In this paper, a method based on Chebyshev polynomials is developed for examination of geometrically nonlinear behaviour of thin rectangular composite laminated plates under end-shortening strain. Different boundary conditions and lay-up configurations are investigated and classical laminated plate theory is used for developing the equilibrium equations. The equilibrium equations are solved dir...

We investigate a class of convection–diffusion equations in an expanding domain involving parameter, where we consider integral boundary conditions that depend non-locally on unknown solutions. Generally, the uniqueness result this type equation is unclear. In work, obtain when sufficiently large or small. This approach has advantage transforming into new Dirichlet so can refined estimates, and...

this paper presents a novel formulation and numerical solutions for adhesively bonded composite joints with non-linear (softening) adhesive behaviour. the presented approach has the capability of choosing arbitrary loadings and boundary conditions. in this model adherends are orthotropic laminates that obey classical lamination theory. the stacking sequences can be either symmetric or asymmetri...

The governing equation of turbulence, that we are interested in, is the incompressible 2D Navier– Stokes equation under periodic boundary conditions. We are particularly interested in investigating the dynamics of 2D Navier–Stokes equation in the infinite Reynolds number limit and of 2D Euler equation. Our approach is different from many other studies on 2D Navier–Stokes equation in which one s...

Motivated by boundary problems for linear differential equations, we define an abstract boundary problem as a pair consisting of a surjective linear map (“differential operator”) and an orthogonally closed subspace of the dual space (“boundary conditions”). Defining the composition of boundary problems corresponding to their Green’s operators in reverse order, we characterize and construct all ...

We prove null controllability for linear and semilinear heat equations with dynamic boundary conditions of surface diffusion type. The results are based on a new Carleman estimate for this type of boundary conditions.