Authors : Ildar B. Badriev, Gulnaz Z. Garipova, Maxim V. Makarov and Vitaly N. Paymushin
Abstract: One-dimensional geometrically nonlinear problem of stability loss mixed forms for outer layers of a sandwich plate composed of two carrier layers and disposed there between transversely with a soft filler related to carrier layers with adhesive bonding at face axial compression of one outer layer among other outer ones. We assume that the edges of the plate carrier layers are hinged. The problem is described by the system of nonlinear differential equations. Using the method of summation identities the finite-difference problem approximations were developed. In order to solve the difference scheme a two-layer iterative process was used with the lowering of non-linearity to the lower layer. The central place is occupied by the determination of critical bifurcation points and respective critical loads. The bifurcation points are determined as the points of branching for the problem solution. These points may be found by the linearization of nonlinear equations in some area of solution. At that the need to address a non-linear (quadratic) eigenvalue problem on eigen values appears. The set of programs was developed in Matlab for the numerical realization of the proposed iterative method. The numerical experiments were performed for the model problem. An optimal iteration parameter (by the number of iterations) is selected empirically. In order to solve polynomial (quadratic) issue on eigenvalues the Matlab medium was used. As the result of numerical experiments, the dependence of end load on the deflection at the central point of the carrier layer was developed. The behavior of the plate near the critical point which is the bifurcation point is studied. The critical loads are determined. It is established that the result of a geometrically nonlinear problem solution by tabulating according to kinematic loading parameter as well as the linearized problem in the area of a nonlinear problem solution have almost identical values of the critical load.
Ildar B. Badriev, Gulnaz Z. Garipova, Maxim V. Makarov and Vitaly N. Paymushin, 2015. Numerical Solution of the Issue about Geometrically Nonlinear Behavior of Sandwich Plate with Transversal Soft Filler. Research Journal of Applied Sciences, 10: 428-435.