Nonlinear thermo-mechanical bending analysis of variable-thickness parallelogram plates in curved hull via a homotopy-based wavelet method

Abstract

Due to the variable-thickness parallelogram plates in ocean structure are characterized by the presence of strong moment singularity at supported obtuse corners, the wide application has turned the nonlinear mechanical analysis into one of the most important engineering concerns. In the paper, a refined geometrically nonlinear bending model of variable-thickness orthotropic parallelogram plates in curved hull under thermo-mechanical loads is proposed, while influences of linearly or quadratically thickened thickness in symmetrical or unsymmetrical profile on mechanical properties are thoroughly investigated. Three kinds of spatially thermal field in parallelogram domain are formulated on account of the coupled interaction of effects between in-plane distribution and thickness variation corresponding to the Dirichlet, Neumann and Robin thermal boundaries. A novel thickness-dependent Airy stress function is introduced overcoming the failure of traditional Airy stress function in equilibrium of in-plane forces, while the highly coupled and variable-coefficient nonlinear governing partial differential equations are firstly derived. The homotopy-based wavelet method is adopted to investigate the nonlinear thermo-elastic bending behaviors, while convergent process is verified and precision of obtained series solutions has been validated in excellent agreement with published results. The significant conclusion can be made that large-deflection nonlinear bending of such plates can be simplified with little discrepancy by omitting terms involving the derivatives of thickness variation in compatibility equation of deformation, which is generalized to the thermo-mechanical bending and greatly simplifies the analyzing procedures.