On drilling degrees of freedom
Computer Methods in Applied Mechanics and Engineering
A novel membrane finite element with an enhanced displacement interpolation
Finite Elements in Analysis and Design - Special issue on Robert J. Melosh Medal Competition
Use of incompatible displacement modes for the calculation of element stiffnesses or stresses
Finite Elements in Analysis and Design
Finite Elements in Analysis and Design
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A new quadrilateral four node membrane finite element based on a mixed Hellinger-Reissner variational formulation is proposed. Displacement and stress interpolations are defined by 12 kinematical DOFs (two displacements and one drilling rotation per node) and 9 stress parameters. The displacement interpolation is obtained as a sum of three contributions. The first two correspond to compatible modes that assume a linear and quadratic (Allman-like) shape along the sides. The latter corresponds to a cubic incompatible mode depending on the average nodal rotations of the element. The stress interpolation is obtained from a complete quadratic polynomial by enforcing the internal bulk equilibrium and three further u"@l Pian equilibrium conditions, so obtaining an equilibrated and non-redundant field. The compliance and compatibility matrices are derived analytically, using an efficient boundary integration scheme. Numerical comparisons show that the proposed element performs better and is less sensitive to mesh distortion than similar elements in the literature. The constant stress states are recovered exactly and a very accurate recovery, for both stress and rotation fields, is also obtained in bending as well as in shear contexts. As shown by some numerical tests in buckling problems, the element is suitable for extension to nonlinear analysis.