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Reproducing kernel particle methods for large deformation analysis of nonlinear structures. (English) Zbl 0918.73330
Large deformation analysis of nonlinear elastic and inelastic structures based on reproducing kernel particle methods (RKPM) is presented. The method requires no explicit mesh in computation and therefore avoids mesh distortion difficulties in large deformation analysis. The current formulation considers hyperelastic and elasto-plastic materials since they represent path-independent material behaviors, respectively. The essential boundary conditions are introduced by the use of a transformation method. The numerical results indicated that RKPM handles large material distortion more effectively than finite elements due to its smoother shape functions and, consequently, provides a higher solution accuracy under large deformation.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74K99 Thin bodies, structures
74B99 Elastic materials
74C99 Plastic materials, materials of stress-rate and internal-variable type
74D99 Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
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[1] Liu, W.K.; Chang, H.; Chen, J.S.; Belytschko, T., Arbitrary Lagrangian Eulerian Petrov-Galerkin finite elements for nonlinear continua, Comput. methods appl. mech. engrg., 68, 3, 259-310, (1988) · Zbl 0626.73076
[2] Liu, W.K.; Chen, J.S.; Belytschko, B.; Zhang, Y.F., Adaptive ALE finite elements with particular reference to external work rate on frictional interface, Comput. methods appl. mech. engrg., 93, 189-216, (1991) · Zbl 0743.73028
[3] Lucy, L., Numerical approach to testing the fission hypothesis, Astron, J., 82, 1013-1024, (1977)
[4] Gingold, R.A.; Monaghan, J.J., Smoothed particle hydrodynamics: theory and application to non-spherical stars, Monthly notices royal astron. soc., 181, 375-389, (1977) · Zbl 0421.76032
[5] Monaghan, J.J., Why particle methods work, SIAM J. sci. stat. comput., 3, 4, 422-433, (1982) · Zbl 0498.76010
[6] Monaghan, J.J., An introduction to SPH, Comput. phys. comm., 48, 89-96, (1988) · Zbl 0673.76089
[7] Liberkey, L.D.; Petschek, A.G.; Carney, T.C.; Hipp, J.R.; Alliahdadi, F.Z., High strain Lagrangian hydrodynamics, J. comput. phys., 109, 67-75, (1993)
[8] Harlow, F.H., The particle-in-cell computing method for fluid dynamics, (), 319-343
[9] Brackbill, J.U., FLIP: A method for adaptivity zoned, particle-in-cell calculations of fluid flows in two dimensions, J. comput. phys., 65, 314-343, (1986) · Zbl 0592.76090
[10] Sulsky, D.; Chen, Z.; Schreyer, H.L., A particle method for history-dependent materials, Comput. methods appl. mech. engrg., 118, 179-196, (1994) · Zbl 0851.73078
[11] Nayroles, B.; Touzot, G.; Villon, P., Generalizing the finite element method: diffuse approximation and diffuse elements, Comput. mech., 10, 307-318, (1992) · Zbl 0764.65068
[12] Belytschko, T.; Lu, Y.Y.; Gu, L., Element-free Galerkin methods, Int. J. numer. methods engrg., 37, 229-256, (1994) · Zbl 0796.73077
[13] Lu, Y.Y.; Belytschko, T.; Gu, L., A new implementation of the element-free Galerkin method, Comput. methods appl. mech. engrg., 113, 397-414, (1994) · Zbl 0847.73064
[14] Belytschko, T., Are finite elements passé?, USACM bulletin, 7, 3, (1994)
[15] Belytschko, T.; Gu, L.; Lu, Y.Y., Fracture and crack growth by EFG method, Model. simul. mater. sci. engrg., 2, 519-534, (1994)
[16] Belytschko, T.; Krongauz, Y.; Fleming, M.; Organ, D.; Liu, W.K., Smoothing and accelerated computations in the element-free Galerkin method, J. comput. appl. math., (1995), accepted
[17] Liu, W.K.; Jun, S.; Li, S.; Adee, J.; Belytschko, T., Reproducing kernel particle methods for structural dynamics, Int. J. numer. methods engrg., 38, 1655-1679, (1995) · Zbl 0840.73078
[18] Liu, W.K.; Jun, S.; Zhang, Y.F., Reproducing kernel particle method, Int. J. numer. methods fluids, 20, 1081-1106, (1995) · Zbl 0881.76072
[19] Liu, W.K., An introduction to wavelet reproducing kernel particle methods, USACM bull., 8, 1, 3-16, (1995)
[20] Liu, W.K.; Chen, Y.J., Wavelet and multiple scale reproducing kernel methods, Int. J. numer. methods fluids, 21, 901-932, (1995) · Zbl 0885.76078
[21] Liu, W.K.; Li, S.; Belytschko, T., Moving least square reproducing kernel method (I) methodology and convergence, Comput. methods appl. mech. engrg., (1995), submitted
[22] Liu, W.K.; Chen, Y.; Chang, C.T.; Belytschko, T., Advances in multiple scale kernel particle methods, Comput. mech., 18, 2, 73-111, (1996) · Zbl 0868.73091
[23] Liu, W.K.; Chen, Y.; Jun, S.; Chen, J.S.; Belytschko, T.; Pan, C.; Uras, R.A.; Chang, C.T., Overview and applications of the reproducing kernel particle methods, Archives comput. methods engrg. state of the art rev., 3, 3-80, (1996)
[24] J.S. Chen, C. Pan and C.T. Wu, Reproducing Kernel Particle Methods for rubber hyperelasticity, Comput. Mech., in press.
[25] Lancaster, P.; Salkauskas, K., Surfaces generated by moving least squares methods, Math. comput., 37, 141-158, (1981) · Zbl 0469.41005
[26] Liu, W.K.; Belytschko, T.; Chen, J.S., Nonlinear versions of flexurally superconvergent elements, Comput. methods appl. mech. engrg., 71, 3, 241-258, (1988) · Zbl 0679.73028
[27] Chen, J.S.; Wu, C.T.; Pan, C.; Chen, J.S.; Wu, C.T.; Pan, C., A pressure projection method for nearly incompressible rubber hyperelasticity, part II: applications, ASME J. appl. mech., ASME J. appl. mech., (1995), in press
[28] Gent, A.N.; Meinecke, E.A., Compression, bending and shear of bonded rubber blocks, Polymer engrg. sci., 10, 48-53, (1970)
[29] Tseng, N.T.; Satyamurthy, K.; Chang, J.P., Nonlinear finite element analysis of rubber based products, ()
[30] Hinton, E.; Hellen, T.K.; Lyons, L.R.R., On elasto-plastic benchmark philosophies, (), 389-408
[31] Taylor, G.I., The use of flat-ended projectiles for determining dynamic yield stress, part I, (), 289-299
[32] Wilkins, M.L.; Guinan, M.W., Impact of cylinders on rigid boundary, J. appl. phys., 44, 1200-1206, (1973)
[33] Predebon, W.W.; Anderson, C.E.; Walker, J.D., Inclusion of evolutionary damage measures in Eulerian wavecodes, Comput. mech., 7, 221-236, (1991) · Zbl 0735.73087
[34] Sulsky, D.; Zhou, S.-J.; Schreyer, H.L., Application of a particle-in-cell method to solid mechanics, Comput. phys. comm., (1995), submitted · Zbl 0918.73334
[35] Norris, D.M.; Moran, B.; Scudder, J.K.; Quinones, D.F., A computer simulation of the tension test, J. mech. phys. solids, 26, 1-19, (1978)
[36] Chang, T.Y.P.; Saleeb, A.F.; Li, G., Large strain analysis of rubber-like materials based on a perturbed Lagrangian variational principle, Comput. mech., 8, 221-233, (1991) · Zbl 0850.73281
[37] Penn, R.W., Volume changes accompanying the extension of rubber, Trans. soc. rheol., 14, 4, 509-517, (1970)
[38] Hughes, T.J.R.; Winget, J., Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis, Int. J. numer. methods engrg., 15, 12, 1862-1867, (1980) · Zbl 0463.73081
[39] Krieg, R.D.; Key, S.W., Implementation of a time independent plasticity theory into structural computer programs, (), 125-137
[40] Simo, J.C.; Taylor, R.L., Consistent tangent operators for rate-independent elastoplasticity, Comput. methods appl. mech. engrg., 48, 101-118, (1985) · Zbl 0535.73025
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