A refined sine-based finite element with transverse normal deformation for the analysis of laminated beams under thermomechanical loads

Abstract

In the framework of a sine model family, two new three-node beam finite elements including the transverse normal effect are designed for the analysis of laminated beams. They are based on a sine distribution with layer refinement and a second-order expansion for the deflection. The transverse shear strain is obtained using a cosine function, avoiding the use of shear correction factors. This kinematics accounts for the interlaminar continuity conditions on the interfaces between layers, and the boundary conditions on the upper and lower surfaces of the beam. A conforming FE approach is carried out using Lagrange and Hermite interpolations. It is important to notice that the number of unknowns is independent of the number of layers.Both mechanical and thermomechanical tests for thin and thick beams are presented in order to evaluate the capability of these new finite elements to give accurate results with respect to elasticity or finite element reference solutions. Both convergence velocity and accuracy are discussed and this new finite element yields very satisfactory results at a low computational cost. In particular, the transverse stress computed from the constitutive relation is well estimated with regards to classical equivalent single layer models. This work focuses on the necessity to take into account the transverse normal stress, especially for thick beam and coupled analysis.

Layerwise zig‐zag model with selective refinement across the thickness

“…by Reddy and Arciniega [6]. Even models with a totally different representation for the displacements can be found, such as the model by Vidal and Polit [43] with a sinus representation for the in-plane displacements and a second-order polynomial representation for the transverse displacement…”

A Refined Sine Finite Element with Transverse Normal Stress for Thermoelastic Analysis of Laminated Composite in Cylindrical Bending

“…This refined model (see [42,43]) takes into account the continuity conditions between layers of the laminate for both displacements, transverse shear stress and transverse normal stress, and the free conditions on the upper and lower surfaces.…”

NURBS-based isogeometric analysis of laminated composite beams using refined sinus model

“…Then, it was extended to take into account the interlaminar continuity of the transverse shear stresses by Polit and Touratier [68] for plates, and by Dau et al [69] for shells. The original sinus model has been enriched by Vidal and Polit [70] by introducing a layer refinement in the kinematics, and then extended to thermal and piezoelectric effects [71][72][73][74]. In this framework, this study is focused on the integrating of these last works into the isogeometric analysis.…”