A galerkin symmetric and direct bie method for Kirchhoff elastic plates: formulation and implementation

A variational Boundary Element formulation is proposed for the solution of the elastic Kirchhoff plate bending problem. The stationarity conditions of an augmented potential energy functional are first discussed. After addressing the topic of die choice of the test functions, a regularization process based on integrations by parts is developed, which allows to express the formulation in terms of double integrals, the inner being at most weakly singular and the outer regular. Standard integration procedures may then be applied for their numerical evaluation in the presence of both straight and curved boundaries. The normal slope and the vertical displacement must be C⁰ and C¹ continuous, respectively. Numerical examples show, through comparisons with analytical solutions, that a high accuracy is achieved.