ON CONTINUOUS ASSUMED GRADIENT ELEMENTS OF SECOND ORDER

This paper presents and compares continuous assumed gradient (CAG) methods when applied to structural elasticity. CAG elements are finite elements where the strain, i.e., the deformation gradient, is replaced by a C0-continuous interpolation. Similar approaches are found in nodal integration and SFEM. Recently, interpolation schemes for a continuous assumed deformation gradient were proposed for first order tetrahedral and hexahedral finite elements. These schemes try to balance accuracy and numerical efficiency. At the same time, the stability of the interpolation with respect to hourglassing and spurious low energy modes is ensured. This paper recalls the fundamentals of CAG elements, i.e., the formulation and linearization. Furthermore, it extends the approach to second order finite elements. Examples prove convergence and accuracy of the quadratic elements. Two interpolation schemes, one being supported by finite element nodes and interior points and the other being a higher-order tensor-product polynomial, are identified to be most accurate.

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