Hybrid equilibrium finite elements for wave diffraction problems

Hybrid equilibrium finite elements based on the direct approximation of the domain stress and boundary displacement fields are presented. The structure is divided into a far field, which is considered as an infinite super element, and a near field, which is in turn discretized into finite elements. The displacements in the domains of typical finite elements are obtained from the assumed domain stress field by using the dynamic equilibrium equations. The Helmholtz equation is satisfied in the domain of the infinite super element, and the domain stress fields are associated with elastic and compatible displacements. The resulting governing system is symmetric, sparse, and, if well done, positive. Numerical applications are presented to illustrate the performance of the formulation.