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\\\'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. / Ph. D.

Transverse ply cracking often leads to the loss of stiffness and reduction in thermal expansion coefficients. This paper presents the thermoelastic degradation of general cross-ply laminates, containing transverse ply cracks, subjected to biaxial extension, bending and thermal loading. The stress and displacement fields are calculated by using the state space equation method [Zhang D, Ye JQ, Sheng HY. Free-edge and ply cracking effect in cross-ply laminated composites under uniform extension and thermal loading. Compos Struct [in press].]. By this approach, a laminated plate may be composed of an arbitrary number of orthotropic layers, each of which may have different material properties and thickness. The method takes into account all independent material constants and guarantees continuous fields of all interlaminar stresses across interfaces between material layers. After introducing the concept of the effective thermoelastic properties of a laminate, the degradations of axial elastic moduli, Poisson¿s ratios, thermal expansion coefficients and flexural moduli are predicted and compared with numerical results from other methods or available test results. It is found that the theory provides good predictions of the stiffness degradation in both symmetric and antisymmetric cross-ply laminates. The predictions of stiffness reduction in nonsymmetric cross-ply laminates can be used as benchmark test for other methods.

Transverse ply cracking often leads to the loss of stiffness and reduction in thermal expansion coefficients. This paper presents the thermoelastic degradation of general cross-ply laminates, containing transverse ply cracks, subjected to biaxial extension, bending and thermal loading. The stress and displacement fields are calculated by using the state space equation method [Zhang D, Ye JQ, Sheng HY. Free-edge and ply cracking effect in cross-ply laminated composites under uniform extension and thermal loading. Compos Struct [in press].]. By this approach, a laminated plate may be composed of an arbitrary number of orthotropic layers, each of which may have different material properties and thickness. The method takes into account all independent material constants and guarantees continuous fields of all interlaminar stresses across interfaces between material layers. After introducing the concept of the effective thermoelastic properties of a laminate, the degradations of axial elastic moduli, Poisson's ratios, thermal expansion coefficients and flexural moduli are predicted and compared with numerical results from other methods or available test results. It is found that the theory provides good predictions of the stiffness degradation in both symmetric and antisymmetric cross-ply laminates. The predictions of stiffness reduction in nonsymmetric cross-ply laminates can be used as benchmark test for other methods.

This research endeavor develops Isogeometric approach for analysis of composite structures and take advantage of higher order continuity, smoothness and variation diminishing property of Nurbs basis for stress analysis of composite and sandwich beams and plates. This research also computes stress concentration factor in a composite plate with a hole. Isogeometric nonlinear/linear finite element code is developed for static and dynamic analysis of laminated composite plates. Nurbs linear, quadratic, higher-order and k-refined elements are constructed using various refinement procedures and validated with numerical testing. Nurbs post-processor for in-plane and interlaminar stress calculation in laminated composite and sandwich plates is developed. Nurbs post-processor is found to be superior than regular finite element and in good agreement with the literature. Nurbs Isgoemetric analysis is used for stress analysis of laminated composite plate with open-hole. Stress concentration factor is computed along the hole edge and good agreement is obtained with the literature. Nurbs Isogeometric finite element code for free-vibration and linear dynamics analysis of laminated composite plates also obtain good agreement with the literature. Main highlights of the research are newly developed 9 control point linear Nurbs element, k-refined and higher-order Nurbs elements in isogeometric framework. Nurbs elements remove shear-locking and hourglass problems in thin plates in context of first-order shear deformation theory without the additional step and compute better stresses than Lagrange finite element and higher order shear deformation theory for comparatively thick plates i.e. a/h = 4. Also, Nurbs Isogeometric analysis perform well for vibration and dynamic problems and for straight and curved edge problems. / Ph. D.