Nonlinear transient dynamic response of elastic membranes with embedded rigid inclusions

In this paper, the large amplitude transient dynamic response of membranes containing rigid inclusions is examined. These rigid inclusions significantly alter the membrane's stress and strain distributions, and therefore, create major difficulties in the system's analysis and design. The three coupled nonlinear equations in terms of the displacements governing the response of the membrane are solved using a boundary only method, which reduces the problem to the solution of three Poisson's quasistatic equations with fictitious time-dependent domain source densities under the same boundary conditions. The fictitious sources are represented by radial basis functions series and are established using a BEM-based procedure. A direct time-integration scheme is employed for the numerical solution of the equations of rigid body dynamics governing the constraint due to the surrounding membrane motion of the embedded inclusions. Membranes of various shapes are presented, which illustrate the merits of the proposed method and demonstrate its accuracy and efficiency. The method employed for the solution of the respective mathematical models is a boundary-only BEM having all the advantages of the pure BEM.