A semi-analytical approach for the geometrically nonlinear analysis of trapezoidal plates

This paper presents a semi-analytical approach for the geometrically nonlinear analysis of skew and trapezoidal plates subjected to out-of-plane loads. The thin elastic plate theory with nonlinear von Kármán strains is used for the nonlinear large deflection analysis of the plate. The solution of the governing nonlinear partial differential equations with variable coefficients is reduced to an iterative solution of nonlinear ordinary differential equations using the multi-term extended Kantorovich method. The geometry of the trapezoidal plate is mapped into a rectangular computational domain. Parallelogram (skew) plates are considered as a particular case of the general trapezoidal ones. The capabilities and convergence of the method are numerically examined through comparison with other semi-analytical and numerical methods and with finite element analyses. The applicability of the approach to the nonlinear large deflection analysis of skew and trapezoidal plates is demonstrated through various numerical examples. The numerical study focuses on combinations of geometry, loading and boundary conditions that are beyond the applicability of other semi-analytical methods.