Geometrically Nonlinear Stress Recovery in Composite Laminates

Abstract

Composite laminates are increasingly being used as primary load bearing members in structures. However, because of the directional dependence of the properties of composite materials, additional failure modes appear that are absent in homogeneous, isotropic materials. Therefore, a stress analysis of a composite laminate is not complete without an accurate representation of the transverse (out-of-plane) stresses.Stress recovery is a common method to estimate the transverse stresses from a plate or shell analysis. This dissertation extends stress recovery to problems in which geometric nonlinearities, in the sense of von Kármán, are important. The current work presents a less complex formulation for the stress recovery procedure for plate geometries, compared with other implementations, and results in a post-processing procedure which can be applied to data from any plate analyses; analytical or numerical methods, resulting in continuous or discretized data.Recovered transverse stress results are presented for a variety of geometrically nonlinear example problems: a semi-infinite plate subjected to quasi-static transverse and shear loading, and a finite plate subjected to both quasi-static and dynamic transverse loading. For all cases, the corresponding results from a fully three-dimensional stress analysis are shown alongside the distributions from the stress recovery procedure. Good agreement is observed between the stresses obtained from each method for the cases considered. Discussion is included regarding the applicability and accuracy of the technique to varying plate geometries and varying degrees of nonlinearity, as well as the viability of the procedure in replacing a three-dimensional analysis in regard to the time required to obtain a solution.The proposed geometrically nonlinear stress recovery procedure results in estimations for transverse stresses which show good correlation to the three-dimensional finite element solutions. The procedure is accurate for quasi-static and dynamic loading cases and proves to be a viable replacement for more computationally expensive analyses.

Through-the-thickness stress distributions near edges of composite laminates using stress recovery scheme and third order shear and normal deformable theory

“…Chaudhuri and Seide [46] rather than using the 3-D equations of equilibrium used 1-D quadratic shape functions through the thickness of each layer to compute transverse shear stress distributions in the laminate. Engelstad et al [47], Byun and Kapania [48] and Hartman et al [49] extended the use of one-step SRSs to geometrically non-linear problems while Park et al [50] used a two-step SRS similar to that employed by Noor et al [43] to predict interlaminar stresses in the laminated panels undergoing finite rotations.…”

A geometrically nonlinear variable-kinematics continuum shell element for the analyses of laminated composites

“…They first approximate a transverse stress field, whose error is reduced via minimisation of a least square functional at the element level. Later, Hartman et al [39] proposed an iterative stress recovery technique with application to laminated plates, which is then extended to include inertial effects in a later publication [42]. These works demonstrated considerable savings in the computational time for accurate interlaminar stresses.…”

“…In these instances, it is necessary to use models that output accurate 3D stresses directly from the get-go. Firstly, the 3D stress accuracy of the VKCS model is validated with a simple benchmark from Hartman et al [39], as shown in Figure 7. It shall be noted that the benchmarks for nonlinear Cauchy stresses are scarce in the literature, and mostly focus on laminated flat plates [39][40][41][42] that are 2D in nature (plane stress/strain).…”

Geometrically Nonlinear Stress Recovery in Composite Laminates Subjected to Dynamic Loading

“…Details on the discrepancy are presented in the appendix of the first author's dissertation. 13 total of 16 elements through the thickness of the laminate.…”