Abstract: This paper presents an exact analytical model for
optimizing stability of thin-walled, composite, functionally graded
pipes conveying fluid. The critical flow velocity at which divergence
occurs is maximized for a specified total structural mass in order to
ensure the economic feasibility of the attained optimum designs. The
composition of the material of construction is optimized by defining
the spatial distribution of volume fractions of the material
constituents using piecewise variations along the pipe length. The
major aim is to tailor the material distribution in the axial direction so
as to avoid the occurrence of divergence instability without the
penalty of increasing structural mass. Three types of boundary
conditions have been examined; namely, Hinged-Hinged, Clamped-
Hinged and Clamped-Clamped pipelines. The resulting optimization
problem has been formulated as a nonlinear mathematical
programming problem solved by invoking the MatLab optimization
toolbox routines, which implement constrained function
minimization routine named “fmincon" interacting with the
associated eigenvalue problem routines. In fact, the proposed
mathematical models have succeeded in maximizing the critical flow
velocity without mass penalty and producing efficient and economic
designs having enhanced stability characteristics as compared with
the baseline designs.
Abstract: This paper presents a generalized formulation for the
problem of buckling optimization of anisotropic, radially graded,
thin-walled, long cylinders subject to external hydrostatic pressure.
The main structure to be analyzed is built of multi-angle fibrous
laminated composite lay-ups having different volume fractions of the
constituent materials within the individual plies. This yield to a
piecewise grading of the material in the radial direction; that is the
physical and mechanical properties of the composite material are
allowed to vary radially. The objective function is measured by
maximizing the critical buckling pressure while preserving the total
structural mass at a constant value equals to that of a baseline
reference design. In the selection of the significant optimization
variables, the fiber volume fractions adjoin the standard design
variables including fiber orientation angles and ply thicknesses. The
mathematical formulation employs the classical lamination theory,
where an analytical solution that accounts for the effective axial and
flexural stiffness separately as well as the inclusion of the coupling
stiffness terms is presented. The proposed model deals with
dimensionless quantities in order to be valid for thin shells having
arbitrary thickness-to-radius ratios. The critical buckling pressure
level curves augmented with the mass equality constraint are given
for several types of cylinders showing the functional dependence of
the constrained objective function on the selected design variables. It
was shown that material grading can have significant contribution to
the whole optimization process in achieving the required structural
designs with enhanced stability limits.