Generalized mixed variational principles and solutions of ill-conditioned problems in computational mechanics. II: Shear locking. (English) Zbl 1055.74563
Summary: Although the finite element method (FEM) has been extensively applied to various areas of engineering, ill-conditioned problems occurring in many situations are still thorny to deal with. This study attempts to provide a high-performing and simple approach to the solutions of ill-conditioned problems. The theoretical foundation are the parametrized variational principles, called the generalized mixed variational principles (GMVPs) initiated by Rong in 1981. GMVPs can solve many kinds of ill-conditioned problems in computational mechanics. Among them, four cases are investigated in detail: the volumetric locking, the shear locking, the inhomogeneousness and the membrane locking problems, composing four parts of the study, Part I–Part IV, respectively [for Part I see the authors, ibid. 191, No. 3–5, 407–422 (2001; Zbl 1054.74737)]. This paper is Part II, wherein a GMVP (specially suited to Reissner plate theory and Timoshenko beam theory) is constructed, providing a mathematical foundation for establishing FEM formulations which can automatically unlock the shear locking and produce no spurious zero-energy modes.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74G65 | Energy minimization in equilibrium problems in solid mechanics |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 74K20 | Plates |
Citations:
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