Nội dung được dịch bởi AI, chỉ mang tính chất tham khảo
Phương pháp Petrov-Galerkin địa phương không lưới cho các chất viscoelastic tuyến tính không đồng nhất liên tục
Tóm tắt
Một phương pháp không lưới dựa trên cách tiếp cận Petrov-Galerkin địa phương được đề xuất để giải quyết các vấn đề tĩnh gần và động tạm thời trong môi trường viscoelastic tuyến tính không đồng nhất hai chiều (2-D). Một hàm bước đơn vị được sử dụng làm hàm kiểm tra trong dạng yếu địa phương. Phương pháp này dẫn đến các phương trình tích phân biên cục bộ (LBIEs) chỉ liên quan đến một tích phân miền trong trường hợp các vấn đề động tạm thời. Nguyên tắc ứng xử tương ứng được áp dụng cho các chất rắn viscoelastic không đồng nhất như vậy, trong đó các mô-đun thả lỏng có thể tách rời theo các biến không gian và thời gian. Sau đó, các LBIEs được hình thành cho vấn đề viscoelastic được biến đổi Laplace. Miền được phân tích được bao phủ bởi các miền con nhỏ với hình dạng đơn giản như các hình tròn trong các vấn đề 2-D. Phương pháp bình phương tối thiểu dịch chuyển (MLS) được sử dụng để xấp xỉ các đại lượng vật lý trong các LBIEs.
Từ khóa
#Phương pháp không lưới #Petrov-Galerkin #viscoelastic tuyến tính #phương trình tích phân biên cục bộ #phương pháp bình phương tối thiểu dịch chuyểnTài liệu tham khảo
Atluri SN (2004) The Meshless Method, (MLPG) For Domain BIE Discretizations, Tech Science Press
Atluri SN, Shen S (2002) The Meshless Local Petrov-Galerkin (MLPG) Method, Tech Science Press
Atluri SN, Sladek J, Sladek V, Zhu T (2000) The local boundary integral equation (LBIE) and its meshless implementation for linear elasticity. Comput Mech 25: 180–198
Atluri SN, Han ZD, Shen S (2003) Meshless local Petrov-Galerkin (MLPG) approaches for solving the weakly-singular traction & displacement boundary integral equations. CMES: Computer Modeling in Engineering & Sciences 4: 507–516
Balas J, Sladek J, Sladek V (1989) Stress Analysis by Boundary Element Methods, Elsevier, Amsterdam
Belytschko T, Lu Y, Gu L (1994) Element free Galerkin methods. Int J Num Meth Engn 37: 229–256
Belytschko T, Krogauz Y, Organ D, Fleming M, Krysl P (1996) Meshless methods; an overview and recent developments. Comput Meth Appl 139: 3–47
Chan YS, Gray LJ, Kaplan T, Paulino GH (2004) Green's function for a two-dimensional exponentially-graded elastic medium. Proc R Soc London A 460: 1689–1706
Christensen RM (1971) Theory of Viscoelasticity, Academia Press, New York
Divo E, Kassab AJ (2002) Boundary Element Method for Heat Conduction: with Applications in Non-Homogeneous Media Topics in Engineering Series vol. 44, WIT Press, Billerica, MA
Dominguez J (1993) Boundary Elements in Dynamics, Computational Mechanics Publications, Southampton
Gaul L, Schanz M (1994a) A viscoelastic boundary element formulation in time domain. Arch. Mechanics 46: 583–594
Gaul L, Schanz M (1994b) Dynamics of viscoelastic solids treated by boundary element approaches in time domain. Europ J Mechanics A/Solids 13: 43–59
Jin ZH, Paulino GH (2002) A viscoelastic functionally graded strip containing a crack subjected to in-plane loading. Engn Fracture Mechanics 69: 1769–1790
Kim JH, Paulino GH (2002) Isoparametric graded finite elements for nonhomogeneous isotropic and orthotropic materials. ASME J Appl Mech 69: 502–514
Kusama T, Mitsui Y (1982) Boundary element method applied to linear viscoelastic analysis. Appl Math Modelling 6: 285–290
Lee SS, Westmann RA (1995) Application of high-order quadrature rules to time-domain boundary element analysis of viscoelasticity. Int J Num Meth Engn 38: 607–629
Liu, GR (2003) Mesh Free Methods, Moving beyond the Finite Element Method, CRC Press, Boca Raton
Manolis GD, Pavlou S (2002) A Green's function for variable density elastodynamics under plane strain conditions by Hormander's method, CMES: Comp Model Engn Sci. 3: 399–416
Martin PA, Richardson JD, Gray LJ, Berger JR (2002) On Green's function for a three-dimensional exponentially-graded elastic solid, Proc R Soc London A 458: 1931–1947
Mesquita AD, Coda HB, Venturini WS (2001) Alternative time marching process for BEM and FEM viscoelastic analysis. Int J Num Meth Engn 51: 1157–1173
Mikhailov SE (2002) Localized boundary-domain integral formulations for problems with variable coefficients. Engn Analysis with Boundary Elements 26: 681–690
Paulino GH, Jin ZH (2001a) Correspondence principle in viscoelastic functionally graded materials. ASME J Appl Mechanics 68: 129–132
Paulino GH, Jin ZH (2001b) Viscoelastic functionally graded materials subjected to antiplane shear fracture. ASME J Appl Mechanics 68: 284–293
Paulino GH, Jin ZH (2001c) A crack in a viscoelastic functionally graded material layer embedded between two dissimilar homogeneous viscoelastic layers – antiplane shear analysis. Int J. Fracture 111: 283–303
Santare MH, Lambros J (2000) Use of graded finite elements to model the behavior of nonhomogeneous materials. ASME J Appl Mech 67: 819–822
Schanz M, Antes H (1997) A new visco- and elastodynamic time domain boundary element formulation. Comput Mech 20: 452–459
Sladek V, Sladek J, Markechova I (1993) An advanced boundary element method for elasticity problems in nonhomogeneous media. Acta Mechanica 97: 71–90
Sladek J, Sladek V, Atluri SN (2000) Local boundary integral equation (LBIE) method for solving problems of elasticity with nonhomogeneous material properties. Comput Mech 24: 456–462
Sladek J, Sladek V, Van Keer R (2003a) Meshless local boundary integral equation method for 2D elastodynamic problems. Int J Num Meth Engn 57: 235–249
Sladek J, Sladek V, Zhang Ch (2003b) Application of meshless local Petrov-Galerkin (MLPG) method to elastodynamic problems in continuously nonhomogeneous solids, CMES: Computer Modeling in Engn Sciences 4: 637–648
Sladek J, Sladek V, Atluri SN (2004a) Meshless localPetrov-Galerkin method in anisotropic elasticity. CMES: Computer Modeling in Engn Sciences (in print)
Sladek V, Sladek J, Zhang, Ch (2004b) Local integral equations for diffusion problems. In: Yao ZH, Yuan MW and Zhong WX (eds) Computational Mechanics, CD-ROM Proc. 6th World Congress in Computational Mechanics, Paper-No. 451, Tsinghua University Press & Springer-Verlag, 2004
Sladek V, Sladek J, Zhang, Ch (2004c) Domain element local integral equation method for potential problems in anisotropic and functionally graded materials. Comput Mech (submitted)
Sladek V, Sladek J, Tanaka M, Zhang, Ch (2004d) Local integral equation method for potential problems in functionally graded anisotropic materials. Engn. Analysis with Boundary Elements, (submitted)
Sladek V, Sladek J, Zhang, Ch. (2004e) Local integro-differential equations with domain elements for the numerical solution of partial differential equations with variable coefficients. Jour Engn Mathematics, 51: 261–282
Sladek V, Sladek J, Tanaka M (2004f) Local integral equations and two meshless polynomial interpolations with application to potential problems in non-homogeneous media. CMES: Computer Modeling in Engn & Sciences, 7: 69–83
Stehfest, H (1970): Algorithm 368: numerical inversion of Laplace transform. Comm Assoc Comput Mach 13: 47–49
Suresh S, Mortensen A (1998) Functionally Graded Materials, The Institute of Materials, IOM Communications Ltd, London
Zhang Ch, Sladek J, Sladek V (2003a) Effects of material gradients on transient dynamic mode III SIFs in an FGM, Int J Solids Struct 40: 5251–5270
Zhang Ch, Sladek J, Sladek V (2003b) Numerical analysis of cracked functionally graded materials, Key Eng. Materials 251–252: 463–472
Zhang Ch, Sladek J, Sladek V (2004) Crack analysis in unidirectionally and bidirectionally functionally graded materials, Int J Fract 129: 385–406