# zbMATH — the first resource for mathematics

Stability analysis of smoothed finite element methods with explicit method for transient heat transfer problems. (English) Zbl 07124745
##### MSC:
 80 Classical thermodynamics, heat transfer 65 Numerical analysis
JDQR; JDQZ
Full Text:
##### References:
 [1] ,; ,; ,; ,; ,, Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide, (2000), Society for Industrial and Applied Mathematics: Society for Industrial and Applied Mathematics, Philadelphia [2] ,; ,, On a composite implicit time integration procedure for nonlinear dynamics, Comput. Struct., 83, 31-32, 2513-2524, (2005) [3] ,, Conserving energy and momentum in nonlinear dynamics: A simple implicit time integration scheme, Comput. Struct., 85, 7-8, 437-445, (2007) [4] ,; ,; ,, A Collection of Problems on Mathematical Physics, Equations of parabolic type”and “Equations of elliptic type, 331-332 and 456, (1964), Pergamon Press: Pergamon Press, New York [5] ,, A new family of explicit methods for linear structural dynamics, Comput. Struct., 88, 11-12, 755-772, (2010) [6] ,; ,; ,; ,, A stabilized conforming nodal integration for Galerkin mesh-free methods, Int. J. Numer. Methods Eng., 50, 2, 435-466, (2015) [7] ,; ,; ,, Mathematical basis of G spaces, Int. J. Comput. Methods, 13, 4, 1641007-1-1641007-21, (2016) · Zbl 1359.46024 [8] ,; ,, A new family of explicit time integration methods for linear and non-linear structural dynamics, Int. J. Numer. Methods Eng., 37, 23, 3961-3976, (1994) · Zbl 0814.73074 [9] ,; ,; ,, An $$n$$-sided polygonal smoothed finite element method $$(n$$ SFEM) for solid mechanics, Finite Elem. Anal. Des., 43, 11-12, 847-860, (2007) [10] Du, C. F., Zhang, D. G. and Liu, G. R. [2017] “A cell-based smoothed finite element method for free vibration analysis of a rotating plate,” to appear in Int. J.Comput. Methods, doi:10.1142/S0219876218400030. [11] ,; ,; ,; ,; ,; ,; ,, An ES-FEM for accurate analysis of 3D mid-frequency acoustics using tetrahedronmesh, Comput. Struct., 106-107, 125-134, (2012) [12] ,; ,; ,; ,; ,, Topology optimization using node-based smoothed finite element method, Int. J. Appl. Mech., 7, 6, 1550085-1-1550085-23, (2015) [13] ,, Positive definite matrices, Am. Math. Mon., 77, 3, 259-264, (1970) · Zbl 0261.15012 [14] ,; ,; ,; ,, The Finite Element Method in Heat Transfer, (1996), John Wiley & Sons: John Wiley & Sons, Chichester [15] ,; ,; ,, An edge-based smoothed tetrahedron finite element method (ES-T-FEM) for thermomechanical problems, Int. J. Heat Mass Transf., 66, 11, 723-732, (2013) [16] ,; ,; ,; ,, Hybrid smoothed finite element method for acoustic problems, Comput. Methods Appl. Mech. Eng., 283, 1, 664-688, (2015) · Zbl 1423.74902 [17] ,; ,; ,; ,, Volumetric locking issue with uncertainty in the design of locally resonant acoustic metamaterials, Comput. Methods Appl. Mech. Eng., 324, 128-148, (2017) [18] ,; ,, Smoothed Finite Element Methods, (2010), CRC Press: CRC Press, Boca Raton [19] ,; ,, Upper bound solution to elasticity problems: A unique property of the linearly conforming point inter polation method (LC-PIM), Int. J. Numer. Methods Eng., 74, 7, 1128-1161, (2010) [20] ,; ,, Smoothed Point Interpolation Methods: G Space Theory and Weakened Weak Forms, (2013), World Scientific: World Scientific, Singapore [21] ,; ,; ,, A smoothed finite element method for mechanics problems, Comput. Mech., 39, 6, 859-877, (2007) · Zbl 1169.74047 [22] ,; ,; ,, A novel alpha finite element method $$(\alpha$$ FEM) for exact solution to mechanics problems using triangular and tetrahedral elements, Comput. Methods Appl. Mech. Eng., 197, 45-48, 3883-3897, (2008) · Zbl 1194.74433 [23] ,; ,; ,, An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids, J. Sound Vib., 320, 4-5, 1100-1130, (2009) [24] ,; ,; ,; ,, A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems, Comput. Struct., 87, 1-2, 14-26, (2009) [25] ,; ,; ,, Lower bound of vibration modes using the node-based smoothed finite element method (NS-FEM), Int. J. Comput. Methods, 14, 4, 1750036-1-1750036-36, (2017) · Zbl 1404.74163 [26] ,, A generalized gradient smoothing technique and the smoothed bilinear form for Galerkin formulation of a wide class of computational methods, Int. J. Comput. Methods, 5, 2, 199-236, (2008) · Zbl 1222.74044 [27] ,, Mesh Free Methods: Moving Beyond the Finite Element Method, (2009), CRC Press: CRC Press, Boca Raton [28] ,, An overview on meshfree methods: For computational solid mechanics, Int. J. Comput. Methods, 13, 5, 1630001-1-1630001-42, (2016) · Zbl 1359.74388 [29] ,, On partitions of unity property of nodal shape functions: Rigid-body-movement reproduction and mass conservation, Int. J. Comput. Methods, 13, 1640003-1-1640003-13, (2016) · Zbl 1359.65261 [30] ,; ,; ,; ,, A face-based smoothed finite element method (FS-FEM) for 3D linear and geometrically non-linear solid mechanics problems using 4-node tetrahedral elements, Int. J. Numer. Methods Eng., 78, 3, 324-353, (2009) · Zbl 1183.74299 [31] ,; ,, An explicit time integration scheme for the analysis of wave propagations, Comput. Struct., 129, 178-193, (2013) [32] ,; ,; ,, An improved finite point method for tridimensional potential flows, Comput. Mech., 40, 6, 949-963, (2007) · Zbl 1176.76100 [33] ,; ,, Hybrid and Incompatible Finite Element Methods, (2006), CRC Press: CRC Press, Boca Raton [34] ,; ,; ,, Stability of an explicit multi-time step integration algorithm for linear structural dynamics equations, Comput. Mech., 18, 3, 236-244, (1996) · Zbl 0865.73075 [35] ,; ,; ,, Multi-time-step integration using nodal partitioning, Int. J. Numer. Methods Eng., 26, 2, 349-359, (2010) [36] ,, Finite Element Methods, (2003), Tsinghua University Press: Tsinghua University Press, Beijing [37] ,; ,; ,; ,, A quasi-conforming point interpolation method (QC-PIM) for elasticity problems, Int. J. Comput. Methods, 13, 5, 1650026-1-1650026-14, (2016) · Zbl 1359.74452 [38] ,; ,, The Finite Element Method, (2000), Butterworth Heinemann: Butterworth Heinemann, Oxford
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.