A mathematical model of coupled plates and its finite element method
Complex structures are commonly investigated in practice. Although the numerical approaches can easily be applied and in many cases results are satisfactory, the mathematical base has not been sufficiently developed. In the paper the author considers the mathematical modelling of coupled plates and its finite element approximation. The case of two perpendicular rectangular plates is considered for which the total energy of the structure under virtual displacements is determined. Then the mathematical model of the coupled plates is formulated as a variational problem. The existence and uniqueness of the solution are proved. The problem is reduced to the boundary value problem and junction conditions are derived. At the end the finite element approximation is introduced and the approximation error is determined. The paper contains the mathematical consideration of the problem. The concluding formulae give the theoretical view on the convergence of the discrete method and the error estimation. It allows to investigate the properties of some other types of finite elements in the problem mentioned.
scientific article; zbMATH DE number 146820