Application of an automatic hp adaptive Finite Element Method for thin-walled structures

The paper investigates the possibility of solving beam and thin-walled structures with an automatic hp-adaptive Finite Element Method for three-dimensional linear elasticity. This technique generates sequences of meshes with nonuniform distribution of element sizes h and their spectral orders p to minimize the interpolation error for the hypothetical exact solution with constant number of degrees-of-freedom. The intent of using hp method for beam and thin-walled structures is that it should automatically create FE meshes with adequate distribution of the approximation orders to prevent the numerical locking phenomenon and to provide accurate solutions. The method also reduces the human work spent on building the numerical model to generation of the description of the geometry. We discuss energy based and goal-oriented versions of hp-adaptivity. The paper presents a broad spectrum of examples of engineering applications.