الفهرس 
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Abstract
The nonlinear analysis of fib er-reinforced multilayer composite structures
is one of the most formidable problems in solid and structural mechanics. This
problem clearly appears in the stress and deformation analysis of pneumatic tires.
A typical tire construction either conventional or radial is a very complex
structure. such structure exhibites both anisotropy and heterogeneity with its
constituents. In addition to such complex structure, tire response exhibites
geometrical and material nonlinearities. With the impossibility to analyze this
complex problem analytically and the difficulties encountered with the
experimental work, an accurate computational model is needed to handle such
dilemma.
A general and efficient computational model capable of analyzing the non-
linear response of fiber-reinforced multilayer composite structures is presented,
with a especial attention to the stress and deformation analysis of pneumatic tires
in elasto-static contact with rigid surfaces. The geometrical nonlinearity due to
large elastic deformations as well as the material nonlinearity due to stiffness-
deformation dependency are accounted for. The finite element method, as an
efficient numerical tool, is used to construct the discretized three-dimensional
model of the problem. The proposed nonlinear three-dimensional finite element
model is based on the principle of virtual work or the corresponding minimum
potential energy principle, in the general framework of the theory of nonlinear
elasticity. Lagrangian description is adopted to model the nonlinear behavior of the
considered structure. Also, the composite material theories either in microscopic or
macroscopic scale are used to model the fiber-reinforced copmposites. Further, to
formulate the contact problem of the tire-roadway, the mathematical programming
approach, which has been proved to be superior, is adopted to present an efficient
model available for both frictionless and frictional contacts. With frictional