A hybrid stress approach for laminated composite plates within the First-order Shear Deformation Theory

Abstract

This paper presents a hybrid stress approach for the analysis of laminated composite plates. The plate mechanical model is based on the so called First-order Shear Deformation Theory, rationally deduced from the parent three-dimensional theory. Within this framework, a new quadrilateral four-node finite element is developed from a hybrid stress formulation involving, as primary variables, compatible displacements and elementwise equilibrated stress resultants. The element is designed to be simple, stable and locking-free. The displacement interpolation is enhanced by linking the transverse displacement to the nodal rotations and a suitable approximation for stress resultants is selected, ruled by the minimum number of parameters. The transverse stresses through the laminate thickness are reconstructed a posteriori by simply using three-dimensional equilibrium. To improve the results, the stress resultants entering the reconstruction process are first recovered using a superconvergent patch-based procedure called Recovery by Compatibility in Patches, that is properly extended here for laminated plates. This preliminary recovery is very efficient from the computational point of view and generally useful either to accurately evaluate the stress resultants or to estimate the discretization error. Indeed, in the present context, it plays also a key role in effectively predicting the shear stress profiles, since it guarantees the global convergence of the whole reconstruction strategy, that does not need any correction to accommodate equilibrium defects. Actually, this strategy can be adopted together with any plate finite element. Numerical testing demonstrates the excellent performance of both the finite element and the reconstruction strategy.

Patch based stress recovery for plate structures

“…The 9βQ4 is a quadrilateral four-node element recently proposed in [9,11]. The formulation is of hybrid stress type, involving equilibrating stress resultants within each element and compatible displacements along the interelement boundary.…”

Fast and accurate elastic analysis of laminated composite plates via isogeometric collocation and an equilibrium-based stress recovery approach

“…This method is significantly less expensive compared to a layerwise approach since employs a considerably lower number of degrees of freedom. The post-processing approach, first proposed in [23], takes inspiration from recovery techniques which can be found in [16,19,25,42,63,73] and is based on the direct integration of the equilibrium equations to compute the out-of-plane stress components from the in-plane ones directly derived from a coarse displacement solution.…”

A 4-Node Co-Rotational Quadrilateral Composite Shell Element

“…Within the frameworks of¯rst-order shear deformation laminated theories, Kim et al 9 presented a 4-node co-rotational composite shell element combining an enhanced assumed strain in the membrane strains and assumed natural strains in the shear strains; Auricchio and Sacco 15 obtained a 4-node¯nite element for the analysis of laminated composite plates through a mixed-enhanced approach; Chun et al 16 proposed a 4-node laminated shell element with drilling degrees of freedom, where assumed stress and enhanced strain techniques are adopted to prevent locking problems; Daghia et al 17 developed a quadrilateral 4-node¯nite element from a hybrid stress formulation involving compatible displacements and element-wise equilibrated stress resultants as primary variables; Vu-Quoc et al [18][19][20] developed a class of geometrically-exact multilayer shell formulation that can account for large deformation and large overall motion.…”