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Thesis defences

PhD Oral Exam - Nima Shabanijafroudi, Mechanical Engineering

Buckling and Postbuckling response of laminated composite plates with interlaminar flaws

Date & time
Friday, January 15, 2021 (all day)

This event is free


School of Graduate Studies


Daniela Ferrer



When studying for a doctoral degree (PhD), candidates submit a thesis that provides a critical review of the current state of knowledge of the thesis subject as well as the student’s own contributions to the subject. The distinguishing criterion of doctoral graduate research is a significant and original contribution to knowledge.

Once accepted, the candidate presents the thesis orally. This oral exam is open to the public.


High stiffness and strength, corrosion resistance, and ease of manufacturing have made laminated composites an excellent replacement for isotropic materials. The outstanding properties of composites especially appeal to industries such as the aerospace industry where lightweight is of great importance. Despite the said advantages, susceptibility to defects is a major drawback in using these materials. Being composed of several layers bonded together using an adhesive material, delamination or debonding of layers is one the most common flaws in composite laminates. Delamination may drastically impact the mechanical behavior of laminates, especially in unstable conditions. Larger deflections and higher levels of stresses that a laminate experiences in the postbuckling state may, in turn, lead to the growth of a delamination. Given the complications that are caused by delamination, keeping delaminated plates in service requires an in-depth understanding of their postbuckling behavior including the possibility of the growth of the delamination. The objective of this thesis is to develop a comprehensive mathematical and mechanical methodology for accurately predicting the buckling and postbuckling behavior of delaminated composite plates including the fracture mechanical phenomena involved in the postbuckling state.

In all the formulations derived in the framework of the new methodology, the deformations of laminates are approximated using the first-order shear deformation theory and the equilibrium equations were derived using the principle of stationary total potential energy and the Ritz method. In both linear buckling and nonlinear postbuckling analyses, the effect of large rotations is incorporated by adopting Von Kármán’s approximations of the Green strain tensor.

The present thesis work approaches the buckling and postbuckling behavior of delaminated plates through nonlinear analyses. However, conducting nonlinear analyses requires a preliminary knowledge of the potential buckling modes (local, mixed or global) and the loading level at which they may emerge. This preliminary information is used for determining the optimal configuration of imperfections to be incorporated in the nonlinear analyses. In the present work, a novel eigenvalue buckling solution was developed for the required preliminary information. The developed formulation in order to account for the prebuckling stress field nonuniformity caused by in-plane constraints, bases the eigenvalue analysis on a calculated stress field obtained using a prebuckling stress analysis.

For interrogating the details of the postbuckling behavior of delaminated plates, a state of the art postbuckling solution is proposed. The proposed methodology uses a new partitioning scheme that splits the delaminated plate using the plane of the delamination. Outside the delaminated regions the bond between the sublaminates is modeled using a penalty function method. The penalty functions model the effect of an extremely thin layer of elastic adhesive gluing the sublaminates together. The use of the penalty function method offers the advantage of providing the distribution of interlaminar traction in the plane of the delamination. Given the availability of interlaminar tractions in the vicinity of the borders of the delaminated region, Irwin’s crack closure integrals were integrated into the solution for calculating strain energy release rates corresponding to the three fracture modes separately.

Given the importance and the abundant industrial use of curved composite panels especially in the aerospace industries, in an attempt to extend the applicability of the developed methodology to delaminated curved panels, an eigenvalue buckling solution for curved plates subjected to rotational edge restraints is developed.

The validity of the deliverable results of each of the pieces of the developed methodology was verified by comparing the results with experimental data and numerical results obtained using finite element analyses.

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