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Meshless methods for shear-deformable beams and plates. (English) Zbl 0959.74079
Summary: We develop a meshless method to analyze moderately thick and thin structures described by Mindlin-Reissner theory. A uniform discretization is used to allow for efficient integration and for the shape functions to be written explicitly. Irregular boundaries are modeled in a straightforward manner. We employ an unmodified displacement-based Galerkin method; full integration is used to evaluate all energy terms, and convergence is independent of the thickness. Shear and membrane locking are completely eliminated pointwise at the interpolant level using cardinal splines. The continuity of the splines results in continuous stresses. We also give an extension to general meshless methods, and analyze beam and plate examples to show the accuracy of the method for coarse discretization.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74K20 Plates
Software:
pchip; UNCMND
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References:
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