Galerkin–Vlasov Method for Deflection Analysis of Isotropic Sandwich Plates under Uniform Load

Abstract

In this work, the Galerkin–Vlasov method was used to solve the governing partial differential equation of equilibrium for isotropic sandwich plates with simply supported edges (x = ±a, y = ±b) and under uniform load on the plate domain Vlasov procedure was adopted in choosing the displacement shape functions as orthogonal eigen functions of dynamic Euler Bernoulli beams with equivalent spans, simple supports and loading as the plate. The resulting Galerkin-Vlasov equation was solved to obtain the unknown generalised shape function. It was found that the deflections obtained were exact solutions to the problem of bending isotropic sandwich plates. The deflection was found to be made up of two components: flexural deformation and shear deformation.

Keywords

• the Galerkin–Vlasov method was used to solve the governing partial differential equation of equilibrium for isotropic sandwich plates with simply supported edges (x = ±a
• y = ±b) and under uniform load on the plate domain Vlasov procedure was adopted in choosing the displacement shape functions as orthogonal eigen functions of dynamic Euler Bernoulli beams with equivalent spans
• isotropic sandwich plate
• Galerkin–Vlasov method; governing differential equation of equilibrium; orthogonal eigen functions; generalized displacements parameters.
• Galerkin–Vlasov method
• governing differential equation of equilibrium
• orthogonal eigen functions
• generalized displacements parameters