In this paper a boundary element method for analysis of fractured stiffened panels repaired with riveted or adhesively bonded patches is presented. In order to achieve such a formulation, several boundary element formulations involving the membrane and bending of displacement, and, stress resultants are coupled together to analyse the model. The multi-region formulation is used to simulate the stiffeners, which are modelled as an assembly. They are then connected to the sheets to form the stiffened panels by means of a rivet formulation. The dual boundary element method is used to simulate the presence of cracks, and the patches, treated as independent plates, are joined to the panel either with rivets or adhesive. A boundary element formulation for adhesive bonding is implemented to model the adhesively bonded patches. The Crack Opening Displacements (COD) method and the Jintegral are implemented to evalute the required fracture parameters. Examples presented include a wing box with a three spar section, with fully stiffened skin, and, the skin is considered to have a crack and a repair patch is used on top of the crack to stop its growth.Response to Reviewers: Thank you for highlighting the missing references and figures numbers as well as certain typo's. We have corrected all the highlighted items.Thank you for highlighting the missing references and figures numbers as well as certain typo's. We have corrected all the highlighted items. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 Detailed Response to Reviewers AbstractIn this paper a boundary element method for analysis of fractured stiffened panels repaired with riveted or adhesively bonded patches is presented. In order to achieve such a formulation, several boundary element formulations involving the membrane and bending of displacement, and, stress resultants are coupled together to analyse the model. The multi-region formulation is used to simulate the stiffeners, which are modelled as an assembly. They are then connected to the sheets to form the stiffened panels by means of a rivet formulation. The dual boundary element method is used to simulate the presence of cracks, and the patches, treated as independent plates, are joined to the panel either with rivets or adhesive. A boundary element formulation for adhesive bonding is implemented to model the adhesively bonded patches. The Crack Opening Displacements (COD) method and the J-integral are implemented to evalute the required fracture parameters. Examples presented include a wing box with a three spar section, with fully stiffened skin, and, the skin is considered to have a crack and a repair patch is used on top of the crack to stop its growth.

In this paper, the Dual Boundary Element Method is combined with a multi-region formulation to simulate plate assembly undergoing large de ‡ection. The incremental load approach is used to treat the geometrical non-linearity and Radial Basis Functions are used to approximate the derivatives of the large de ‡ection terms. The Dual Reciprocity Method is used to transfer to the boundary all the domain integrals. Once the solution at the boundary is obtained for the assembly, a J-integral for large de ‡ection is implemented to extract the fracture parameters.

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The boundary element method (BEM) for large deflection of shear deformable plates is reformulated to the case of multi-section assembled plate structures. Each plate section is modelled as a BEM region under membrane and bending loads, with force, moments, displacements, and rotations represented by generalized traction and displacement nodal variables on the boundary. Non-linear terms in the boundary integral formulation for each section that arises owing to large deflection are treated as effective body forces, and the associated domain integrals are transformed into boundary integrals using the dual reciprocity method. Derivatives of stresses and deflection on the boundary arise in the non-linear terms, and are evaluated by exploring their values at interior domain points using radial basis functions. Plate sections are joined along their edges using compatibility and equilibrium conditions involving the generalized traction and displacement nodal variables. The resulting non-linear equation system is solved numerically using an incremental load approach. An illustrative example of the method is presented for a transversely loaded plate reinforced with Z-stringers.