Design sensitivity analysis and optimization of nonlinear shell structure with contact problem

Shape and configuration design sensitivity analysis (DSA) and optimization for nonlinear shell structures with contact problem have been developed using continuum approaches. Shell elastoplasticity is considered by performing a return mapping on the subspace defined by the plane stress condition. It is found that the Hughes-Winget objective integration algorithm is advantageous for DSA in finite deformation shell analysis since a consistent tangent stiffness matrix can be obtained. In addition, this algorithm provides the possibility of using an existing small-strain shell elastoplastic integration procedure without modification. The contact problem includes a boundary nonlinearity that can be dealt with using a flexible-rigid contact.; The meshfree method is used for both the response analysis and DSA to resolve the mesh distortion difficulties encountered in finite deformation in response analysis and in large shape change in DSA. In order to resolve the locking problem in a meshfree shell formulation, a stabilized conforming nodal integration method is used. The implicit method is used for elastoplastic shell analysis. In the implicit method, the sensitivity analysis is linear at each time step, and thus no iterative procedure is required even though the response analysis is nonlinear, provided that the consistent stiffness matrix is used. The updated Lagrangian method is used with the direct differentiation method for DSA. In this updated Lagrangian formulation, the design velocity field that describes the mapping relationship from the original design to the perturbed design should be updated according to the response results. The updated design velocity field is used to predict the design sensitivity information at the next configuration.; Proposed approach is accurate and efficient to compute the sensitivity information compared to the finite difference method. The accurate sensitivity information reduces the number of design iterations during the design optimization procedure. The accuracy and efficiency of the proposed method is demonstrated using several numerical examples for DSA and optimization: spherical shell structure, pinched cylinder, pinched hemisphere, unconstrained cylindrical bending and springback, roof, deep drawing problem, and s-rail problem.