A coupled BEM-flexibility force method for bending analysis of internally supported plates

This paper presents a new method for the analysis of plates in bending with internal supports. The proposed method can be regarded as an extension of the well-known force method (the exibility matrix method) in the matrix analysis of structures. The solution is performed through two phases: the released plate phase, in which the plate is released from all internal supports and solved using the Boundary Element Method (BEM). The e ect of internal supports is considered in the second phase, where a series of unit virtual loads is placed instead of the unknown redundant reactions at internal supports. The exibility matrix is formed and compatibility of deformations at the locations of internal supports is satis ed. Hence, the corresponding system of equations is solved for the unknown redundant forces at internal supports. The nal solution of the problem consists of the summation of two phases: the released plate phase and the cases of virtual unit loads phase. An e cient solution algorithm is developed to solve both phases simultaneously. The main advantages of the present formulation are: (1) the present formulation increases the versatility of the BEM as it allows the re-usability of standard BEM codes for solution of plates in bending to be used in solving problems having internal supports, with even no modi cations; and (2) the two solution phases are completely uncoupled; therefore it is easy to trace behaviour of the plate due to failure of one or more of the internal supports without re-analysis. Several numerical examples are analysed. The results are compared to those of analytical and nite element models to demonstrate the accuracy and the validity of the present formulation. The present formulation is used also to study the di erences between the nite element and boundary element modelling for building slabs