A three-dimensional semi-analytical model for the composite laminated plates with a stepped lap repair

A three-dimensional semi-analytical model of the static response and sensitivity analysis was established based on the state space methods and meshless method for the composite laminated plates with a stepped lap repair. Firstly, the meshfree formulations of Hamilton canonical equation and the linear spring-layer were deduced by the radial point interpolation method (RPIM) shape functions and the modified Hellinger–Reissner (H–R) variational principle of elastic solids. And then a three-dimensional hybrid governing equation of the static response analysis and sensitivity analysis were developed for the composite laminated plates with a stepped lap repair. The present three-dimensional semi-analytical model with no initial assumptions regarding displacement and stress accounts for the transverse shear deformation and rotary in the governing equation of structure. By using the hybrid governing equation in the response analysis and sensitivity analysis, the convoluted algorithm can be avoided in sensitivity analysis, and the response quantities and the sensitivity coefficients can be obtained simultaneously.