Application of the generalized equations of the finite difference method in the analysis of constant stiffness isotropic thin Shells

Abstract

• The study demonstrates the effectiveness and accuracy of the GFDM for analysing thin isotropic shells with single and double curvatures. • The deformation equations are transformed and simplified into algebraic equations using dimensionless parameters. • The validated methodology shows significant convergence and error reduction with finer meshes. • ANOVA analysis and quadratic models indicate that the L/a ratio has a more significant impact on deformations than the Poisson's ratio. • The results offer practical applications for the design of complex structures and pave the way for future advancements in civil and mechanical engineering. This study aims to extend the application of the generalised finite difference method (GFDM) equations to isotropic thin shells with single and double curvatures to fully explore their behaviour under certain boundary conditions. To overcome the complexity of solving fourth-order deformation equations, a new approach, adapted from a methodology previously used for plates, is employed. This approach transforms the complex deformation equations into a more manageable system of second-order partial differential equations, incorporates dimensionless parameters, and adapts the equations to the GFDM to obtain algebraic solutions. The results highlight the capability of GFDM to produce accurate solutions for curved shells subjected to various constraints and loads. A comparative numerical analysis shows the convergence of results towards reference solutionsunderscoring the efficiency and relevance of the GFDM. The study also emphasises the importance of digital design in analysing the combined effect of the length-to-radius ratio and the Poisson's ratio on the maximum deformation and moment of the shells. These findings are crucial for optimising the performance and durability of complex structures such as pressure vessels, architectural structures, ship hulls, and aerospace components.