In this paper the Analog Equation Method (AEM) a boundary-only method is presented for solving nonlinear static and dynamic problems in continuum mechanics. General bodies are considered, that is bodies whose properties may be position or direction dependent and their response is nonlinear. The no linearity may result from both nonlinear constitutive relations (material no linearity) and large deflections (geometrical no linearity). The quintessence of the method is the replacement of the coupled nonlinear partial differential equations with variable coefficients governing the response of the body by an equivalent set of linear uncoupled equations under fictitious sources. The fictitious sources are established using a BEM-based technique and the solution of the original problem is obtained from the integral representation of the solution of the substitute problem. A variety of static and dynamic problems are solved using the AEM are presented to illustrate the method and demonstrate its efficiency and accuracy

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In this paper a solution to the problem of plates reinforced with beams is presented. The adopted model takes into account the resulting inplane forces and deformations of the plate as well as the axial forces and deformations of the beam, due to combined response of the system. The analysis consists in isolating the beams from the plate by sections parallel to the lower outer surface of the plate. The forces at the interface, which produce lateral de¯ection and inplane deformation to the plate and lateral de¯ection and axial deformation to the beam, are established using continuity conditions at the interface. The solution of the arising plate and beam problems which are nonlinearly coupled, is achieved using the analog equation method (AEM). The adopted model describes better the actual response of the plate±beams system and permits the evaluation of the shear forces at the interface, the knowledge of which is very important in the design of composite or prefabricated ribbed plates. The resulting de¯ections are considerably smaller than those obtained by other models.

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