Analytical optimisation of composite cylindrical shells to meet given cross sectional stiffness properties

This paper examines the design of 4-ply composite cylindrical shells to meet given cross-sectional stiffness properties from an analytical perspective. In doing so, it validates the findings of previous work. In this earlier paper, each individual target variable (EA, EI, and GJ) was linearised about the current design point using the finite difference method from several FE analyses. These linear equations were converted to matrix form and the resulting matrix equation solved to produce an optimal design. The current paper derives the values of the same cross sectional stiffness properties but does so analytically in terms of the material properties and the design variables. These values are compared with the values obtained by the FE method in the previous paper and good agreement is found. These analytical expressions are differentiated to obtain the terms in the coefficient matrix. This can be coded directly into the optimisation routine to further improve the speed of solution and remove the need for finite element analysis in this problem.