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Application of Mathematica to the Optimal Design of Composite Shells for Improved Buckling Strength

M. Walker
T. Reiss
S. Adali
P. Weaver
Journal / Anthology

Engineering Computations
Year: 1998
Volume: 15
Issue: 2
Page range: 260-267

Composite materials have seen increasing applications in various fields of engineering such as the marine and aerospace industries. This is mainly due to the high strength and stiffness weight ratios that these materials can offer (Walker et al., 1994). Another advantage of these materials over conventional materials is the possibility of tailoring their properties to the specific requirements of a given application. This is particularly useful when the composite structure is subjected to different combinations of loading conditions. In these cases, multiobjective design techniques can maximise the performance of such structures, and lead to efficient designs.

Optimal design of structures made of composite materials involve computations handling the transformation of geometric and material axes as well as the implementation of an analysis/optimisation interface. For such problems, symbolic computational techniques become quite effective as computer algebra systems (CASes) are efficient tools in symbolic and numerical computations. Ioakimidis (1992a, 1992b, 1992c) has demonstrated the use of MATHEMATICA in semi-analytica-numerical structural applications, particularly those involving finite element methods. Similarly CASes have been used in other engineering fields including computational fluid dynamics (Ball et al., 1988). Beltzer (1990) gives a comprehensive review of symbolic computation packages and analytical applications.

A system such as MATHEMATICA is ideally suited for many analytical applications in small engineering boundary value problems. This study details the use of MATHEMATICA to maximise the buckling strength of laminated cylindrical shells subject to both axial and torsional loads. The layer fiber angle is chosen as the optimising variable.

*Engineering > Mechanical and Structural Engineering