A nonlinear SDOF model for blast response simulation of elastic thin rectangular plates

Abstract

The present paper aims at studying the blast response of rectangular elastic thin plates that undergo large deflections. The geometrically nonlinear behavior of the rectangular plate is presented in a nonlinear SDOF model and its detailed analysis is followed. Deflections, as well as bending stresses and membrane stresses for plates with immovable edges and with fully clamped or simply supported flexural edge conditions, are calculated to a uniformly distributed blast pressure loading. Validation of the SDOF technique is carried out through numerous comparisons of large amplitude response of square and rectangular plates under real blast loading, for both clamped and simply supported boundary conditions, with several experimental data as well as with numerical solutions obtained by various authors using the nonlinear Von Karman theory of plates. The coefficients of the nonlinear SDOF model are presented for various support (simple support and clamped) and edge stress conditions (immovable constrained, movable, and stress free). The useful expressions of the Airy function as well as of the dynamic membrane stresses are obtained for the above boundary conditions. A comparison of static and dynamic nonlinear solutions is performed. The relationship between the dimensionless deflection and the maximum membrane stresses is studied as well as their relationship with the corresponding maximum bending stresses. The nonlinear SDOF model has been compared with experimental data and with numerical (FEM, FDM) predictions and good agreement is obtained.