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A spline strip kernel particle method and its application to two-dimensional elasticity problems. (English) Zbl 1062.74659
Summary: In this paper we present a novel spline strip kernel particle method (SSKPM) that has been developed for solving a class of two-dimensional (2D) elasticity problems. This new approach combines the concepts of the mesh-free methods and the spline strip method. For the interpolation of the assumed displacement field, we employed the kernel particle shape functions in the transverse direction, and the B$$_3$$-spline function in the longitudinal direction. The formulation is validated on several beam and semi-infinite plate problems. The numerical results of these test problems are then compared with the existing solutions obtained by the exact or numerical methods. From this study we conclude that the SSKPM is a potential alternative to the classical finite strip method (FSM).

##### MSC:
 74S30 Other numerical methods in solid mechanics (MSC2010) 74B05 Classical linear elasticity
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##### References:
 [1] Cheung, Proceedings of the Institution of Civil Engineers 40 pp 1– (1968) [2] Finite Strip Method in Structural Analysis. Pergamon: Oxford, 1976. · Zbl 0375.73073 [3] Dawe, International Journal for Numerical Methods in Engineering 35 pp 1087– (1992) [4] Lam, International Journal for Numerical Methods in Engineering 36 pp 1045– (1993) [5] Lam, International Journal for Numerical Methods in Engineering 49 pp 797– (2000) [6] Cheung, Proceedings of the Institution of Civil Engineers 75 pp 311– (1983) [7] Fan, Journal of Sound and Vibrations 93 pp 81– (1984) [8] Lau, Thin-Walled Structures 12 pp 295– (1991) [9] Kwon, Thin-Walled Structures 12 pp 295– (1991) [10] Dawe, International Journal for Numerical Methods in Engineering 33 pp 819– (1992) [11] Dawe, International Journal of Mechanical Sciences 37 pp 645– (1995) [12] Dawe, Thin-Walled Structures 30 pp 159– (1998) [13] Azhari, International Journal for Numerical Methods in Engineering 48 pp 583– (2000) [14] Yang, International Journal for Numerical Methods in Engineering 44 pp 131– (1999) [15] Liu, International Journal for Numerical Methods in Engineering 38 pp 1655– (1995) [16] Chen, Computer Methods in Applied Mechanics and Engineering 139 pp 195– (1996) [17] Liew, Engineering Structures 24 pp 543– (2002) [18] Liew, International Journal for Numerical Methods in Engineering 55 pp 669– (2002) [19] Belytschko, Computer Methods in Applied Mechanics and Engineering 139 pp 3– (1996) [20] Theory of Elasticity (3rd edn). McGraw-Hill: New York, 1970. [21] Belytschko, International Journal for Numerical Methods in Engineering 37 pp 229– (1994) [22] Mathematical Theory of Elasticity. Krieger Publishing Company: Malabar, FL, 1946. [23] Pang, Communications in Numerical Methods in Engineering 16 pp 335– (2000) [24] Applied Elasticity. Wiley Eastern Limited: New Delhi, 1992.
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