Contact interaction of two rectangular plates made from different materials with an account of physical nonlinearity

Abstract

A mathematical model of a contact interaction between two plates made from materials with different elasticity modulus is derived taking into account physical and design nonlinearities. In order to study the stress-strain state of this complex mechanical structure, the method of variational iteration has been employed allowing for reduction of partial differential equations to ordinary differential equations (ODEs). The theorem regarding convergence of this method is formulated for the class of similar-like problems. The convergence of the proposed iterational procedure used for obtaining a solution to contact problems of two plates is proved. In the studied case, the physical nonlinearity is introduced with the help of variable parameters associated with plate stiffness. The work is supplemented with a few numerical examples. Both

Mathematical modeling of physically nonlinear 3D beams and plates made of multimodulus materials

“…In [59], a mathematical model of the contact interaction of two plates (Kirchhoff's kinematic model) was constructed, taking into account different modulus of materials, physical and structural nonlinearities. To study the stress-strain state of this complex mechanical system, the method of variational iterations was applied, which makes it possible to reduce the partial differential equations (PDEs) to ordinary differential equations (ODEs).…”