An iterative solution algorithm for thin elastic plate flexure with variable rigidity and in-plane loading

Abstract

An algorithm was developed to solve the thin elastic plate flexure equation in the case of variable rigidity which can be used to model the bending of the Earth's lithosphere in response to lateral and in-plane loading. In the oceanic lithosphere, variable rigidity corresponds to changes in elastic thickness, which could occur in the incoming plate at deep-sea trenches. The proposed method relies on numerical Fourier transforms as it computes successive approximations of the flexural deflection of the plate. This formulation is intended to enable studies of the effects of material properties on lithospheric flexure at subduction zones, but it could potentially be applied to other systems in geophysics that involve flexural deformation such as the elastic response of the crust to unloading from the melting of an ice sheet.An algorithm was developed to solve the thin elastic plate flexure equation in the case of variable rigidity which can be used to model the bending of the Earth's lithosphere in response to lateral and in-plane loading. In the oceanic lithosphere, variable rigidity corresponds to changes in elastic thickness, which could occur in the incoming plate at deep-sea trenches. The proposed method relies on numerical Fourier transforms as it computes successive approximations of the flexural deflection of the plate. This formulation is intended to enable studies of the effects of material properties on lithospheric flexure at subduction zones, but it could potentially be applied to other systems in geophysics that involve flexural deformation such as the elastic response of the crust to unloading from the melting of an ice sheet.