Abstract: The Resource-Constrained Project Scheduling
Problem (RCPSP) is concerned with single-item or small batch
production where limited resources have to be allocated to dependent
activities over time. Over the past few decades, a lot of work has
been made with the use of optimal solution procedures for this basic
problem type and its extensions. Brucker and Knust[1] discuss, how
timetabling problems can be modeled as a RCPSP. Authors discuss
high school timetabling and university course timetabling problem as
an example. We have formulated two mathematical formulations of
course timetabling problem in a new way which are the prototype of
single-mode RCPSP. Our focus is to show, how course timetabling
problem can be transformed into RCPSP. We solve this
transformation model with genetic algorithm.
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.