Continuum-based design sensitivity analysis and optimization of nonlinear shell structures using meshfree method

A continuum-based shape and configuration design sensitivity analysis (DSA) method for a finite deformation elastoplastic shell structure has been developed. Shell elastoplasticity is treated using the projection method that performs the return mapping on the subspace defined by the zero-normal stress condition. An incrementally objective integration scheme is used in the context of finite deformation shell analysis, wherein the stress objectivity is preserved for finite rotation increments. The material derivative concept is used to develop a continuum-based shape and configuration DSA method. Significant computational efficiency is obtained by solving the design sensitivity equation without iteration at each converged load step using the same consistent tangent stiffness matrix. Numerical implementation of the proposed shape and configuration DSA is carried out using the meshfree method. The accuracy and efficiency of the proposed method is illustrated using numerical examples. Copyright 2006 John Wiley & Sons, Ltd.