A new 12 DOF quadrilateral element for analysis of thick and thin plates. (English) Zbl 0854.73067
The paper presents a quadrilateral finite element for plate bending. A simple 12 degrees of freedom element is derived on the base of a modified version of hybrid Trefftz method. Two independent fields of displacements are used in the formulation: a nonconforming Trefftz field satisfying the differential equations of Reissner-Mindlin theory, and an auxiliary conforming field with the variable linked to rotations by the requirement of constant boundary distribution of the corresponding tangential component of the transverse shear. The element proposed in the paper was widely tested and proved to be robust in all practical situations. It is free of shear locking. Having 12 degrees of freedom, it preserves the same order of boundary interpolations as an other 16 degrees of freedom element, it is quadratic for deflection and linear for rotations. It has also lowered the number of terms in the nonconforming Trefftz field. The formulation concerns both thin and thick plates (the latter will be described in an prepared paper).
Reviewer: Cz.I.Bajer (Warszawa)
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74K20 | Plates |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
Keywords:
thin plate; thick plate; \(h\)-convergence; modified hybrid Trefftz method; nonconforming Trefftz field; Reissner-Mindlin theory; auxiliary conforming field; shear lockingReferences:
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