators, calculated on the element patches that surrounds each node, are used to control a refinement procedure. Numerical examples in plane elasticity are presented, outlining in particular the effectivity index of the error estimator proposed. Finally, the ‐adaptive procedure is described and its good performance is illustrated by the last numerical example. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
4.
Suvranu De Klaus‐Jürgen Bathe 《International journal for numerical methods in engineering》2001,51(3):275-292
The displacement‐based formulation of the method of finite spheres is observed to exhibit volumetric ‘locking’ when incompressible or nearly incompressible deformations are encountered. In this paper, we present a displacement/pressure mixed formulation as a solution to this problem. We analyse the stability and optimality of the formulation for several discretization schemes using numerical inf–sup tests. Issues concerning computational efficiency are also discussed. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
5.
J. Bonet S. Kulasegaram 《International journal for numerical methods in engineering》2000,47(6):1189-1214
Smooth particle hydrodynamics (SPH) is a robust and conceptually simple method which suffers from unsatisfactory performance due to lack of consistency. The kernel function can be corrected to enforce the consistency conditions and improve the accuracy. For simplicity in this paper the SPH method with the corrected kernel is referred to as corrected smooth particle hydrodynamics (CSPH). The numerical solutions of CSPH can be further improved by introducing an integration correction which also enables the method to pass patch tests. It is also shown that the nodal integration of this corrected SPH method suffers from spurious singular modes. This spatial instability results from under integration of the weak form, and it is treated by a least‐squares stabilization procedure which is discussed in detail in Section 4. The effects of the stabilization and improvement in the accuracy are illustrated via examples. Further, the application of CSPH method to metal‐forming simulations is discussed by formulating the governing equation associated with the process. Finally, the numerical examples showing the effectiveness of the method in simulating metal‐forming problems are presented. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
6.
I Made Wiragunarsa;Lavi Rizki Zuhal;Tatacipta Dirgantara;Ichsan Setya Putra; 《International journal for numerical methods in engineering》2024,125(7):e7431
Total Lagrangian SPH (TLSPH) offers many advantages that can overcome instability and computational time issues. However, it is not naturally applicable to problems with contact. Many problems in solid dynamics and structural analysis require contact definition. In order to use the total Lagrangian formulation, further development for the contact algorithm is required. This research proposes an algorithm to implement inter-particle contact in TLSPH using an adaptive hybrid-kernel scheme for the first time. A combination of the updated and total Lagrangian formulations at the contact surface is introduced, in which the kernel type change automatically when particles from a different body are detected. In kernel change from the updated to the total Lagrangian formulation, the gradient correction cannot be performed using a common correction method because different frames of reference are used. Therefore, a hybrid-kernel correction technique is proposed to maintain the zeroth- and first-order completeness. Then, the contact force is obtained from the inter-particle force using the conservation of momentum. The proposed method does not require a user-defined parameter that makes the application straightforward. Based on the test, the proposed method agrees well with the data available in published literature and the finite element method. Compared with the contact method in classical SPH, the proposed TLSPH shows a significant stability improvement. 相似文献
7.
Javier Bonet Sivakumar Kulasegaram 《International journal for numerical methods in engineering》2001,52(11):1203-1220
The paper discusses the problem of tension instability of particle‐based methods such as smooth particle hydrodynamics (SPH) or corrected SPH (CSPH). It is shown that tension instability is a property of a continuum where the stress tensor is isotropic and the value of the pressure is a function of the density or volume ratio. The paper will show that, for this material model, the non‐linear continuum equations fail to satisfy the stability condition in the presence of tension. Consequently, any discretization of this continuum will result in negative eigenvalues in the tangent stiffness matrix that will lead to instabilities in the time integration process. An important exception is the 1‐D case where the continuum becomes stable but SPH or CSPH can still exhibit negative eigenvalues. The paper will show that these negative eigenvalues can be eliminated if a Lagrangian formulation is used whereby all derivatives are referred to a fixed reference configuration. The resulting formulation maintains the momentum preservation properties of its Eulerian equivalent. Finally a simple 1‐D wave propagation example will be used to demonstrate that a stable solution can be obtained using Lagrangian CSPH without the need for any artificial viscosity. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
8.
B. Maurel A. Combescure 《International journal for numerical methods in engineering》2008,76(7):949-971
This paper introduces a new modeling method suitable for the simulation of shell fracture under impact. This method relies on an entirely meshless approach based on the smoothed particle hydrodynamics (SPH) method. The paper also presents the SPH shell formulation being used as well as the different test cases used for its validation. A plasticity model of the global type throughout the thickness is also proposed and validated. Finally, in order to illustrate the capabilities of the method, fracture simulations using a simplified fracture criterion are presented. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
9.
F. Caleyron A. Combescure S. Potapov 《International journal for numerical methods in engineering》2012,90(6):707-738
This paper presents a meshless method for the modeling of shell‐type structures in fast dynamics. The model is based on the Mindlin–Reissner theory and takes into account material and geometric nonlinearities. The phenomena that occur prior to rupture are dealt with using damage laws, while the rupture itself is represented through the introduction of sharp discontinuities. The method does not represent cracks explicitly, which makes the treatment of multicracking easier. The time discretization is carried out in the framework of explicit dynamics, and the spatial discretization is handled through the smoothed particles hydrodynamics method and the use of moving least square functions. The capabilities of the method are demonstrated using cracking, puncturing and fragmentation examples. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
10.
Long Cu Ngo Hyoung Gwon Choi 《International journal for numerical methods in engineering》2017,110(10):947-971
An adaptive mesh refinement (AMR) technique is proposed for level set simulations of incompressible multiphase flows. The present AMR technique is implemented for two‐dimensional/three‐dimensional unstructured meshes and extended to multi‐level refinement. Smooth variation of the element size is guaranteed near the interface region with the use of multi‐level refinement. A Courant–Friedrich–Lewy condition for zone adaption frequency is newly introduced to obtain a mass‐conservative solution of incompressible multiphase flows. Finite elements around the interface are dynamically refined using the classical element subdivision method. Accordingly, finite element method is employed to solve the problems governed by the incompressible Navier–Stokes equations, using the level set method for dynamically updated meshes. The accuracy of the adaptive solutions is found to be comparable with that of non‐adaptive solutions only if a similar mesh resolution near the interface is provided. Because of the substantial reduction in the total number of nodes, the adaptive simulations with two‐level refinement used to solve the incompressible Navier–Stokes equations with a free surface are about four times faster than the non‐adaptive ones. Further, the overhead of the present AMR procedure is found to be very small, as compared with the total CPU time for an adaptive simulation. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
11.
J. Yvonnet P. Villon F. Chinesta 《International journal for numerical methods in engineering》2006,66(7):1125-1152
In this paper, a new approach is proposed to address issues associated with incompressibility in the context of the meshfree natural element method (NEM). The NEM possesses attractive features such as interpolant shape functions or auto‐adaptive domain of influence, which alleviates some of the most common difficulties in meshless methods. Nevertheless, the shape functions can only reproduce linear polynomials, and in contrast to moving least squares methods, it is not easy to define interpolations with arbitrary approximation consistency. In order to treat mechanical models involving incompressible media in the framework of mixed formulations, the associated functional approximations must satisfy the well‐known inf–sup, or LBB condition. In the proposed approach, additional degrees of freedom are associated with some topological entities of the underlying Delaunay tessellation, i.e. edges, triangles and tetrahedrons. The associated shape functions are computed from the product of the NEM shape functions related to the original nodes. Different combinations can be used to construct new families of NEM approximations. As these new approximations functions are not related to any node, as they vanish at the nodes, from now on we refer these shape functions as bubbles. The shape functions can be corrected enforcing different reproducing conditions, when they are used as weights in the moving least square (MLS) framework. In this manner, the effects of the obtained higher approximation consistency can be evaluated. In this work, we restrict our attention to the 2D case, and the following constructions will be considered: (a) bubble functions associated with the Delaunay triangles, called b1‐NEM and (b) bubble functions associated with the Delaunay edges, called b2‐NEM. We prove that all these approximation schemes allow direct enforcement of essential boundary conditions. The bubble‐NEM schemes are then used to approximate the displacements in the linear elasticity mixed formulation, the pressure being approximated by the standard NEM. The numerical LBB test is passed for all the bubble‐NEM approximations, and pressure oscillations are removed in the incompressible limit. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
12.
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
13.
T. BELYTSCHKO M. TABBARA 《International journal for numerical methods in engineering》1996,39(6):923-938
The element-free Galerkin method for dynamic crack propagation is described and applied to several problems. This method is a gridless method, which facilitates the modelling of growing crack problems because it does not require remeshing; the growth of the crack is modelled by extending its surfaces. The essential feature of the method is the use of moving least-squares interpolants for the trial-and-test functions. In these interpolants, the dependent variable is obtained at any point by minimizing a weighted quadratic form involving the nodal variables within a small domain surrounding the point. The discrete equations are obtained by a Galerkin method. The procedures for modelling dynamic crack propagation based on dynamic stress intensity factors are also described. 相似文献
14.
Weilong Ai Charles E. Augarde 《International journal for numerical methods in engineering》2016,108(13):1626-1648
Computational modelling of fracture has been attempted in the past with a range of numerical approaches including finite element, extended finite element and meshless methods. The cracking particle method (CPM) of Rabczuk is a pragmatic alternative to explicit modelling of crack surfaces in which a crack is represented by a set of cracking particles that can be easily updated when the crack propagates. The change of cracking angle is recorded in discrete segments of broken lines, which makes this methodology suitable to model discontinuous cracks. In this paper, a new CPM is presented that improves on two counts: firstly, crack path curvature modelling is improved by the use of bilinear segments centred at each particle and secondly, efficiency for larger problems is improved via an adaptive process of both refinement and recovery. The system stiffness is calculated and stored in local matrices, so only a small influenced domain should be recalculated for each step while the remainder can be read directly from storage, which greatly reduces the computational expense. The methodology is applied to several 2D crack problems, and good agreement to analytical solutions and previous work is obtained. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
15.
H. Huang C. T. Dyka S. Saigal 《International journal for numerical methods in engineering》2004,61(13):2250-2272
The dual particle dynamic (DPD) methods which employ two sets of particles have been demonstrated to have better accuracy and stability than the co‐locational particle methods, such as the smooth particle hydrodynamics (SPH). The hybrid particle method (HPM) is an extension of the DPD method. Besides the advantages of the DPD method, the HPM possesses features which better facilitate the simulation of large deformations. This paper presents the continued development of the HPM for the numerical solution of two‐dimensional frictionless contact problems. The interface contact force algorithm which employs a modified kinematic constraints method is used to determine the contact tractions. In this method, both the impenetrability condition and the traction condition are simultaneously enforced. In the original kinematic constraints method, only the former condition is satisfied. A new formulation to find stress derivatives at stress‐free corners by imposing stress‐free boundary conditions is also developed. The results for 1‐D and 2‐D contact problems indicate good accuracy for the contact formulation as well as the corner treatment when compared to analytical solutions and explicit finite element results using the commercial code LS‐DYNA. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
16.
Probabilistic theories aim at describing the properties of systems subjected to random excitations by means of statistical characteristics such as the probability density function ψ (pdf). The time evolution of the pdf of the response of a randomly excited deterministic system is commonly described with the transient Fokker–Planck–Kolmogorov (FPK) equation. The FPK equation is a conservation equation of a hypothetical or abstract fluid, which models the transport of probability. This paper presents a generalized formalism for the resolution of the transient FPK equation by using the well‐known mesh‐free Lagrangian method, smoothed particle hydrodynamics). Numerical implementation shows notable advantages of this method in an unbounded state space: (1) the conservation of total probability in the state space is explicitly written; (2) no artifact is required to manage far‐field boundary conditions; (3) the positivity of the pdf is ensured; and (4) the extension to higher dimensions is straightforward. Furthermore, thanks to the moving particles, this method is adapted for a large kind of initial conditions, even slightly dispersed distributions. The FPK equation is solved without any a priori knowledge of the stationary distribution, just a precise representation of the initial distribution is required.Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
17.
Mostafa Safdari Shadloo Amir Zainali Mehmet Yildiz Afzal Suleman 《International journal for numerical methods in engineering》2012,89(8):939-956
This paper presents a comparative study for the weakly compressible (WCSPH) and incompressible (ISPH) smoothed particle hydrodynamics methods by providing numerical solutions for fluid flows over an airfoil and a square obstacle. Improved WCSPH and ISPH techniques are used to solve these two bluff body flow problems. It is shown that both approaches can handle complex geometries using the multiple boundary tangents (MBT) method, and eliminate particle clustering‐induced instabilities with the implementation of a particle fracture repair procedure as well as the corrected SPH discretization scheme. WCSPH and ISPH simulation results are compared and validated with those of a finite element method (FEM). The quantitative comparisons of WCSPH, ISPH and FEM results in terms of Strouhal number for the square obstacle test case, and the pressure envelope, surface traction forces, and velocity gradients on the airfoil boundaries as well as the lift and drag values for the airfoil geometry indicate that the WCSPH method with the suggested implementation produces numerical results as accurate and reliable as those of the ISPH and FEM methods. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
18.
O. J. B. Almeida Pereira J. P. Moitinho de Almeida 《International journal for numerical methods in engineering》2010,83(3):347-365
In this paper, we summarize how dual analysis techniques can be used to determine upper bounds of the discretization error, both in terms of global and local outputs. We present formulas for the bounds of the error in local outputs, based on the approach proposed by Greenberg in 1948 and we show that the resulting intervals are the same as those previously presented, based on the approach proposed by Washizu in 1953. We then explain how the elemental contributions to these bounds can be used to define an adaptive strategy that considers multiple quantities and we present its application to a simple plane stress problem. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
19.
S. Liapis 《Engineering Analysis with Boundary Elements》1994,14(4):315-323
When using the boundary element method, the accuracy of the numerical solution depends critically on the discretization of the boundary into elements (panels). The distribution of the panels is one of the most important decisions taken when analyzing a problem, but still the vast majority of users employ empirical guidelines to distribute the panels. This paper reviews the various adaptive schemes that have been proposed for boundary elements. Numerical results are obtained for infinite fluid flow problems and free surface problems and are used to assess the reliability and effectiveness of each method. 相似文献
20.
目的 随着爬壁机器人技术的发展,为解决其产品应用化问题,对爬壁机器人的研究进展进行梳理、分析和归纳,讨论未来的发展方向,为设计应用于高危环境和特殊场景的爬壁机器人提供思路和参考。方法 将爬壁机器人按移动方式分为履带式、轮式、足式及混合式,通过文献研究法对不同移动方式的爬壁机器人进行综述;将真空吸附、磁吸附、推力吸附等不同吸附方式的爬壁机器人进行对比,介绍了爬壁机器人自适应技术的研究现状及存在问题;总结并分析了爬壁机器人在工业、军事等领域的发展趋势。结论 总结了不同移动方式的爬壁机器人的国内外研究现状,分析了爬壁机器人不同吸附方式的优缺点,归纳预测了爬壁机器人的发展方向。 相似文献