Geometrically Nonlinear Stress Recovery in Composite Laminates

Abstract

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