## A triangular hybrid equilibrium plate element of general degree.(English)Zbl 1140.74555

Summary: Hybrid stress-based finite elements with side displacement fields have been used to generate equilibrium models having the property of equilibrium in a strong form. This paper establishes the static and kinematic characteristics of a flat triangular hybrid equilibrium element with both membrane and plate bending actions of general polynomial degree $$p$$. The principal characteristics concern the existence of hyperstatic stress fields and spurious kinematic modes. The former are shown to exist for $$p > 3$$, and their significance to finite element analysis is reviewed. Knowledge of the latter is crucial to the determination of the stability of a mesh of triangular elements, and to the choice of procedure adopted for the solution of the system of equations. Both types of characteristic are dependent on $$p$$, and are established as regards their numbers and general algebraic forms. Graphical illustrations of these forms are included in the paper.

### MSC:

 74S05 Finite element methods applied to problems in solid mechanics 74K20 Plates

### Keywords:

finite elements; hybrid; equilibrium; statics; kinematics

MA47
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### References:

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