Non-Linear Finite Element Analyses of Composite Shells by Total Lagrangian Decomposition with Application to the Aircraft Tire

Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Aeronautics and Astronautics

First Advisor

Anthony N. Palazotto, PhD


A total Lagrangian finite element scheme for arbitrarily large displacements and rotations is applied to a wide range of shell geometries. The scheme decomposes the deformation into stretches and rigid-body rotations, examining the deformed state with respect to an orthogonal, rigidly translated and rotated triad located at the point of interest on the deformed structure. The Jaumann stresses and strains, which are resolved along the axes of this triad, are employed in the algorithm. Local and layer-wise thickness stretching and shear warping functions are used to model the three-dimensional behavior of the shell. These functions are developed through the use of the constitutive equations, certain stress and displacement continuity requirements at ply interfaces and laminate surfaces, and the behavior of the shell reference surface. Two finite elements are employed in the analyses: an eight-noded, 36 degree-of-freedom (DOF) element, and a four-noded, 44 DOF element. The 36 DOF element, which is not a compatible element with respect to the derivatives of in-plane deformations proves adequate for moderate rotation problems, hut fails in modeling very large rotation problems. The use of the 44 DOF element provides dramatically improved results in the large rotation problem. The scheme is used to analyze isotropic and anisotropic beams, plates, arches, and shells. As a special application, a detailed finite element model of an aircraft tire is analyzed with regard to deformations resulting from inflation pressure. Finally, the feasibility of static contact analysis is also demonstrated.

AFIT Designator


DTIC Accession Number

ADA302984 (incomplete file at DTIC)


The DTIC copy of this dissertation is an incomplete scan of the document. The PDF is omitted from AFIT Scholar. The D'Azzo Research Library will make a scan of the full dissertation in the future.

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