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  • 1
    Electronic Resource
    Electronic Resource
    Element-free Galerkin method for contact problems in metal forming analysis (2001)
    Bradford : Emerald
    Engineering computations 18 (2001), S. 62-78 
    Details
    ISSN: 0264-4401
    Source: Emerald Fulltext Archive Database 1994-2005
    Topics: Technology
    Notes: The total Lagrangian formulation and implementation of the element-free Galerkin method (EFG) is presented for the analysis of contact-impact problems with large deformations and for the simulation of metal forming processes. An integration scheme based on stress points is used, so no mesh is needed. A simple but general contact searching algorithm is used to treat the contact interface and an algorithm for the contact force is presented. Numerical results for Taylor bar impact are compared to finite element solutions and agree well. Solutions to upsetting, extrusion of metals with large material distortions are given to show the effectiveness of the algorithm. In particular, EFG is shown to be more capable of treating motions of the workpiece around corners of the punch than finite element methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1108/02644400110365806
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Self-Similar Crack Expansion method for the stress intensity factor analysis (1996)
    Springer
    Acta mechanica solida Sinica 9 (1996), S. 104-123 
    Details
    ISSN: 0894-9166
    Keywords: self-similar crack expansion ; stress intensity factor ; crack extension method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The Self-Similar Crack Expansion(SSCE) method is proposed to evaluate stress intensity factors at crack tips, whereby stress intensity factors of a crack can be determined by the crack opening displacement over the crack, not just by the local displacement around the crack tip. The crack expansion rate is estimated by taking advantage of the crack self-similarity. Therefore, the accuracy of the calculation is improved. The singular integrals on crack tip elements are also analyzed and are precisely evaluated in terms of a special integral analysis. Combination of these two techniques greatly increases the accuracy in estimating the stress distribution around the crack tip. A variety of two-dimensional cracks, such as subsurface cracks, edge cracks, and their interactions are calculated in terms of the self-similar expansion rate. Solutions are satisfied with errors less than 0. 5% as compared with the analytical solutions. Based on the calculations of the crack interactions, a theory for crack interactions is proposed such that for a group of aligned cracks the summation of the square of SIFs at the right tips of cracks is always equal to that at the left tips of cracks. This theory was proved by the mehtod of Self-Similar Crack Expansion in this paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02209156
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A Self-Similar Crack Expansion method for three-dimensional cracks in an infinite or semi-infinite medium (1996)
    Springer
    Acta mechanica solida Sinica 9 (1996), S. 217-235 
    Details
    ISSN: 0894-9166
    Keywords: self-similar crack expansion ; stress intensity ; crack extension method ; 3-D cracks
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The Self-Similar Crack Expansion (SSCE) method is used to calculate stress intensity factors for three-dimensional cracks in an infinite medium or semi-infinite medium by the boundary integral element technique, whereby, the stress intensity factors at crack tips are determined by calculating the crack-opening displacements over the crack surface. For elements on the crack surface, regular integrals and singular integrals are precisely evaluated based on closed form expressions, which improves the accuracy. Examples show that this method yields very accurate results for stress intensity factors of penny-shaped cracks and elliptical cracks in the full space, with errors of less than 1% as compared with analytical solutions. The stress intensity factors of subsurface cracks are in good agreement with other analytical solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02208305
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  • 4
    Electronic Resource
    Electronic Resource
    Numerical integration of the Galerkin weak form in meshfree methods (1999)
    Springer
    Computational mechanics 23 (1999), S. 219-230 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The numerical integration of Galerkin weak forms for meshfree methods is investigated and some improvements are presented. The character of the shape functions in meshfree methods is reviewed and compared to those used in the Finite Element Method (FEM). Emphasis is placed on the relationship between the supports of the shape functions and the subdomains used to integrate the discrete equations. The construction of quadrature cells without regard to the local supports of the shape functions is shown to result in the possibility of considerable integration error. Numerical studies using the meshfree Element Free Galerkin (EFG) method illustrate the effect of these errors on solutions to elliptic problems. A construct for integration cells which reduces quadrature error is presented. The observations and conclusions apply to all Galerkin methods which use meshfree approximations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004660050403
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  • 5
    Electronic Resource
    Electronic Resource
    Reproducing kernel particle methods for structural dynamics (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 1655-1679 
    Details
    ISSN: 0029-5981
    Keywords: smooth particle hydrodynamics ; wavelets ; elastic-plastic large deformation ; tensile instability ; correction function ; aliasing control ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper explores a Reproducing Kernel Particle Method (RKPM) which incorporates several attractive features. The emphasis is away from classical mesh generated elements in favour of a mesh free system which only requires a set of nodes or particles in space. Using a Gaussian function or a cubic spline function, flexible window functions are implemented to provide refinement in the solution process. It also creates the ability to analyse a specific frequency range in dynamic problems reducing the computer time required. This advantage is achieved through an increase in the critical time step when the frequency range is low and a large window is used. The stability of the window function as well as the critical time step formula are investigated to provide insight into RKPMs. The predictions of the theories are confirmed through numerical experiments by performing reconstructions of given functions and solving elastic and elastic-plastic one-dimensional (1-D) bar problems for both small and large deformation as well as three 2-D large deformation non-linear elastic problems. Numerical and theoretical results show the proposed reproducing kernel interpolation functions satisfy the consistency conditions and the critical time step prediction; furthermore, the RKPM provides better stability than Smooth Particle Hydrodynamics (SPH) methods. In contrast with what has been reported in SPH literature, we do not find any tensile instability with RKPMs.
    Additional Material: 21 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620381005
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Explicit Reproducing Kernel Particle Methods for large deformation problems (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 41 (1998), S. 137-166 
    Details
    ISSN: 0029-5981
    Keywords: meshless methods ; reproducing kernel particle methods ; large deformation ; non-linear elasticity ; underwater bubble dynamics ; reference configuration ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The explicit Reproducing Kernel Particle Method (RKPM) is presented and applied to the simulations of large deformation problems. RKPM is a meshless method which does not need a mesh structure in its formulation. Because of this mesh-free property, RKPM is able to simulate large deformation problems without remeshing which is often required for the mesh-based methods such as the finite element method. The RKPM shape function and its derivatives are constructed by imposing the consistency conditions. An efficient treatment of essential boundary conditions is also proposed for explicit time integration. The Lagrangian method based on the reference configuration is employed for the RKPM simulation of large deformation problems. Several examples of non-linear elastic materials are solved to demonstrate the performance of the method. The numerical experiment for the problem of underwater bubble explosion is also performed using the explicit Lagrangian RKPM formulation. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
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