Assumed stress formulation of high order quadrilateral elements with an improved in-plane bending behaviour

Finite Element formulation for nonlinear analysis of masonry walls

“…We base the Finite Element formulation on the 5b element, first proposed by Pian and Sumihara [9] and widely used in several works, as in [10]. In details, the 5b element is a quadrilateral assumed stress Finite Element formulated in a mixed form.…”

“…interpolate the displacement field in terms of 2 Â 4 corner node parameters, collected in the vector d. According with the assumed stress formulation as recast in particular in [10], the stress field interpolation is obtained first by expanding the polynomial representation of the strain field, and then by reducing it at the element level through equilibrium conditions imposed in weak form on auxiliary displacement test-fields. We finally have, for a regular mesh grid:…”

A mixed isostatic 16 dof quadrilateral membrane element with drilling rotations, based on Airy stresses

“…17. Similar tests have been analyzed in many papers (see [32,35,36]). The analysis was performed with different meshes and repeated, for comparison, using the Abaqus S8R element and the results are shown in Table 14 and Fig.…”

“…The related literature is very rich and many finite elements have also been developed recently. Briefly we recall the membrane part of the shell element, called HBQ8, proposed by Darilmaz and Kumbasar [31] and the 8-node element called Flex8 proposed in [32]. In the former, the membrane kinematics is controlled by three dofs per node (two displacements and one drilling rotation) and then by 24 dofs in total.…”

Imperfection sensitivity analysis of laminated folded plates

“…For the Hellinger-Reissner formulation used here, the components of u are the global displacements/ rotations of the nodes of the elements and the stress parameters of each element. Using static condensation, the stress parameters can be eliminated at the element level, and then a compatible scheme can be employed [42].…”