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Analytical sensitivities of a shear deformable laminated composite plates

A sinus shear deformable theory is used to develop discrete model for the sensitivity analysis and optimisation of moderate thickness and thin multi-layered angle ply composite plate structure. The structural analysis and sensitivity analysis formulation is developed for a family of C six-node triangular finite element. The finite element has been shown to have good properties (e.g. no spurious energy mode, very fast convergence, no shear locking). The design sensitivity of static structural response for objective and/or constraint functions with respect to ply angle and ply thickness for linear and non-linear geometric analysis are developed. The design sensitivities are evaluated analytically despite their complexity. Construction of the sensitivity matrix is thus computed at the same time as the assembly of the structural stiffness matrix. The validity of analytical sensitivity is demonstrated by comparison with finite different approximations.