عنوان مقاله
روش بدون شبکه و کاربردهایش در مسائل الاستوپلاستیکی
فهرست مطالب
چکیده
مقدمه
مرور RKPM
کاربرد RKPM در مسائل الاستو پلاستیکی
مطالعه موردی
نتیجه گیری
بخشی از مقاله
طبقه بندی و بررسی اجمالی روشهای بدون شبکه، با مزایا و معایبشان، در Matthies (2003) وFries مطرح شده اند. در میان این روشها، EFG وRKPM ، مناسب ترین راه حل برای آنالیز ساختاری به شمار می روند. با توجه به اینکهRKPM فرمولی عمومی برای ساخت توابع شکل روشهای بدون شبکه فراهم می کند، و تشخیص معادله حاصل شده، روشهایSPH وEFG را می توان بازیابی نمود.
کلمات کلیدی:
A meshfree method and its applications to elasto-plastic problems ZHANG Ji-fa (张继发) †1,2, ZHANG Wen-pu (张文普) 1,3, ZHENG Yao (郑 耀) 1,2 ( 1 Center for Engineering and Scientific Computation; 2 School of Computer Science; 3 Department of Mechanics, Zhejiang University, Hangzhou 310027, China) † E-mail: jifa_zhang@yahoo.com.cn Received Feb. 23, 2004; revision accepted June 21, 2004 Abstract: Standard finite element approaches are still ineffective in handling extreme material deformation, such as cases of large deformations and moving discontinuities due to severe mesh distortion. Among meshfree methods developed to overcome the ineffectiveness, Reproducing Kernel Particle Method (RKPM) has demonstrated its great suitability for structural analysis. This paper presents applications of RKPM in elasto-plastic problems after a review of meshfree methods and an introduction to RKPM. A slope stability problem in geotechnical engineering is analyzed as an illustrative case. The corresponding numerical simulations are carried out on an SGI Onyx3900 supercomputer. Comparison of the RKPM and the FEM under identical conditions showed that the RKPM is more suitable for problems where there exists extremely large strain such as in the case of slope sliding. Key words: Meshfree methods, RKPM, Elasto-plasticity, Geotechnical engineering doi:10.1631/jzus.2005.A0148 Document code: A CLC number: O241; TU31 INTRODUCTION Geotechnical engineering’s well-developed finite element methods (FEMs) for geometrical and material nonlinearities facilitated much of the work accomplished. Nevertheless, standard finite element approaches are still ineffective in handling extreme material deformation, such as cases of large deformations and moving discontinuities due to severe mesh distortion. In order to overcome the ineffectiveness, some FEMs, such as Arbitrary Lagrangian Eulerian (ALE) method, which allow continuous remeshing during computation, were introduced (Hirt, 1974) and developed (Hughes et al., 1981; Belytschko et al., 1982; Donea, 1983). However, more effort is still required to go around the problem of the oscillation caused by the convective effect (Chen et al., 1996). To deal with these disadvantages, a new family of numerical methods was developed. All methods in this family, such as Smooth Particle Hydrodynamics (SPH) (Lucy, 1977; Monaghan, 1982), Particle in Cell Methods (PIC) (Harlow, 1964; Brackbill, 1986; Sulsky et al., 1994), Diffuse Element Methods (DEM) (Nayroles et al., 1992), Element Free Galerkin Methods (EFG) (Belytschko et al., 1994; Lu et al., 1994) and Reproducing Kernel Particle Methods (RKPM) (Liu et al., 1995; 1997), share a common feature in that no mesh is required and shape functions are formulated based on nodes, which distribute in the domain we want. More detailed classification and overview of meshfree methods, with their advantages and disadvantages, are presented in Fries and Matthies (2003). Among these methods, the EFG and the RKPM have been demonstrated as most suitable for structural analysis. Taking into account that the RKPM provides a general formulation for the construction of shape functions for meshfree methods, with specific discretization of the reproduced equation, so that the SPH and the EFG methods can be recovered. We present only the implementation of RKPM in this paper. Chen et al.(1997) extended RKPM to hyper-elasticity with large deformation. In the present paper, after a brief introduction to the RKPM, we present a meshfree discretization method for elasto-plastic problems with the Drucker
